Metrics for UniformSampleCone, z

start0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage

analyze135.0ms (4%)

Memory

9.0MiB live, 103.1MiB allocated; 195ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0.1%	99.9%	0%	0%	0%	0
0%	0%	0.1%	99.9%	0%	0%	0%	1
0%	0%	0.1%	99.9%	0%	0%	0%	2
25%	0%	0.1%	99.9%	0%	0%	0%	3
25%	0%	0.1%	99.9%	0%	0%	0%	4
37.5%	0%	0.1%	99.9%	0%	0%	0%	5
56.2%	0.1%	0%	99.9%	0%	0%	0%	6
56.2%	0.1%	0%	99.9%	0%	0%	0%	7
65.6%	0.1%	0%	99.9%	0%	0%	0%	8
76.6%	0.1%	0%	99.9%	0%	0%	0%	9
76.6%	0.1%	0%	99.9%	0%	0%	0%	10
82%	0.1%	0%	99.9%	0%	0%	0%	11
87.9%	0.1%	0%	99.9%	0%	0%	0%	12

Compiler

Compiled 31 to 21 computations (32.3% saved)

sample1.3s (40%)

Memory

63.5MiB live, 1 333.2MiB allocated; 900ms collecting garbage

Samples

1.0s	8 185×	0	valid
7.0ms	71×	1	valid

Precisions

Click to see histograms. Total time spent on operations: 791.0ms

ival-add: 379.0ms (47.9% of total)

const: 142.0ms (18% of total)

ival-<=: 121.0ms (15.3% of total)

ival-mult: 55.0ms (7% of total)

ival-sub: 47.0ms (5.9% of total)

ival-and: 30.0ms (3.8% of total)

exact: 8.0ms (1% of total)

adjust: 4.0ms (0.5% of total)

ival-assert: 3.0ms (0.4% of total)

Bogosity

explain59.0ms (1.8%)

Memory

-2.3MiB live, 87.8MiB allocated; 10ms collecting garbage

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`#s(literal 1 binary32)`
-	-	`(*.f32 ux maxCos)`
-	-	`maxCos`
-	-	`ux`
-	-	`(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))`
-	-	`(-.f32 #s(literal 1 binary32) ux)`

Confusion

	Predicted +	Predicted -
+	0	0
-	0	256

Precision

0/0

Recall

0/0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	256

Precision?

0/0

Recall?

0/0

Freqs

test

number	freq
0	256

Total Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	0	0	0
-	0	0	1

Precision?

0/0

Recall?

0/0

Samples

27.0ms	510×	0	valid
0.0ms	2×	1	valid

Compiler

Compiled 43 to 25 computations (41.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 13.0ms

ival-mult: 7.0ms (55.3% of total)

ival-add: 2.0ms (15.8% of total)

ival-sub: 2.0ms (15.8% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

preprocess109.0ms (3.3%)

Memory

3.8MiB live, 66.3MiB allocated; 33ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	70
1	75	68
2	156	68
3	246	66
4	320	63
5	437	63
6	654	63
7	1145	63
8	1556	63
9	1958	63
10	2234	63
11	2607	63
12	3106	63
13	3232	63
14	3245	63
15	3245	63
0	6	7
0	9	7
1	18	7
2	30	7
3	48	7
4	74	7
5	97	7
6	141	7
7	245	7
8	399	7
9	566	7
10	606	7
11	631	7
12	660	7
13	721	7
14	1005	7
15	1049	7
0	1049	6

Stop Event

1×	iter limit
1×	saturated
1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))

Outputs
(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))

Symmetry

(abs uy)

Compiler

Compiled 7 to 7 computations (0% saved)

eval0.0ms (0%)

Memory: 0.1MiB live, 0.1MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 3 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.7MiB live, 0.7MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))

Compiler

Compiled 7 to 7 computations (0% saved)

simplify26.0ms (0.8%)

Memory

-22.1MiB live, 22.3MiB allocated; 5ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f32 ux maxCos)
cost-diff	0	(-.f32 #s(literal 1 binary32) ux)
cost-diff	1	(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	16
0	9	16
1	18	16
2	30	16
3	48	16
4	74	16
5	97	16
6	141	16
7	245	16
8	399	16
9	566	16
10	606	16
11	631	16
12	660	16
13	721	16
14	1005	16
15	1049	16
0	1049	15

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
(-.f32 #s(literal 1 binary32) ux)
#s(literal 1 binary32)
ux
(*.f32 ux maxCos)
maxCos

Outputs
(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
(-.f32 #s(literal 1 binary32) ux)
#s(literal 1 binary32)
ux
(*.f32 ux maxCos)
(*.f32 maxCos ux)
maxCos

localize15.0ms (0.4%)

Memory

22.5MiB live, 22.5MiB allocated; 0ms collecting garbage

Localize:

Found 3 expressions of interest:

New	Metric	Score
accuracy	0.0	(-.f32 #s(literal 1 binary32) ux)
accuracy	0.0	(*.f32 ux maxCos)
accuracy	0.02734375	(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))

Samples

10.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 18 to 9 computations (50% saved)

Precisions

Click to see histograms. Total time spent on operations: 4.0ms

ival-add: 1.0ms (22.5% of total)

ival-mult: 1.0ms (22.5% of total)

ival-sub: 1.0ms (22.5% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

5.5MiB live, 5.5MiB allocated; 0ms collecting garbage

Counts

3 → 15

Calls

Call 1

Inputs
(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
(-.f32 #s(literal 1 binary32) ux)
(*.f32 ux maxCos)

Outputs
1
(+ 1 (* ux (- maxCos 1)))
(+ 1 (* -1 ux))
(* maxCos ux)
(* ux (- maxCos 1))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(* -1 ux)
(* ux (- (/ 1 ux) 1))
(* -1 (* ux (+ 1 (* -1 maxCos))))
(* -1 (* ux (- (+ 1 (* -1 maxCos)) (/ 1 ux))))
(* -1 (* ux (- 1 (/ 1 ux))))
(- 1 ux)
(- (+ 1 (* maxCos ux)) ux)
(* maxCos (- (+ ux (/ 1 maxCos)) (/ ux maxCos)))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (- 1 ux) maxCos)))))

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	ux	@	inf	((+ (- 1 ux) (* ux maxCos)) (- 1 ux) (* ux maxCos))
1.0ms	ux	@	-inf	((+ (- 1 ux) (* ux maxCos)) (- 1 ux) (* ux maxCos))
1.0ms	maxCos	@	0	((+ (- 1 ux) (* ux maxCos)) (- 1 ux) (* ux maxCos))
0.0ms	ux	@	0	((+ (- 1 ux) (* ux maxCos)) (- 1 ux) (* ux maxCos))
0.0ms	maxCos	@	-inf	((+ (- 1 ux) (* ux maxCos)) (- 1 ux) (* ux maxCos))

simplify86.0ms (2.6%)

Memory

-17.3MiB live, 71.1MiB allocated; 11ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	39	81
1	110	79
2	301	79
3	754	79
4	1937	79
5	4059	79
6	6828	79
0	8041	73

Stop Event

1×	iter limit
1×	node limit

Counts

15 → 15

Calls

Call 1

Inputs
1
(+ 1 (* ux (- maxCos 1)))
(+ 1 (* -1 ux))
(* maxCos ux)
(* ux (- maxCos 1))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(* -1 ux)
(* ux (- (/ 1 ux) 1))
(* -1 (* ux (+ 1 (* -1 maxCos))))
(* -1 (* ux (- (+ 1 (* -1 maxCos)) (/ 1 ux))))
(* -1 (* ux (- 1 (/ 1 ux))))
(- 1 ux)
(- (+ 1 (* maxCos ux)) ux)
(* maxCos (- (+ ux (/ 1 maxCos)) (/ ux maxCos)))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (- 1 ux) maxCos)))))

Outputs
1
#s(literal 1 binary32)
(+ 1 (* ux (- maxCos 1)))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
(+ 1 (* -1 ux))
(-.f32 #s(literal 1 binary32) ux)
(* maxCos ux)
(*.f32 maxCos ux)
(* ux (- maxCos 1))
(*.f32 (-.f32 maxCos #s(literal 1 binary32)) ux)
(* ux (- (+ maxCos (/ 1 ux)) 1))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
(* -1 ux)
(neg.f32 ux)
(* ux (- (/ 1 ux) 1))
(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)
(* -1 (* ux (+ 1 (* -1 maxCos))))
(*.f32 (-.f32 maxCos #s(literal 1 binary32)) ux)
(* -1 (* ux (- (+ 1 (* -1 maxCos)) (/ 1 ux))))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
(* -1 (* ux (- 1 (/ 1 ux))))
(*.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal 1 binary32) ux)) (neg.f32 ux))
(- 1 ux)
(-.f32 #s(literal 1 binary32) ux)
(- (+ 1 (* maxCos ux)) ux)
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
(* maxCos (- (+ ux (/ 1 maxCos)) (/ ux maxCos)))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (- 1 ux) maxCos)))))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))

rewrite192.0ms (5.8%)

Memory

33.4MiB live, 210.0MiB allocated; 30ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
0	9	13
1	44	13
2	327	13
3	4373	13
0	8540	12

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

3 → 192

Calls

Call 1

Inputs
(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
(-.f32 #s(literal 1 binary32) ux)
(*.f32 ux maxCos)

Outputs
(.f32 (/.f32 (-.f32 (pow.f32 (.f32 maxCos ux) #s(literal 3 binary32)) (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 3 binary32))) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 4 binary32)) (pow.f32 (.f32 (.f32 maxCos ux) (fma.f32 maxCos ux (fma.f32 #s(literal -1 binary32) ux #s(literal -1 binary32)))) #s(literal 2 binary32)))) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32)) (.f32 (.f32 maxCos ux) (fma.f32 maxCos ux (fma.f32 #s(literal -1 binary32) ux #s(literal -1 binary32))))))
(.f32 (/.f32 (-.f32 (pow.f32 (.f32 maxCos ux) #s(literal 3 binary32)) (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 3 binary32))) (+.f32 (pow.f32 (.f32 (.f32 maxCos ux) (fma.f32 maxCos ux (fma.f32 #s(literal -1 binary32) ux #s(literal -1 binary32)))) #s(literal 3 binary32)) (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 6 binary32)))) (fma.f32 (.f32 (.f32 maxCos ux) (fma.f32 maxCos ux (fma.f32 #s(literal -1 binary32) ux #s(literal -1 binary32)))) (-.f32 (.f32 (.f32 maxCos ux) (fma.f32 maxCos ux (fma.f32 #s(literal -1 binary32) ux #s(literal -1 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32))) (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 4 binary32))))
(.f32 (/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32)) (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32))) (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32)) (pow.f32 (*.f32 maxCos ux) #s(literal 2 binary32)))) (fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux)))
(.f32 (/.f32 (-.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32)) (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32))) (-.f32 (pow.f32 (.f32 maxCos ux) #s(literal 3 binary32)) (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 3 binary32)))) (fma.f32 (.f32 maxCos ux) (fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux)) (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32))))
(.f32 (fma.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32))) (/.f32 (fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux)) (fma.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (pow.f32 (*.f32 maxCos ux) #s(literal 2 binary32)))))
(*.f32 (fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux)) (/.f32 (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux))))
(/.f32 (-.f32 (pow.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) #s(literal 2 binary32)) (*.f32 ux ux)) (+.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux))
(/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux))) #s(literal 2 binary32)) (pow.f32 (/.f32 (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux))) #s(literal 2 binary32))) (+.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux))) (/.f32 (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)))))
(/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 3 binary32)) (fma.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32)))) #s(literal 2 binary32)) (pow.f32 (/.f32 (pow.f32 (.f32 maxCos ux) #s(literal 3 binary32)) (fma.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (pow.f32 (*.f32 maxCos ux) #s(literal 2 binary32)))) #s(literal 2 binary32))) (fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux)))
(/.f32 (-.f32 (pow.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) #s(literal 3 binary32)) (pow.f32 ux #s(literal 3 binary32))) (+.f32 (pow.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) #s(literal 2 binary32)) (fma.f32 ux ux (*.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux))))
(/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux))) #s(literal 3 binary32)) (pow.f32 (/.f32 (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux))) #s(literal 3 binary32))) (+.f32 (pow.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux))) #s(literal 2 binary32)) (+.f32 (pow.f32 (/.f32 (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux))) #s(literal 2 binary32)) (.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux))) (/.f32 (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)))))))
(/.f32 (+.f32 (pow.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 3 binary32)) (fma.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32)))) #s(literal 3 binary32)) (pow.f32 (/.f32 (pow.f32 (.f32 maxCos ux) #s(literal 3 binary32)) (fma.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32)))) #s(literal 3 binary32))) (+.f32 (pow.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 3 binary32)) (fma.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32)))) #s(literal 2 binary32)) (-.f32 (pow.f32 (/.f32 (pow.f32 (.f32 maxCos ux) #s(literal 3 binary32)) (fma.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32)))) #s(literal 2 binary32)) (.f32 (/.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 3 binary32)) (fma.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32)))) (/.f32 (pow.f32 (.f32 maxCos ux) #s(literal 3 binary32)) (fma.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32))))))))
(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (-.f32 ux (*.f32 maxCos ux)) #s(literal 2 binary32)))) (neg.f32 (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux))))
(/.f32 (neg.f32 (-.f32 (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32)) (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32)))) (neg.f32 (-.f32 (.f32 maxCos ux) (-.f32 #s(literal 1 binary32) ux))))
(/.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (pow.f32 (-.f32 ux (.f32 maxCos ux)) #s(literal 3 binary32)))) (neg.f32 (fma.f32 (-.f32 ux (.f32 maxCos ux)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) #s(literal 1 binary32))))
(/.f32 (neg.f32 (+.f32 (neg.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32))) (pow.f32 (*.f32 maxCos ux) #s(literal 2 binary32)))) (neg.f32 (neg.f32 (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)))))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 (.f32 maxCos ux) #s(literal 3 binary32)) (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 3 binary32))))) (neg.f32 (neg.f32 (fma.f32 (-.f32 #s(literal 1 binary32) ux) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32))))))
(/.f32 (-.f32 (.f32 (pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 2 binary32)) (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux))) (.f32 (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) (pow.f32 (*.f32 maxCos ux) #s(literal 2 binary32)))) (pow.f32 (-.f32 #s(literal 1 binary32) (fma.f32 maxCos ux ux)) #s(literal 2 binary32)))
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(-.f32 #s(literal 1 binary32) (neg.f32 ux))
(-.f32 #s(literal 1 binary32) ux)
(fma.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (+.f32 #s(literal -1 binary32) (.f32 ux ux))) #s(literal -1 binary32)) (pow.f32 (fma.f32 #s(literal -1 binary32) ux #s(literal -1 binary32)) #s(literal -1 binary32)) (/.f32 (*.f32 (neg.f32 ux) ux) (-.f32 #s(literal 1 binary32) ux)))
(fma.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (neg.f32 (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal 3 binary32))))) #s(literal -1 binary32)) (pow.f32 (neg.f32 (fma.f32 (-.f32 #s(literal 1 binary32) ux) ux #s(literal 1 binary32))) #s(literal -1 binary32)) (/.f32 (.f32 (neg.f32 ux) ux) (-.f32 #s(literal 1 binary32) ux)))
(fma.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal 3 binary32)))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) ux) ux #s(literal 1 binary32))) (/.f32 (.f32 (neg.f32 ux) ux) (-.f32 #s(literal 1 binary32) ux)))
(fma.f32 (pow.f32 (/.f32 (-.f32 #s(literal 1 binary32) (.f32 ux ux)) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) #s(literal -1 binary32)) (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) ux)) (/.f32 (*.f32 (neg.f32 ux) ux) (-.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (pow.f32 (fma.f32 ux ux ux) #s(literal 2 binary32)))) (-.f32 #s(literal 1 binary32) (fma.f32 ux ux ux)) (/.f32 (pow.f32 ux #s(literal 3 binary32)) (fma.f32 (-.f32 #s(literal 1 binary32) ux) ux #s(literal 1 binary32))))
(fma.f32 (/.f32 #s(literal 1 binary32) (+.f32 (pow.f32 (fma.f32 ux ux ux) #s(literal 3 binary32)) #s(literal 1 binary32))) (fma.f32 (fma.f32 ux ux ux) (-.f32 (fma.f32 ux ux ux) #s(literal 1 binary32)) #s(literal 1 binary32)) (/.f32 (pow.f32 ux #s(literal 3 binary32)) (fma.f32 (-.f32 #s(literal 1 binary32) ux) ux #s(literal 1 binary32))))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (.f32 ux ux))) (-.f32 #s(literal 1 binary32) ux) (/.f32 (.f32 (neg.f32 ux) ux) (-.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal 3 binary32)))) (fma.f32 (-.f32 #s(literal 1 binary32) ux) ux #s(literal 1 binary32)) (/.f32 (*.f32 (neg.f32 ux) ux) (-.f32 #s(literal 1 binary32) ux)))
(fma.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) ux)) #s(literal 1 binary32) (/.f32 (*.f32 (neg.f32 ux) ux) (-.f32 #s(literal 1 binary32) ux)))
(fma.f32 ux #s(literal 1 binary32) #s(literal 1 binary32))
(fma.f32 #s(literal 1 binary32) ux #s(literal 1 binary32))
(pow.f32 (-.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32))
(+.f32 (cosh.f32 (log1p.f32 ux)) (sinh.f32 (log1p.f32 ux)))
(+.f32 (/.f32 #s(literal 1 binary32) (-.f32 #s(literal 1 binary32) ux)) (/.f32 (*.f32 (neg.f32 ux) ux) (-.f32 #s(literal 1 binary32) ux)))
(+.f32 (/.f32 #s(literal 1 binary32) (fma.f32 (-.f32 #s(literal 1 binary32) ux) ux #s(literal 1 binary32))) (/.f32 (pow.f32 ux #s(literal 3 binary32)) (fma.f32 (-.f32 #s(literal 1 binary32) ux) ux #s(literal 1 binary32))))
(+.f32 ux #s(literal 1 binary32))
(+.f32 #s(literal 1 binary32) (neg.f32 ux))
(+.f32 #s(literal 1 binary32) ux)
(exp.f32 (*.f32 (log1p.f32 ux) #s(literal 1 binary32)))
(exp.f32 (log1p.f32 ux))
(neg.f32 (fma.f32 #s(literal -1 binary32) ux #s(literal -1 binary32)))
(*.f32 (exp.f32 (log.f32 maxCos)) ux)
(.f32 (pow.f32 (.f32 maxCos #s(literal 1 binary32)) #s(literal 1 binary32)) ux)
(*.f32 (pow.f32 maxCos #s(literal 1 binary32)) ux)
(.f32 (.f32 maxCos #s(literal 1 binary32)) ux)
(.f32 (.f32 maxCos ux) #s(literal 1 binary32))
(*.f32 maxCos ux)
(*.f32 ux (exp.f32 (log.f32 maxCos)))
(.f32 ux (pow.f32 (.f32 #s(literal 1 binary32) maxCos) #s(literal 1 binary32)))
(*.f32 ux (pow.f32 maxCos #s(literal 1 binary32)))
(.f32 ux (.f32 #s(literal 1 binary32) maxCos))
(*.f32 ux maxCos)
(.f32 #s(literal 1 binary32) (.f32 maxCos ux))
(pow.f32 (*.f32 maxCos ux) #s(literal 1 binary32))
(+.f32 (cosh.f32 (log.f32 (.f32 maxCos ux))) (sinh.f32 (log.f32 (.f32 maxCos ux))))
(exp.f32 (.f32 (log.f32 (.f32 maxCos ux)) #s(literal 1 binary32)))
(exp.f32 (log.f32 (*.f32 maxCos ux)))
(neg.f32 (*.f32 (neg.f32 ux) maxCos))

eval47.0ms (1.4%)

Memory: -11.9MiB live, 80.8MiB allocated; 23ms collecting garbage
Compiler: Compiled 4 877 to 575 computations (88.2% saved)

prune4.0ms (0.1%)

Memory

15.2MiB live, 15.2MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	195	6	201
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	196	6	202

Accuracy

100.0%

Counts

202 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))
▶	99.8%	(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
▶	99.9%	(-.f32 #s(literal 1 binary32) (-.f32 ux (*.f32 maxCos ux)))
	98.7%	(+.f32 #s(approx (- 1 ux) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)) (.f32 ux maxCos))
▶	97.9%	#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
▶	71.9%	#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))

Compiler

Compiled 108 to 100 computations (7.4% saved)

simplify31.0ms (0.9%)

Memory

-14.8MiB live, 29.6MiB allocated; 15ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 10 expressions of interest:

New	Metric	Score
cost-diff	0	(*.f32 maxCos ux)
cost-diff	0	(-.f32 ux (*.f32 maxCos ux))
cost-diff	1	(-.f32 #s(literal 1 binary32) (-.f32 ux (*.f32 maxCos ux)))
cost-diff	0	(fma.f32 maxCos ux #s(literal 1 binary32))
cost-diff	0	(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
cost-diff	0	(-.f32 #s(literal 1 binary32) ux)
cost-diff	0	#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
cost-diff	0	#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))
cost-diff	0	(-.f32 #s(literal 1 binary32) ux)
cost-diff	0	(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	69
0	22	66
1	37	66
2	55	66
3	81	66
4	110	66
5	143	66
6	247	66
7	402	66
8	569	66
9	609	66
10	634	66
11	663	66
12	724	66
13	1008	66
14	1052	66
0	1052	66

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))
ux
maxCos
(-.f32 #s(literal 1 binary32) ux)
#s(literal 1 binary32)
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))
#s(literal 1 binary32)
#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
(-.f32 #s(literal 1 binary32) ux)
#s(literal 1 binary32)
ux
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
(fma.f32 maxCos ux #s(literal 1 binary32))
maxCos
ux
#s(literal 1 binary32)
(-.f32 #s(literal 1 binary32) (-.f32 ux (*.f32 maxCos ux)))
#s(literal 1 binary32)
(-.f32 ux (*.f32 maxCos ux))
ux
(*.f32 maxCos ux)
maxCos

Outputs
(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
ux
maxCos
(-.f32 #s(literal 1 binary32) ux)
#s(literal 1 binary32)
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))
#s(literal 1 binary32)
#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
(-.f32 #s(literal 1 binary32) ux)
#s(literal 1 binary32)
ux
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
(fma.f32 maxCos ux #s(literal 1 binary32))
maxCos
ux
#s(literal 1 binary32)
(-.f32 #s(literal 1 binary32) (-.f32 ux (*.f32 maxCos ux)))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
#s(literal 1 binary32)
(-.f32 ux (*.f32 maxCos ux))
ux
(*.f32 maxCos ux)
maxCos

localize40.0ms (1.2%)

Memory

8.9MiB live, 52.8MiB allocated; 23ms collecting garbage

Localize:

Found 10 expressions of interest:

New	Metric	Score
accuracy	0.0	(*.f32 maxCos ux)
accuracy	0.00390625	(-.f32 ux (*.f32 maxCos ux))
accuracy	0.029628759768442016	(-.f32 #s(literal 1 binary32) (-.f32 ux (*.f32 maxCos ux)))
accuracy	0.0	(fma.f32 maxCos ux #s(literal 1 binary32))
accuracy	0.06707001953688403	(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
accuracy	0.0	(-.f32 #s(literal 1 binary32) ux)
accuracy	0.6790785222771178	#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
accuracy	8.996013320673084	#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))
accuracy	0.0	(-.f32 #s(literal 1 binary32) ux)
accuracy	0.02734375	(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))

Samples

33.0ms	255×	0	valid
0.0ms	1×	1	valid

Compiler

Compiled 68 to 15 computations (77.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 24.0ms

ival-mult: 15.0ms (63.4% of total)

ival-sub: 5.0ms (21.1% of total)

ival-add: 3.0ms (12.7% of total)

adjust: 0.0ms (0% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series4.0ms (0.1%)

Memory

7.5MiB live, 7.5MiB allocated; 0ms collecting garbage

Counts

9 → 27

Calls

Call 1

Inputs
(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))
(-.f32 #s(literal 1 binary32) ux)
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))
#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
(fma.f32 maxCos ux #s(literal 1 binary32))
(-.f32 #s(literal 1 binary32) (-.f32 ux (*.f32 maxCos ux)))
(-.f32 ux (*.f32 maxCos ux))
(*.f32 maxCos ux)

Outputs
1
(+ 1 (* ux (- maxCos 1)))
(+ 1 (* -1 ux))
(+ 1 (* maxCos ux))
(* ux (- 1 maxCos))
(* maxCos ux)
(* ux (- maxCos 1))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(* -1 ux)
(* ux (- (/ 1 ux) 1))
(* ux (+ maxCos (/ 1 ux)))
(* -1 (* ux (+ 1 (* -1 maxCos))))
(* -1 (* ux (- (+ 1 (* -1 maxCos)) (/ 1 ux))))
(* -1 (* ux (- 1 (/ 1 ux))))
(* -1 (* ux (- (* -1 maxCos) (/ 1 ux))))
(* ux (+ 1 (* -1 maxCos)))
(- 1 ux)
(- (+ 1 (* maxCos ux)) ux)
ux
(+ ux (* -1 (* maxCos ux)))
(* maxCos (- (+ ux (/ 1 maxCos)) (/ ux maxCos)))
(* maxCos (+ ux (/ 1 maxCos)))
(* -1 (* maxCos ux))
(* maxCos (- (/ ux maxCos) ux))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (- 1 ux) maxCos)))))
(* -1 (* maxCos (- (* -1 ux) (/ 1 maxCos))))
(* -1 (* maxCos (- (* -1 (/ ux maxCos)) (* -1 ux))))

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	ux	@	-inf	((+ (* ux maxCos) (- 1 ux)) (- 1 ux) (+ (- 1 ux) (* ux maxCos)) (+ (- 1 ux) (* ux maxCos)) (- (+ (* maxCos ux) 1) ux) (+ (* maxCos ux) 1) (- 1 (- ux (* maxCos ux))) (- ux (* maxCos ux)) (* maxCos ux))
1.0ms	maxCos	@	-inf	((+ (* ux maxCos) (- 1 ux)) (- 1 ux) (+ (- 1 ux) (* ux maxCos)) (+ (- 1 ux) (* ux maxCos)) (- (+ (* maxCos ux) 1) ux) (+ (* maxCos ux) 1) (- 1 (- ux (* maxCos ux))) (- ux (* maxCos ux)) (* maxCos ux))
1.0ms	ux	@	inf	((+ (* ux maxCos) (- 1 ux)) (- 1 ux) (+ (- 1 ux) (* ux maxCos)) (+ (- 1 ux) (* ux maxCos)) (- (+ (* maxCos ux) 1) ux) (+ (* maxCos ux) 1) (- 1 (- ux (* maxCos ux))) (- ux (* maxCos ux)) (* maxCos ux))
0.0ms	maxCos	@	inf	((+ (* ux maxCos) (- 1 ux)) (- 1 ux) (+ (- 1 ux) (* ux maxCos)) (+ (- 1 ux) (* ux maxCos)) (- (+ (* maxCos ux) 1) ux) (+ (* maxCos ux) 1) (- 1 (- ux (* maxCos ux))) (- ux (* maxCos ux)) (* maxCos ux))
0.0ms	ux	@	0	((+ (* ux maxCos) (- 1 ux)) (- 1 ux) (+ (- 1 ux) (* ux maxCos)) (+ (- 1 ux) (* ux maxCos)) (- (+ (* maxCos ux) 1) ux) (+ (* maxCos ux) 1) (- 1 (- ux (* maxCos ux))) (- ux (* maxCos ux)) (* maxCos ux))

simplify121.0ms (3.6%)

Memory

-4.2MiB live, 93.8MiB allocated; 68ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	129
1	164	129
2	422	129
3	1032	129
4	2502	129
5	5139	129
6	6528	129
7	7773	129
0	8002	118

Stop Event

1×	iter limit
1×	node limit

Counts

27 → 26

Calls

Call 1

Inputs
1
(+ 1 (* ux (- maxCos 1)))
(+ 1 (* -1 ux))
(+ 1 (* maxCos ux))
(* ux (- 1 maxCos))
(* maxCos ux)
(* ux (- maxCos 1))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(* -1 ux)
(* ux (- (/ 1 ux) 1))
(* ux (+ maxCos (/ 1 ux)))
(* -1 (* ux (+ 1 (* -1 maxCos))))
(* -1 (* ux (- (+ 1 (* -1 maxCos)) (/ 1 ux))))
(* -1 (* ux (- 1 (/ 1 ux))))
(* -1 (* ux (- (* -1 maxCos) (/ 1 ux))))
(* ux (+ 1 (* -1 maxCos)))
(- 1 ux)
(- (+ 1 (* maxCos ux)) ux)
ux
(+ ux (* -1 (* maxCos ux)))
(* maxCos (- (+ ux (/ 1 maxCos)) (/ ux maxCos)))
(* maxCos (+ ux (/ 1 maxCos)))
(* -1 (* maxCos ux))
(* maxCos (- (/ ux maxCos) ux))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (- 1 ux) maxCos)))))
(* -1 (* maxCos (- (* -1 ux) (/ 1 maxCos))))
(* -1 (* maxCos (- (* -1 (/ ux maxCos)) (* -1 ux))))

Outputs
1
#s(literal 1 binary32)
(+ 1 (* ux (- maxCos 1)))
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
(+ 1 (* -1 ux))
(-.f32 #s(literal 1 binary32) ux)
(+ 1 (* maxCos ux))
(fma.f32 maxCos ux #s(literal 1 binary32))
(* ux (- 1 maxCos))
(*.f32 (-.f32 #s(literal 1 binary32) maxCos) ux)
(* maxCos ux)
(*.f32 maxCos ux)
(* ux (- maxCos 1))
(*.f32 (-.f32 maxCos #s(literal 1 binary32)) ux)
(* ux (- (+ maxCos (/ 1 ux)) 1))
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
(* -1 ux)
(neg.f32 ux)
(* ux (- (/ 1 ux) 1))
(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)
(* ux (+ maxCos (/ 1 ux)))
(fma.f32 maxCos ux #s(literal 1 binary32))
(* -1 (* ux (+ 1 (* -1 maxCos))))
(*.f32 (-.f32 maxCos #s(literal 1 binary32)) ux)
(* -1 (* ux (- (+ 1 (* -1 maxCos)) (/ 1 ux))))
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
(* -1 (* ux (- 1 (/ 1 ux))))
(-.f32 #s(literal 1 binary32) ux)
(* -1 (* ux (- (* -1 maxCos) (/ 1 ux))))
(fma.f32 maxCos ux #s(literal 1 binary32))
(* ux (+ 1 (* -1 maxCos)))
(*.f32 (-.f32 #s(literal 1 binary32) maxCos) ux)
(- 1 ux)
(-.f32 #s(literal 1 binary32) ux)
(- (+ 1 (* maxCos ux)) ux)
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
ux
(+ ux (* -1 (* maxCos ux)))
(*.f32 (-.f32 #s(literal 1 binary32) maxCos) ux)
(* maxCos (- (+ ux (/ 1 maxCos)) (/ ux maxCos)))
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
(* maxCos (+ ux (/ 1 maxCos)))
(fma.f32 maxCos ux #s(literal 1 binary32))
(* -1 (* maxCos ux))
(*.f32 (neg.f32 maxCos) ux)
(* maxCos (- (/ ux maxCos) ux))
(*.f32 (-.f32 #s(literal 1 binary32) maxCos) ux)
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (- 1 ux) maxCos)))))
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
(* -1 (* maxCos (- (* -1 ux) (/ 1 maxCos))))
(fma.f32 maxCos ux #s(literal 1 binary32))
(* -1 (* maxCos (- (* -1 (/ ux maxCos)) (* -1 ux))))
(*.f32 (-.f32 #s(literal 1 binary32) maxCos) ux)

rewrite255.0ms (7.6%)

Memory

-30.3MiB live, 290.2MiB allocated; 168ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	54
0	22	51
1	119	51
2	869	51
0	8553	51

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

9 → 435

Calls

Call 1

Inputs
(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))
(-.f32 #s(literal 1 binary32) ux)
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))
#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
(fma.f32 maxCos ux #s(literal 1 binary32))
(-.f32 #s(literal 1 binary32) (-.f32 ux (*.f32 maxCos ux)))
(-.f32 ux (*.f32 maxCos ux))
(*.f32 maxCos ux)

Outputs
(/.f32 (-.f32 (.f32 (/.f32 (pow.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) #s(literal 2 binary32)) (fma.f32 maxCos ux (+.f32 #s(literal 1 binary32) ux))) (/.f32 (pow.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) #s(literal 2 binary32)) (fma.f32 maxCos ux (+.f32 #s(literal 1 binary32) ux)))) (.f32 (/.f32 (.f32 ux ux) (fma.f32 maxCos ux (+.f32 #s(literal 1 binary32) ux))) (/.f32 (.f32 ux ux) (fma.f32 maxCos ux (+.f32 #s(literal 1 binary32) ux))))) (+.f32 (/.f32 (pow.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) #s(literal 2 binary32)) (fma.f32 maxCos ux (+.f32 #s(literal 1 binary32) ux))) (/.f32 (*.f32 ux ux) (fma.f32 maxCos ux (+.f32 #s(literal 1 binary32) ux)))))
(/.f32 (-.f32 (.f32 (/.f32 #s(literal -1 binary32) (fma.f32 ux (-.f32 maxCos #s(literal 1 binary32)) #s(literal -1 binary32))) (/.f32 #s(literal -1 binary32) (fma.f32 ux (-.f32 maxCos #s(literal 1 binary32)) #s(literal -1 binary32)))) (.f32 (/.f32 (pow.f32 (-.f32 ux (.f32 maxCos ux)) #s(literal 2 binary32)) (fma.f32 ux (-.f32 #s(literal 1 binary32) maxCos) #s(literal 1 binary32))) (/.f32 (pow.f32 (-.f32 ux (.f32 maxCos ux)) #s(literal 2 binary32)) (fma.f32 ux (-.f32 #s(literal 1 binary32) maxCos) #s(literal 1 binary32))))) (+.f32 (/.f32 #s(literal -1 binary32) (fma.f32 ux (-.f32 maxCos #s(literal 1 binary32)) #s(literal -1 binary32))) (/.f32 (pow.f32 (-.f32 ux (*.f32 maxCos ux)) #s(literal 2 binary32)) (fma.f32 ux (-.f32 #s(literal 1 binary32) maxCos) #s(literal 1 binary32)))))
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(fma.f32 (neg.f32 maxCos) ux ux)
(fma.f32 (*.f32 (neg.f32 ux) maxCos) #s(literal 1 binary32) ux)
(fma.f32 (neg.f32 ux) maxCos ux)
(fma.f32 (*.f32 maxCos ux) #s(literal -1 binary32) ux)
(fma.f32 #s(literal 1 binary32) (*.f32 (neg.f32 ux) maxCos) ux)
(fma.f32 #s(literal 1 binary32) ux (*.f32 (neg.f32 ux) maxCos))
(fma.f32 maxCos (neg.f32 ux) ux)
(fma.f32 ux (neg.f32 maxCos) ux)
(fma.f32 ux #s(literal 1 binary32) (*.f32 (neg.f32 ux) maxCos))
(+.f32 (/.f32 (.f32 ux ux) (fma.f32 maxCos ux ux)) (/.f32 (neg.f32 (pow.f32 (.f32 maxCos ux) #s(literal 2 binary32))) (fma.f32 maxCos ux ux)))
(+.f32 (/.f32 (pow.f32 ux #s(literal 3 binary32)) (fma.f32 (.f32 ux ux) (fma.f32 maxCos maxCos maxCos) (.f32 ux ux))) (/.f32 (pow.f32 (.f32 (neg.f32 ux) maxCos) #s(literal 3 binary32)) (fma.f32 (.f32 ux ux) (fma.f32 maxCos maxCos maxCos) (*.f32 ux ux))))
(+.f32 (*.f32 (neg.f32 ux) maxCos) ux)
(+.f32 ux (*.f32 (neg.f32 ux) maxCos))
(neg.f32 (-.f32 (*.f32 maxCos ux) ux))
(.f32 (.f32 #s(literal 1 binary32) maxCos) ux)
(.f32 (.f32 maxCos ux) #s(literal 1 binary32))
(.f32 #s(literal 1 binary32) (.f32 maxCos ux))
(*.f32 maxCos ux)
(*.f32 ux maxCos)
(neg.f32 (*.f32 (neg.f32 ux) maxCos))

eval26.0ms (0.8%)

Memory: 1.5MiB live, 57.6MiB allocated; 5ms collecting garbage
Compiler: Compiled 7 604 to 810 computations (89.3% saved)

prune5.0ms (0.1%)

Memory

17.9MiB live, 17.9MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (1 fresh and 5 done)

	Pruned	Kept	Total
New	254	1	255
Fresh	1	0	1
Picked	0	5	5
Done	0	0	0
Total	255	6	261

Accuracy

100.0%

Counts

261 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))
✓	99.8%	(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
✓	99.9%	(-.f32 #s(literal 1 binary32) (-.f32 ux (*.f32 maxCos ux)))
✓	97.9%	#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
▶	96.8%	#s(approx (+ (- 1 ux) (* ux maxCos)) #s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)))
✓	71.9%	#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))

Compiler

Compiled 58 to 51 computations (12.1% saved)

simplify25.0ms (0.7%)

Memory

-12.1MiB live, 35.1MiB allocated; 1ms collecting garbage

Algorithm

1×	egg-herbie

Localize:

Found 4 expressions of interest:

New	Metric	Score	Program
cost-diff	0	(-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32))
cost-diff	0	(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)
cost-diff	0	#s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux))
cost-diff	0	#s(approx (+ (- 1 ux) (* ux maxCos)) #s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)))

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	47
0	14	47
1	24	47
2	36	47
3	54	47
4	86	47
5	115	47
6	166	47
7	291	47
8	477	47
9	650	47
10	684	47
11	709	47
12	738	47
13	799	47
14	1083	47
15	1127	47
0	1127	46

Stop Event

1×	iter limit
1×	saturated
1×	iter limit

Calls

Call 1

Inputs
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)))
#s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux))
(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)
(-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32))
(/.f32 #s(literal 1 binary32) ux)
#s(literal 1 binary32)
ux

Outputs
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)))
#s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux))
(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)
(-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32))
(/.f32 #s(literal 1 binary32) ux)
#s(literal 1 binary32)
ux

localize25.0ms (0.8%)

Memory

-4.6MiB live, 41.4MiB allocated; 2ms collecting garbage

Localize:

Found 4 expressions of interest:

New	Metric	Score
accuracy	0.0	#s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux))
accuracy	0.1274514155563831	(-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32))
accuracy	0.29296875	(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)
accuracy	0.6751722722771178	#s(approx (+ (- 1 ux) (* ux maxCos)) #s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)))

Samples

18.0ms	252×	0	valid
1.0ms	4×	5	exit

Compiler

Compiled 29 to 12 computations (58.6% saved)

Precisions

Click to see histograms. Total time spent on operations: 10.0ms

ival-mult: 3.0ms (31.1% of total)

ival-sub: 3.0ms (31.1% of total)

ival-div: 2.0ms (20.8% of total)

adjust: 1.0ms (10.4% of total)

ival-add: 1.0ms (10.4% of total)

ival-assert: 0.0ms (0% of total)

ival-true: 0.0ms (0% of total)

exact: 0.0ms (0% of total)

series3.0ms (0.1%)

Memory

4.5MiB live, 4.5MiB allocated; 0ms collecting garbage

Counts

4 → 19

Calls

Call 1

Inputs
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)))
#s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux))
(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)
(-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32))

Outputs
1
(+ 1 (* ux (- maxCos 1)))
(+ 1 (* -1 ux))
(/ 1 ux)
(/ (+ 1 (* -1 ux)) ux)
(* ux (- maxCos 1))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(* -1 ux)
(* ux (- (/ 1 ux) 1))
-1
(- (/ 1 ux) 1)
(* -1 (* ux (+ 1 (* -1 maxCos))))
(* -1 (* ux (- (+ 1 (* -1 maxCos)) (/ 1 ux))))
(* -1 (* ux (- 1 (/ 1 ux))))
(- 1 ux)
(- (+ 1 (* maxCos ux)) ux)
(* maxCos ux)
(* maxCos (- (+ ux (/ 1 maxCos)) (/ ux maxCos)))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (- 1 ux) maxCos)))))

Calls

9 calls:

Time	Variable		Point	Expression
1.0ms	ux	@	-inf	((+ (- 1 ux) (* ux maxCos)) (- 1 ux) (* (- (/ 1 ux) 1) ux) (- (/ 1 ux) 1))
0.0ms	ux	@	0	((+ (- 1 ux) (* ux maxCos)) (- 1 ux) (* (- (/ 1 ux) 1) ux) (- (/ 1 ux) 1))
0.0ms	ux	@	inf	((+ (- 1 ux) (* ux maxCos)) (- 1 ux) (* (- (/ 1 ux) 1) ux) (- (/ 1 ux) 1))
0.0ms	maxCos	@	-inf	((+ (- 1 ux) (* ux maxCos)) (- 1 ux) (* (- (/ 1 ux) 1) ux) (- (/ 1 ux) 1))
0.0ms	maxCos	@	inf	((+ (- 1 ux) (* ux maxCos)) (- 1 ux) (* (- (/ 1 ux) 1) ux) (- (/ 1 ux) 1))

simplify92.0ms (2.8%)

Memory

6.2MiB live, 51.0MiB allocated; 8ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	86
1	113	84
2	314	84
3	793	84
4	2004	84
5	3999	84
6	5277	84
7	7035	84
0	8055	78

Stop Event

1×	iter limit
1×	node limit

Counts

19 → 19

Calls

Call 1

Inputs
1
(+ 1 (* ux (- maxCos 1)))
(+ 1 (* -1 ux))
(/ 1 ux)
(/ (+ 1 (* -1 ux)) ux)
(* ux (- maxCos 1))
(* ux (- (+ maxCos (/ 1 ux)) 1))
(* -1 ux)
(* ux (- (/ 1 ux) 1))
-1
(- (/ 1 ux) 1)
(* -1 (* ux (+ 1 (* -1 maxCos))))
(* -1 (* ux (- (+ 1 (* -1 maxCos)) (/ 1 ux))))
(* -1 (* ux (- 1 (/ 1 ux))))
(- 1 ux)
(- (+ 1 (* maxCos ux)) ux)
(* maxCos ux)
(* maxCos (- (+ ux (/ 1 maxCos)) (/ ux maxCos)))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (- 1 ux) maxCos)))))

Outputs
1
#s(literal 1 binary32)
(+ 1 (* ux (- maxCos 1)))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
(+ 1 (* -1 ux))
(-.f32 #s(literal 1 binary32) ux)
(/ 1 ux)
(/.f32 #s(literal 1 binary32) ux)
(/ (+ 1 (* -1 ux)) ux)
(/.f32 (-.f32 #s(literal 1 binary32) ux) ux)
(* ux (- maxCos 1))
(*.f32 (-.f32 maxCos #s(literal 1 binary32)) ux)
(* ux (- (+ maxCos (/ 1 ux)) 1))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
(* -1 ux)
(neg.f32 ux)
(* ux (- (/ 1 ux) 1))
(-.f32 #s(literal 1 binary32) ux)
-1
#s(literal -1 binary32)
(- (/ 1 ux) 1)
(/.f32 (-.f32 #s(literal 1 binary32) ux) ux)
(* -1 (* ux (+ 1 (* -1 maxCos))))
(*.f32 (-.f32 maxCos #s(literal 1 binary32)) ux)
(* -1 (* ux (- (+ 1 (* -1 maxCos)) (/ 1 ux))))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
(* -1 (* ux (- 1 (/ 1 ux))))
(-.f32 #s(literal 1 binary32) ux)
(- 1 ux)
(-.f32 #s(literal 1 binary32) ux)
(- (+ 1 (* maxCos ux)) ux)
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
(* maxCos ux)
(*.f32 maxCos ux)
(* maxCos (- (+ ux (/ 1 maxCos)) (/ ux maxCos)))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))
(* -1 (* maxCos (+ (* -1 ux) (* -1 (/ (- 1 ux) maxCos)))))
(fma.f32 maxCos ux (-.f32 #s(literal 1 binary32) ux))

rewrite227.0ms (6.8%)

Memory

-18.9MiB live, 159.9MiB allocated; 24ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	42
0	14	42
1	64	42
2	475	42
3	6218	42
0	8758	37

Stop Event

1×	iter limit
1×	node limit
1×	iter limit

Counts

4 → 65

Calls

Call 1

Inputs
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)))
#s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux))
(*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)
(-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32))

Outputs
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(approx (- 1 ux) (*.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux)))
#s(approx (- 1 ux) (*.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux))
(.f32 (/.f32 (.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32)) ux) (-.f32 (pow.f32 ux #s(literal -4 binary32)) (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal -2 binary32))))) (-.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)))
(.f32 (/.f32 (.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32)) ux) (+.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)) #s(literal 3 binary32)) (pow.f32 ux #s(literal -6 binary32)))) (+.f32 (-.f32 (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal -2 binary32))) (+.f32 (pow.f32 ux #s(literal -2 binary32)) (pow.f32 ux #s(literal -3 binary32)))) (pow.f32 ux #s(literal -4 binary32))))
(.f32 (/.f32 (.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)) ux) (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal -2 binary32)))) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)))
(.f32 (/.f32 (.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)) ux) (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal -3 binary32)))) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)))
(.f32 (/.f32 (.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)) ux) (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32))) (expm1.f32 (neg.f32 (log.f32 ux))))
(*.f32 (/.f32 ux (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux))) (/.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)) #s(literal 1 binary32)))
(.f32 (.f32 (expm1.f32 (neg.f32 (log.f32 ux))) #s(literal 1 binary32)) ux)
(*.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)) (/.f32 ux (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux))))
(*.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32)) (/.f32 ux (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))))
(.f32 (.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))
(*.f32 (expm1.f32 (neg.f32 (log.f32 ux))) (/.f32 ux #s(literal 1 binary32)))
(*.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux)
(.f32 ux (.f32 #s(literal 1 binary32) (expm1.f32 (neg.f32 (log.f32 ux)))))
(*.f32 ux (expm1.f32 (neg.f32 (log.f32 ux))))
(.f32 #s(literal 1 binary32) (.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux))
(/.f32 (*.f32 (neg.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32))) ux) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32)))
(/.f32 (*.f32 (neg.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32))) ux) (-.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)))
(/.f32 (*.f32 ux (neg.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)))) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32)))
(/.f32 (*.f32 ux (neg.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32)))) (-.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)))
(/.f32 (neg.f32 (*.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32)) ux)) (-.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)))
(/.f32 (neg.f32 (*.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)) ux)) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32)))
(/.f32 (*.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32)) ux) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)))
(/.f32 (*.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)) ux) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)))
(/.f32 (*.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))
(expm1.f32 (*.f32 (log.f32 (fabs.f32 ux)) #s(literal -1 binary32)))
(expm1.f32 (*.f32 (neg.f32 (log.f32 ux)) #s(literal 1 binary32)))
(expm1.f32 (*.f32 (log.f32 (exp.f32 (log.f32 ux))) #s(literal -1 binary32)))
(expm1.f32 (.f32 (.f32 #s(literal -1/2 binary32) (log.f32 ux)) #s(literal 2 binary32)))
(expm1.f32 (.f32 (.f32 #s(literal 2 binary32) (log.f32 ux)) #s(literal -1/2 binary32)))
(expm1.f32 (*.f32 (log.f32 (neg.f32 ux)) #s(literal -1 binary32)))
(expm1.f32 (neg.f32 (log.f32 ux)))
(*.f32 (/.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)) (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal -2 binary32)))) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)))
(*.f32 (/.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)) (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal -3 binary32)))) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)))
(*.f32 (/.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32)) (-.f32 (pow.f32 ux #s(literal -4 binary32)) (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal -2 binary32))))) (-.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)))
(*.f32 (/.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32)) (+.f32 (pow.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)) #s(literal 3 binary32)) (pow.f32 ux #s(literal -6 binary32)))) (+.f32 (-.f32 (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal -2 binary32))) (+.f32 (pow.f32 ux #s(literal -2 binary32)) (pow.f32 ux #s(literal -3 binary32)))) (pow.f32 ux #s(literal -4 binary32))))
(*.f32 (/.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)) (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32))) (expm1.f32 (neg.f32 (log.f32 ux))))
(*.f32 (+.f32 (pow.f32 ux #s(literal -1/2 binary32)) #s(literal 1 binary32)) (-.f32 (pow.f32 ux #s(literal -1/2 binary32)) #s(literal 1 binary32)))
(*.f32 (/.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux))) (expm1.f32 (neg.f32 (log.f32 ux))))
(*.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)) (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux))))
(/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 ux #s(literal -2 binary32)) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32))) #s(literal 2 binary32)) (pow.f32 (/.f32 #s(literal -1 binary32) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32))) #s(literal 2 binary32))) (+.f32 (/.f32 (pow.f32 ux #s(literal -2 binary32)) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32))) (/.f32 #s(literal -1 binary32) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32)))))
(/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 ux #s(literal -3 binary32)) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))) #s(literal 2 binary32)) (pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))) #s(literal 2 binary32))) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)))
(/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 ux #s(literal -2 binary32)) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32))) #s(literal 3 binary32)) (pow.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)) #s(literal -3 binary32))) (+.f32 (pow.f32 (/.f32 (pow.f32 ux #s(literal -2 binary32)) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32))) #s(literal 2 binary32)) (+.f32 (pow.f32 (/.f32 #s(literal -1 binary32) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32))) #s(literal 2 binary32)) (*.f32 (/.f32 (pow.f32 ux #s(literal -2 binary32)) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32))) (/.f32 #s(literal -1 binary32) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32)))))))
(/.f32 (-.f32 (pow.f32 (/.f32 (pow.f32 ux #s(literal -3 binary32)) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))) #s(literal 3 binary32)) (pow.f32 (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)) #s(literal -3 binary32))) (+.f32 (pow.f32 (/.f32 (pow.f32 ux #s(literal -3 binary32)) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))) #s(literal 2 binary32)) (+.f32 (pow.f32 (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))) #s(literal 2 binary32)) (*.f32 (/.f32 (pow.f32 ux #s(literal -3 binary32)) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)))))))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)))) (neg.f32 (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32))))
(/.f32 (neg.f32 (neg.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32)))) (neg.f32 (-.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))))
(/.f32 (-.f32 (+.f32 (pow.f32 ux #s(literal -2 binary32)) (pow.f32 ux #s(literal -3 binary32))) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux))) (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal -2 binary32))))
(/.f32 (-.f32 (.f32 (pow.f32 ux #s(literal -3 binary32)) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))) (.f32 (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)) #s(literal 1 binary32))) (pow.f32 (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)) #s(literal 2 binary32)))
(/.f32 (-.f32 (pow.f32 ux #s(literal -4 binary32)) #s(literal 1 binary32)) (pow.f32 (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)) #s(literal 3 binary32)))
(/.f32 (-.f32 (pow.f32 ux #s(literal -6 binary32)) #s(literal 1 binary32)) (*.f32 (+.f32 (+.f32 (pow.f32 ux #s(literal -4 binary32)) #s(literal 1 binary32)) (pow.f32 ux #s(literal -2 binary32))) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux))))
(/.f32 (-.f32 (pow.f32 ux #s(literal -6 binary32)) #s(literal 1 binary32)) (*.f32 (-.f32 #s(literal 1 binary32) (pow.f32 ux #s(literal -3 binary32))) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))))
(/.f32 (-.f32 (pow.f32 ux #s(literal -9 binary32)) #s(literal 1 binary32)) (*.f32 (+.f32 (+.f32 (pow.f32 ux #s(literal -6 binary32)) #s(literal 1 binary32)) (pow.f32 ux #s(literal -3 binary32))) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))))
(/.f32 (neg.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32))) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32)))
(/.f32 (neg.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32))) (-.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)))
(/.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux)))
(/.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32)) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32)))
(/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) #s(literal 1 binary32))
(-.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal 1 binary32))
(-.f32 (/.f32 (pow.f32 ux #s(literal -2 binary32)) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32))) (/.f32 #s(literal -1 binary32) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32))))
(-.f32 (/.f32 (pow.f32 ux #s(literal -3 binary32)) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))) (/.f32 #s(literal 1 binary32) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))))
(neg.f32 (/.f32 (neg.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32))) (-.f32 #s(literal 1 binary32) (/.f32 #s(literal -1 binary32) ux))))
(neg.f32 (/.f32 (neg.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32))) (+.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))))
(neg.f32 (/.f32 (-.f32 (pow.f32 ux #s(literal -2 binary32)) #s(literal 1 binary32)) (+.f32 (/.f32 #s(literal -1 binary32) ux) #s(literal -1 binary32))))
(neg.f32 (/.f32 (-.f32 (pow.f32 ux #s(literal -3 binary32)) #s(literal 1 binary32)) (-.f32 (/.f32 (expm1.f32 (neg.f32 (log.f32 ux))) ux) #s(literal 1 binary32))))

eval6.0ms (0.2%)

Memory: 14.6MiB live, 14.6MiB allocated; 0ms collecting garbage
Compiler: Compiled 2 101 to 386 computations (81.6% saved)

prune3.0ms (0.1%)

Memory

7.9MiB live, 7.9MiB allocated; 0ms collecting garbage

Pruning

6 alts after pruning (0 fresh and 6 done)

	Pruned	Kept	Total
New	75	0	75
Fresh	0	0	0
Picked	0	1	1
Done	0	5	5
Total	75	6	81

Accuracy

100.0%

Counts

81 → 6

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))
✓	99.8%	(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
✓	99.9%	(-.f32 #s(literal 1 binary32) (-.f32 ux (*.f32 maxCos ux)))
✓	97.9%	#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
✓	96.8%	#s(approx (+ (- 1 ux) (* ux maxCos)) #s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)))
✓	71.9%	#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))

Compiler

Compiled 138 to 76 computations (44.9% saved)

regimes11.0ms (0.3%)

Memory

19.8MiB live, 19.8MiB allocated; 0ms collecting garbage

Counts

8 → 1

Calls

Call 1

Inputs
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))
#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))
(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
(-.f32 #s(literal 1 binary32) (-.f32 ux (*.f32 maxCos ux)))
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(approx (- 1 ux) (*.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)))
(+.f32 #s(approx (- 1 ux) (.f32 (-.f32 (/.f32 #s(literal 1 binary32) ux) #s(literal 1 binary32)) ux)) (.f32 ux maxCos))

Outputs
(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))

Calls

4 calls:

3.0ms	(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
3.0ms	uy
3.0ms	ux
3.0ms	maxCos

Results

Accuracy	Segments	Branch
99.9%	1	`(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))`
99.9%	1	`ux`
99.9%	1	`uy`
99.9%	1	`maxCos`

Compiler

Compiled 10 to 16 computations (-60% saved)

regimes47.0ms (1.4%)

Memory

-40.2MiB live, 16.0MiB allocated; 9ms collecting garbage

Counts

3 → 1

Calls

Call 1

Inputs
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))
#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)

Outputs
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)

Calls

4 calls:

41.0ms	maxCos
2.0ms	uy
2.0ms	(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
2.0ms	ux

Results

Accuracy	Segments	Branch
99.8%	1	`(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))`
99.8%	1	`ux`
99.8%	1	`uy`
99.8%	1	`maxCos`

Compiler

Compiled 10 to 16 computations (-60% saved)

regimes6.0ms (0.2%)

Memory

9.9MiB live, 9.9MiB allocated; 0ms collecting garbage

Counts

2 → 1

Calls

Call 1

Inputs
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))
#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))

Outputs
#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))

Calls

4 calls:

1.0ms	maxCos
1.0ms	(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
1.0ms	uy
1.0ms	ux

Results

Accuracy	Segments	Branch
97.9%	1	`(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))`
97.9%	1	`ux`
97.9%	1	`uy`
97.9%	1	`maxCos`

Compiler

Compiled 10 to 16 computations (-60% saved)

regimes4.0ms (0.1%)

Memory

9.5MiB live, 9.5MiB allocated; 0ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))

Outputs
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))

Calls

4 calls:

1.0ms	maxCos
1.0ms	(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))
1.0ms	uy
1.0ms	ux

Results

Accuracy	Segments	Branch
71.9%	1	`ux`
71.9%	1	`uy`
71.9%	1	`(+.f32 (-.f32 #s(literal 1 binary32) ux) (*.f32 ux maxCos))`
71.9%	1	`maxCos`

Compiler

Compiled 10 to 16 computations (-60% saved)

simplify24.0ms (0.7%)

Memory

-28.4MiB live, 15.7MiB allocated; 4ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	32
1	24	32
2	43	32
3	62	32
4	88	32
5	110	32
6	156	32
7	280	32
8	518	32
9	729	32
10	753	32
11	778	32
12	802	32
13	811	32

Stop Event

1×

saturated

Calls

Call 1

Inputs
(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))

Outputs
(fma.f32 ux maxCos (-.f32 #s(literal 1 binary32) ux))
(-.f32 (fma.f32 maxCos ux #s(literal 1 binary32)) ux)
#s(approx (+ (- 1 ux) (* ux maxCos)) (-.f32 #s(literal 1 binary32) ux))
#s(approx (+ (- 1 ux) (* ux maxCos)) #s(literal 1 binary32))

derivations351.0ms (10.5%)

Memory

9.8MiB live, 239.4MiB allocated; 39ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	13
0	9	13
1	44	13
2	327	13
3	4373	13
0	8540	12
0	39	81
1	110	79
2	301	79
3	754	79
4	1937	79
5	4059	79
6	6828	79
0	8041	73

Stop Event

1×	done
1×	iter limit
1×	node limit
1×	iter limit
1×	node limit
1×	iter limit

Compiler

Compiled 32 to 14 computations (56.3% saved)

preprocess17.0ms (0.5%)

Memory: 28.9MiB live, 28.9MiB allocated; 0ms collecting garbage
Remove: (abs uy)
Compiler: Compiled 90 to 54 computations (40% saved)

end0.0ms (0%)

Memory: 0.0MiB live, 0.0MiB allocated; 0ms collecting garbage

Iter	Nodes	Cost
0	12	32
1	24	32
2	43	32
3	62	32
4	88	32
5	110	32
6	156	32
7	280	32
8	518	32
9	729	32
10	753	32
11	778	32
12	802	32
13	811	32

Iter	Nodes	Cost
0	12	32
1	24	32
2	43	32
3	62	32
4	88	32
5	110	32
6	156	32
7	280	32
8	518	32
9	729	32
10	753	32
11	778	32
12	802	32
13	811	32

start0.0ms (0%)

analyze135.0ms (4%)

sample1.3s (40%)

explain59.0ms (1.8%)

preprocess109.0ms (3.3%)

eval0.0ms (0%)

prune0.0ms (0%)

simplify26.0ms (0.8%)

localize15.0ms (0.4%)

series4.0ms (0.1%)

simplify86.0ms (2.6%)

rewrite192.0ms (5.8%)

eval47.0ms (1.4%)

prune4.0ms (0.1%)

simplify31.0ms (0.9%)

localize40.0ms (1.2%)

series4.0ms (0.1%)

simplify121.0ms (3.6%)

rewrite255.0ms (7.6%)

eval26.0ms (0.8%)

prune5.0ms (0.1%)

simplify25.0ms (0.7%)

localize25.0ms (0.8%)

series3.0ms (0.1%)

simplify92.0ms (2.8%)

rewrite227.0ms (6.8%)

eval6.0ms (0.2%)

prune3.0ms (0.1%)

regimes11.0ms (0.3%)

regimes47.0ms (1.4%)

regimes6.0ms (0.2%)

regimes4.0ms (0.1%)

simplify24.0ms (0.7%)

derivations351.0ms (10.5%)

preprocess17.0ms (0.5%)

end0.0ms (0%)

Profiling

Iter	Nodes	Cost
0	12	32
1	24	32
2	43	32
3	62	32
4	88	32
5	110	32
6	156	32
7	280	32
8	518	32
9	729	32
10	753	32
11	778	32
12	802	32
13	811	32