Metrics for Difference of squares

start0.0ms (0%)

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

analyze0.0ms (0%)

Memory

0.3MiB live, 0.3MiB allocated; 0ms collecting garbage

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	99.9%	0.1%	0%	0%	0%	0
100%	99.9%	0%	0.1%	0%	0%	0%	1

Compiler

Compiled 9 to 7 computations (22.2% saved)

sample819.0ms (33.4%)

Memory

26.3MiB live, 603.0MiB allocated; 150ms collecting garbage

Samples

409.0ms

8 256×

valid

Precisions

Click to see histograms. Total time spent on operations: 189.0ms

ival-mult: 144.0ms (76.4% of total)

ival-sub: 34.0ms (18% of total)

ival-true: 6.0ms (3.2% of total)

ival-assert: 3.0ms (1.6% of total)

adjust: 2.0ms (1.1% of total)

Bogosity

explain96.0ms (3.9%)

Memory

-35.7MiB live, 110.6MiB allocated; 18ms collecting garbage

FPErrors

Click to see full error table

Ground Truth	Example	Example	Subexpression
19	-	-	`(-.f64 (.f64 a a) (.f64 b b))`
0	-	-	`(*.f64 a a)`
0	-	-	`a`
0	-	-	`b`
0	-	-	`(*.f64 b b)`

Explanations

Click to see full explanations table

Operator	Subexpression	Explanation	Count
`-.f64`	`(-.f64 (.f64 a a) (.f64 b b))`	nan-rescue	19	0
↳	`(*.f64 a a)`	overflow	60
↳	`(*.f64 b b)`	overflow	66

Confusion

	Predicted +	Predicted -
+	19	0
-	0	237

Precision

1.0

Recall

1.0

Confusion?

	Predicted +	Predicted Maybe	Predicted -
+	19	0	0
-	0	0	237

Precision?

1.0

Recall?

1.0

Freqs

test

number	freq
0	237
1	19

Total Confusion?

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

Precision?

1.0

Recall?

1.0

Samples

22.0ms

512×

valid

Compiler

Compiled 41 to 19 computations (53.7% saved)

Precisions

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

ival-mult: 7.0ms (70% of total)

ival-sub: 2.0ms (20% of total)

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

adjust: 0.0ms (0% of total)

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

preprocess123.0ms (5%)

Memory

-1.8MiB live, 94.7MiB allocated; 14ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	38
1	48	35
2	215	35
3	371	35
4	909	35
5	1923	35
6	2926	35
7	3269	35
8	3347	35
9	3347	35
10	3546	35
0	5	7
0	8	7
1	21	7
2	81	7
3	223	7
4	403	7
5	836	7
6	1385	7
7	2069	7
8	2898	7
9	3208	7
10	3270	7
11	3270	7
12	3348	7
0	3348	7

Stop Event

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

Calls

Call 1

Inputs
(-.f64 (.f64 a a) (.f64 b b))

Outputs
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 (-.f64 a b) (+.f64 b a))

Symmetry

(abs b)

(abs a)

Compiler

Compiled 7 to 5 computations (28.6% saved)

eval5.0ms (0.2%)

Memory: 4.4MiB live, 4.4MiB allocated; 0ms collecting garbage
Compiler: Compiled 0 to 2 computations (-∞% saved)

prune0.0ms (0%)

Memory

0.8MiB live, 0.8MiB allocated; 0ms collecting garbage

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	92.6%	(-.f64 (.f64 a a) (.f64 b b))

Compiler

Compiled 7 to 5 computations (28.6% saved)

simplify0.0ms (0%)

Memory: 0.1MiB live, 0.0MiB allocated; 0ms collecting garbage

series4.0ms (0.2%)

Memory

6.9MiB live, 6.9MiB allocated; 0ms collecting garbage

Counts

5 → 9

Calls

Call 1

Inputs
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 a a)
a
(*.f64 b b)
b

Outputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
a
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(+ (* -1 (pow b 2)) (pow a 2))
(pow b 2)
b
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a	@	inf	((- (* a a) (* b b)) (* a a) a (* b b) b)
1.0ms	a	@	-inf	((- (* a a) (* b b)) (* a a) a (* b b) b)
1.0ms	b	@	inf	((- (* a a) (* b b)) (* a a) a (* b b) b)
1.0ms	b	@	-inf	((- (* a a) (* b b)) (* a a) a (* b b) b)
1.0ms	a	@	0	((- (* a a) (* b b)) (* a a) a (* b b) b)

simplify108.0ms (4.4%)

Memory

20.5MiB live, 110.1MiB allocated; 8ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	46
1	40	46
2	136	46
3	829	46
4	3437	46
0	8613	45

Stop Event

1×	iter limit
1×	node limit

Counts

9 → 7

Calls

Call 1

Inputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
a
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(+ (* -1 (pow b 2)) (pow a 2))
(pow b 2)
b
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))

Outputs
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(- (pow a 2) (pow b 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(pow a 2)
(*.f64 a a)
a
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(+ (* -1 (pow b 2)) (pow a 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(pow b 2)
(*.f64 b b)
b
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(.f64 (fma.f64 (/.f64 (/.f64 a b) b) a #s(literal -1 binary64)) (.f64 b b))

rewrite94.0ms (3.8%)

Memory

6.8MiB live, 109.2MiB allocated; 12ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	37	15
2	329	15
3	4470	15
0	8291	14

Stop Event

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

Counts

5 → 115

Calls

Call 1

Inputs
(-.f64 (.f64 a a) (.f64 b b))
(*.f64 a a)
a
(*.f64 b b)
b

Outputs
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (fma.f64 b b (.f64 a a)))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (.f64 b a) #s(literal 4 binary64))))) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (+.f64 (pow.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 a #s(literal 12 binary64)))) (fma.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (pow.f64 a #s(literal 8 binary64))))
(*.f64 (-.f64 a b) (+.f64 b a))
(*.f64 (+.f64 b a) (-.f64 a b))
(.f64 (fma.f64 b b (.f64 a a)) (/.f64 (fma.f64 b b (.f64 a a)) (fma.f64 b b (.f64 a a))))
(.f64 (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (/.f64 (fma.f64 b b (.f64 a a)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (-.f64 a b)) (+.f64 b a))
(/.f64 (/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (+.f64 b a)) (-.f64 a b))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (+.f64 b a)) (fma.f64 b (+.f64 b a) (.f64 a a)))
(/.f64 (.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (-.f64 a b)) (fma.f64 b (+.f64 b a) (.f64 a a)))
(/.f64 (.f64 (-.f64 a b) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (fma.f64 b (+.f64 b a) (.f64 a a)))
(/.f64 (.f64 (-.f64 a b) (fma.f64 b b (.f64 a a))) (-.f64 a b))
(/.f64 (.f64 (+.f64 b a) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (fma.f64 b (+.f64 b a) (.f64 a a)))
(/.f64 (.f64 (+.f64 b a) (fma.f64 b b (.f64 a a))) (+.f64 b a))
(/.f64 (.f64 (fma.f64 b b (.f64 a a)) (-.f64 a b)) (-.f64 a b))
(/.f64 (.f64 (fma.f64 b b (.f64 a a)) (+.f64 b a)) (+.f64 b a))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 2 binary64))) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64))) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (pow.f64 b #s(literal 4 binary64)) (pow.f64 a #s(literal 4 binary64))) (fma.f64 b b (*.f64 a a)))
(/.f64 (-.f64 (/.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 (fma.f64 b b (.f64 a a)) #s(literal 3 binary64))) (/.f64 (pow.f64 b #s(literal 12 binary64)) (pow.f64 (fma.f64 b b (.f64 a a)) #s(literal 3 binary64)))) (+.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 3 binary64))) (+.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (+.f64 (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 2 binary64)) (.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))))))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (.f64 (fma.f64 b (+.f64 b a) (.f64 a a)) (fma.f64 b (+.f64 b a) (.f64 a a))))
(/.f64 (.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (fma.f64 b b (.f64 a a))) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 b b (.f64 a a)) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (.f64 (+.f64 b a) (fma.f64 b (+.f64 b a) (.f64 a a))))
(/.f64 (.f64 (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (fma.f64 b b (.f64 a a))) (+.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))
(/.f64 (.f64 (fma.f64 b b (.f64 a a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (.f64 (-.f64 a b) (fma.f64 b (+.f64 b a) (.f64 a a))))
(/.f64 (-.f64 (.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (.f64 (fma.f64 b b (.f64 a a)) (pow.f64 b #s(literal 4 binary64)))) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))))
(/.f64 (-.f64 (.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (.f64 (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (pow.f64 b #s(literal 6 binary64)))) (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (*.f64 b a) #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (pow.f64 b #s(literal 8 binary64))) (pow.f64 (fma.f64 b b (*.f64 a a)) #s(literal 3 binary64)))
(/.f64 (-.f64 (pow.f64 a #s(literal 18 binary64)) (pow.f64 b #s(literal 18 binary64))) (.f64 (+.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (pow.f64 (.f64 b a) #s(literal 6 binary64))) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (.f64 (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (.f64 b a) #s(literal 4 binary64)))) (fma.f64 b b (*.f64 a a))))
(/.f64 (-.f64 (pow.f64 a #s(literal 12 binary64)) (pow.f64 b #s(literal 12 binary64))) (.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 (*.f64 b a) #s(literal 2 binary64)))))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (.f64 (fma.f64 b (+.f64 b a) (.f64 a a)) (fma.f64 b (+.f64 b a) (*.f64 a a))))
(/.f64 (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64))) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))))
(/.f64 (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64))) (fma.f64 b b (*.f64 a a)))
(neg.f64 (fma.f64 b b (*.f64 a a)))
(fma.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 a #s(literal 8 binary64)) (-.f64 (pow.f64 b #s(literal 8 binary64)) (pow.f64 (.f64 b a) #s(literal 4 binary64))))) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(fma.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (+.f64 (pow.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) #s(literal 3 binary64)) (pow.f64 a #s(literal 12 binary64)))) (fma.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (pow.f64 a #s(literal 8 binary64))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(fma.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 6 binary64)) (pow.f64 b #s(literal 6 binary64)))) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(fma.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (pow.f64 b #s(literal 4 binary64)))) (fma.f64 b b (.f64 a a)) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(fma.f64 (pow.f64 a #s(literal 3 binary64)) (/.f64 (pow.f64 a #s(literal 3 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(fma.f64 (pow.f64 a #s(literal 3 binary64)) (/.f64 a (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(fma.f64 (-.f64 a b) b (*.f64 (-.f64 a b) a))
(fma.f64 (-.f64 a b) a (*.f64 (-.f64 a b) b))
(fma.f64 (pow.f64 a #s(literal 4 binary64)) (/.f64 (.f64 a a) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(fma.f64 b (-.f64 a b) (*.f64 a (-.f64 a b)))
(fma.f64 b b (*.f64 a a))
(fma.f64 (.f64 a a) (/.f64 (pow.f64 a #s(literal 4 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (*.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(fma.f64 (.f64 a a) (/.f64 (.f64 a a) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(fma.f64 a (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(fma.f64 a (-.f64 a b) (*.f64 b (-.f64 a b)))
(fma.f64 a a (*.f64 b b))
(-.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(-.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(-.f64 (.f64 b b) (.f64 a a))
(-.f64 (.f64 a a) (.f64 b b))
(+.f64 (.f64 b (-.f64 a b)) (.f64 a (-.f64 a b)))
(+.f64 (.f64 a (-.f64 a b)) (.f64 b (-.f64 a b)))
(+.f64 (.f64 (-.f64 a b) b) (.f64 (-.f64 a b) a))
(+.f64 (.f64 (-.f64 a b) a) (.f64 (-.f64 a b) b))
(+.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))
(+.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (-.f64 (pow.f64 (.f64 b (+.f64 b a)) #s(literal 2 binary64)) (pow.f64 a #s(literal 4 binary64)))))
(+.f64 (.f64 b b) (.f64 a a))
(+.f64 (.f64 a a) (.f64 b b))
(*.f64 a a)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 a))
(pow.f64 (pow.f64 a #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 a #s(literal 2 binary64))
(neg.f64 (*.f64 a a))
(sqrt.f64 (pow.f64 a #s(literal 4 binary64)))
(fabs.f64 (*.f64 a a))
(exp.f64 (/.f64 (*.f64 (log.f64 a) #s(literal 4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 a) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 a) #s(literal 2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 a) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 a) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 a) (sqrt.f64 a))
(pow.f64 (sqrt.f64 a) #s(literal 2 binary64))
(pow.f64 (*.f64 a a) #s(literal 1/2 binary64))
(pow.f64 a #s(literal 1 binary64))
(neg.f64 a)
(sqrt.f64 (*.f64 a a))
(fabs.f64 a)
(exp.f64 (.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 a))
(+.f64 (cosh.f64 (log.f64 a)) (sinh.f64 (log.f64 a)))
a
(*.f64 b b)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 b))
(pow.f64 (pow.f64 b #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1 binary64))
(pow.f64 b #s(literal 2 binary64))
(neg.f64 (*.f64 b b))
(sqrt.f64 (pow.f64 b #s(literal 4 binary64)))
(fabs.f64 (*.f64 b b))
(exp.f64 (/.f64 (*.f64 #s(literal 4 binary64) (log.f64 b)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 b) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 b) #s(literal 2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 b) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 b) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 b) (sqrt.f64 b))
(pow.f64 (sqrt.f64 b) #s(literal 2 binary64))
(pow.f64 (*.f64 b b) #s(literal 1/2 binary64))
(pow.f64 b #s(literal 1 binary64))
(neg.f64 b)
(sqrt.f64 (*.f64 b b))
(fabs.f64 b)
(exp.f64 (.f64 (.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 b))
(+.f64 (cosh.f64 (log.f64 b)) (sinh.f64 (log.f64 b)))
b

eval17.0ms (0.7%)

Memory: -4.1MiB live, 40.4MiB allocated; 6ms collecting garbage
Compiler: Compiled 2 360 to 383 computations (83.8% saved)

prune2.0ms (0.1%)

Memory

9.8MiB live, 9.8MiB allocated; 0ms collecting garbage

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	143	2	145

Accuracy

100.0%

Counts

145 → 2

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(*.f64 (-.f64 a b) (+.f64 b a))
▶	54.1%	#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))

Compiler

Compiled 19 to 13 computations (31.6% saved)

simplify0.0ms (0%)

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

series7.0ms (0.3%)

Memory

-31.2MiB live, 14.5MiB allocated; 3ms collecting garbage

Counts

8 → 31

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (neg.f64 b) b)
(neg.f64 b)
b
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
a
(+.f64 b a)

Outputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(* -1 b)
(- a b)
a
b
(+ a b)
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (/ b a)))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ a (* -1 b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* b (- (/ a b) 1))
(* b (+ 1 (/ a b)))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (- (* -1 (/ a b)) 1)))

Calls

6 calls:

Time	Variable		Point	Expression
2.0ms	a	@	-inf	((- (* a a) (* b b)) (* (neg b) b) (neg b) b (* (- a b) (+ b a)) (- a b) a (+ b a))
1.0ms	b	@	-inf	((- (* a a) (* b b)) (* (neg b) b) (neg b) b (* (- a b) (+ b a)) (- a b) a (+ b a))
1.0ms	b	@	inf	((- (* a a) (* b b)) (* (neg b) b) (neg b) b (* (- a b) (+ b a)) (- a b) a (+ b a))
1.0ms	a	@	0	((- (* a a) (* b b)) (* (neg b) b) (neg b) b (* (- a b) (+ b a)) (- a b) a (+ b a))
1.0ms	a	@	inf	((- (* a a) (* b b)) (* (neg b) b) (neg b) b (* (- a b) (+ b a)) (- a b) a (+ b a))

simplify138.0ms (5.6%)

Memory

2.6MiB live, 197.5MiB allocated; 27ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	211
1	299	206
2	1084	205
3	4475	205
0	8193	200

Stop Event

1×	iter limit
1×	node limit

Counts

31 → 29

Calls

Call 1

Inputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(* -1 b)
(- a b)
a
b
(+ a b)
(pow a 2)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(* a (+ 1 (* -1 (/ b a))))
(* a (+ 1 (/ b a)))
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(* -1 (* a (- (/ b a) 1)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(+ (* -1 (pow b 2)) (pow a 2))
(+ (* b (+ a (* -1 a))) (pow a 2))
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(+ a (* -1 b))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(* b (- (/ a b) 1))
(* b (+ 1 (/ a b)))
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(* -1 (* b (- (* -1 (/ a b)) 1)))

Outputs
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(- (pow a 2) (pow b 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(+ (* -1 (pow b 2)) (* a (+ b (* -1 b))))
(*.f64 (neg.f64 b) b)
(+ (* -1 (pow b 2)) (* a (+ a (+ b (* -1 b)))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* -1 b)
(neg.f64 b)
(- a b)
(-.f64 a b)
a
b
(+ a b)
(+.f64 b a)
(pow a 2)
(*.f64 a a)
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(.f64 (fma.f64 (neg.f64 a) (.f64 (/.f64 (/.f64 b a) a) b) a) a)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (/ b a))))
(*.f64 a a)
(* (pow a 2) (+ 1 (+ (* -1 (/ b a)) (+ (* -1 (/ (pow b 2) (pow a 2))) (/ b a)))))
(.f64 (fma.f64 (neg.f64 a) (.f64 (/.f64 (/.f64 b a) a) b) a) a)
(* a (+ 1 (* -1 (/ b a))))
(*.f64 (-.f64 #s(literal 1 binary64) (/.f64 b a)) a)
(* a (+ 1 (/ b a)))
(fma.f64 (/.f64 b a) a a)
(* (pow a 2) (+ 1 (* -1 (/ (+ (* -1 (+ b (* -1 b))) (/ (pow b 2) a)) a))))
(.f64 (fma.f64 (neg.f64 a) (.f64 (/.f64 (/.f64 b a) a) b) a) a)
(* -1 (* a (- (/ b a) 1)))
(*.f64 (neg.f64 a) (-.f64 (/.f64 b a) #s(literal 1 binary64)))
(* -1 (* a (- (* -1 (/ b a)) 1)))
(*.f64 (neg.f64 a) (-.f64 (/.f64 (neg.f64 b) a) #s(literal 1 binary64)))
(+ (* -1 (pow b 2)) (pow a 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(+ (* b (+ a (* -1 a))) (pow a 2))
(*.f64 a a)
(+ (* b (+ a (+ (* -1 a) (* -1 b)))) (pow a 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(+ a (* -1 b))
(-.f64 a b)
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(.f64 (fma.f64 (/.f64 (/.f64 a b) b) a #s(literal -1 binary64)) (.f64 b b))
(* (pow b 2) (- (+ (* -1 (/ a b)) (/ a b)) 1))
(*.f64 (neg.f64 b) b)
(* (pow b 2) (- (+ (* -1 (/ a b)) (+ (/ a b) (/ (pow a 2) (pow b 2)))) 1))
(.f64 (fma.f64 (/.f64 (/.f64 a b) b) a #s(literal -1 binary64)) (.f64 b b))
(* b (- (/ a b) 1))
(*.f64 (-.f64 (/.f64 a b) #s(literal 1 binary64)) b)
(* b (+ 1 (/ a b)))
(fma.f64 (/.f64 a b) b b)
(* (pow b 2) (- (* -1 (/ (+ a (* -1 a)) b)) 1))
(*.f64 (neg.f64 b) b)
(* (pow b 2) (- (* -1 (/ (+ a (+ (* -1 a) (* -1 (/ (pow a 2) b)))) b)) 1))
(.f64 (fma.f64 (/.f64 (/.f64 a b) b) a #s(literal -1 binary64)) (.f64 b b))
(* -1 (* b (+ 1 (* -1 (/ a b)))))
(fma.f64 (/.f64 a b) b (neg.f64 b))
(* -1 (* b (- (* -1 (/ a b)) 1)))
(*.f64 (-.f64 (/.f64 (neg.f64 a) b) #s(literal 1 binary64)) (neg.f64 b))

rewrite131.0ms (5.4%)

Memory

24.2MiB live, 211.7MiB allocated; 21ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	33
0	16	33
1	68	33
2	610	33
0	9914	33

Stop Event

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

Counts

8 → 528

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (neg.f64 b) b)
(neg.f64 b)
b
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 a b)
a
(+.f64 b a)

Outputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (neg.f64 (neg.f64 (neg.f64 b))) (neg.f64 (neg.f64 b)))
(*.f64 (neg.f64 (neg.f64 b)) (neg.f64 (neg.f64 (neg.f64 b))))
(*.f64 (neg.f64 (neg.f64 b)) (neg.f64 b))
(*.f64 (neg.f64 b) (neg.f64 (neg.f64 b)))
(*.f64 (neg.f64 b) b)
(*.f64 b (neg.f64 b))
(neg.f64 (*.f64 b b))
(neg.f64 b)
(*.f64 (pow.f64 b #s(literal 1/2 binary64)) (pow.f64 b #s(literal 1/2 binary64)))
(*.f64 (sqrt.f64 (neg.f64 (neg.f64 b))) (sqrt.f64 (neg.f64 (neg.f64 b))))
(*.f64 (sqrt.f64 (neg.f64 b)) (sqrt.f64 (neg.f64 b)))
(*.f64 (sqrt.f64 b) (sqrt.f64 b))
(pow.f64 (neg.f64 b) #s(literal 1 binary64))
(pow.f64 (*.f64 b b) #s(literal 1/2 binary64))
(pow.f64 b #s(literal 1 binary64))
(sqrt.f64 (*.f64 b b))
(fabs.f64 (neg.f64 (neg.f64 b)))
(fabs.f64 (neg.f64 b))
(fabs.f64 b)
(exp.f64 (/.f64 (*.f64 (log.f64 b) #s(literal 2 binary64)) #s(literal 2 binary64)))
(exp.f64 (*.f64 (log.f64 b) #s(literal 1 binary64)))
b
(*.f64 (neg.f64 (+.f64 b (neg.f64 a))) (-.f64 b (neg.f64 a)))
(*.f64 (+.f64 (neg.f64 (neg.f64 b)) (neg.f64 (neg.f64 a))) (-.f64 (neg.f64 (neg.f64 b)) (neg.f64 (neg.f64 a))))
(*.f64 (+.f64 (neg.f64 (neg.f64 b)) (neg.f64 a)) (-.f64 (neg.f64 (neg.f64 b)) (neg.f64 a)))
(*.f64 (+.f64 (neg.f64 (neg.f64 b)) a) (-.f64 (neg.f64 (neg.f64 b)) a))
(*.f64 (+.f64 (neg.f64 b) (neg.f64 (neg.f64 a))) (-.f64 (neg.f64 b) (neg.f64 (neg.f64 a))))
(*.f64 (+.f64 b (neg.f64 (neg.f64 a))) (-.f64 b (neg.f64 (neg.f64 a))))
(*.f64 (+.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 b))) (-.f64 (neg.f64 (neg.f64 a)) (neg.f64 (neg.f64 b))))
(*.f64 (+.f64 (neg.f64 (neg.f64 a)) (neg.f64 b)) (-.f64 (neg.f64 (neg.f64 a)) (neg.f64 b)))
(*.f64 (+.f64 (neg.f64 (neg.f64 a)) b) (-.f64 (neg.f64 (neg.f64 a)) b))
(*.f64 (+.f64 (neg.f64 a) (neg.f64 (neg.f64 b))) (-.f64 (neg.f64 a) (neg.f64 (neg.f64 b))))
(*.f64 (+.f64 a (neg.f64 (neg.f64 b))) (-.f64 a (neg.f64 (neg.f64 b))))
(*.f64 (-.f64 b (neg.f64 a)) (+.f64 b (neg.f64 a)))
(*.f64 (+.f64 b (neg.f64 a)) (neg.f64 (-.f64 b (neg.f64 a))))
(*.f64 (+.f64 b (neg.f64 a)) (-.f64 b (neg.f64 a)))
(*.f64 (-.f64 b a) (-.f64 b a))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a)))) (.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))))) (*.f64 (-.f64 b a) (-.f64 b a)))
(/.f64 (-.f64 (.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64))))) (.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64)))))) (*.f64 (-.f64 b a) (-.f64 b a)))
(/.f64 (-.f64 (pow.f64 (.f64 (-.f64 b a) a) #s(literal 2 binary64)) (pow.f64 (.f64 (-.f64 b a) b) #s(literal 2 binary64))) (*.f64 (-.f64 b a) (-.f64 b a)))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (fma.f64 (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (fma.f64 b b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (fma.f64 b b (*.f64 a a)))))))
(/.f64 (-.f64 (pow.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 3 binary64)) (pow.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) #s(literal 3 binary64))) (fma.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) (fma.f64 (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) (.f64 (/.f64 (pow.f64 a #s(literal 6 binary64)) (fma.f64 (.f64 b b) (fma.f64 b b (.f64 a a)) (pow.f64 a #s(literal 4 binary64)))) (/.f64 (pow.f64 b #s(literal 6 binary64)) (fma.f64 (.f64 b b) (fma.f64 b b (*.f64 a a)) (pow.f64 a #s(literal 4 binary64))))))))
(/.f64 (-.f64 (pow.f64 (.f64 (-.f64 b a) b) #s(literal 3 binary64)) (pow.f64 (.f64 (-.f64 b a) a) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 b a) b) #s(literal 2 binary64)) (+.f64 (pow.f64 (.f64 (-.f64 b a) a) #s(literal 2 binary64)) (.f64 (.f64 (-.f64 b a) b) (*.f64 (-.f64 b a) a)))))
(/.f64 (+.f64 (pow.f64 b #s(literal 6 binary64)) (pow.f64 (.f64 (neg.f64 a) a) #s(literal 3 binary64))) (+.f64 (pow.f64 b #s(literal 4 binary64)) (-.f64 (pow.f64 a #s(literal 4 binary64)) (.f64 (.f64 b b) (.f64 (neg.f64 a) a)))))
(/.f64 (+.f64 (pow.f64 (.f64 (-.f64 b a) a) #s(literal 3 binary64)) (pow.f64 (.f64 (-.f64 b a) b) #s(literal 3 binary64))) (+.f64 (pow.f64 (.f64 (-.f64 b a) a) #s(literal 2 binary64)) (-.f64 (pow.f64 (.f64 (-.f64 b a) b) #s(literal 2 binary64)) (.f64 (.f64 (-.f64 b a) a) (*.f64 (-.f64 b a) b)))))
(/.f64 (fma.f64 a (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) (.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) b)) (fma.f64 (-.f64 b a) b (.f64 a a)))
(/.f64 (fma.f64 a (.f64 (-.f64 b a) (-.f64 b a)) (.f64 (*.f64 (-.f64 b a) (-.f64 b a)) b)) (-.f64 b a))
(/.f64 (fma.f64 (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))) a (.f64 b (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))) (fma.f64 (-.f64 b a) b (.f64 a a)))
(/.f64 (fma.f64 (.f64 (-.f64 b a) (-.f64 b a)) a (.f64 b (*.f64 (-.f64 b a) (-.f64 b a)))) (-.f64 b a))
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(-.f64 a b)
(+.f64 (.f64 (.f64 (-.f64 b a) a) (/.f64 (.f64 (-.f64 b a) (-.f64 b a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))) (.f64 (.f64 b b) (/.f64 (.f64 (-.f64 b a) (-.f64 b a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))))
(+.f64 (.f64 (.f64 b b) (/.f64 (.f64 (-.f64 b a) (-.f64 b a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))) (.f64 (.f64 (-.f64 b a) a) (/.f64 (.f64 (-.f64 b a) (-.f64 b a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64))))))
(+.f64 (.f64 (/.f64 (.f64 (-.f64 b a) (-.f64 b a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (.f64 (-.f64 b a) a)) (.f64 (/.f64 (.f64 (-.f64 b a) (-.f64 b a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (.f64 b b)))
(+.f64 (.f64 (/.f64 (.f64 (-.f64 b a) (-.f64 b a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (.f64 b b)) (.f64 (/.f64 (.f64 (-.f64 b a) (-.f64 b a)) (-.f64 (pow.f64 a #s(literal 3 binary64)) (pow.f64 b #s(literal 3 binary64)))) (.f64 (-.f64 b a) a)))
(+.f64 (neg.f64 (/.f64 (.f64 (-.f64 b a) b) (-.f64 b a))) (neg.f64 (/.f64 (.f64 (-.f64 b a) a) (-.f64 b a))))
(+.f64 (neg.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 (-.f64 b a) b (.f64 a a)))) (neg.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (-.f64 b a) b (.f64 a a)))))
(+.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 a a (fma.f64 b b (.f64 (neg.f64 a) b)))) (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 a a (fma.f64 b b (.f64 (neg.f64 a) b)))))
(+.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 a a (fma.f64 b b (.f64 (neg.f64 a) b)))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 a a (fma.f64 b b (.f64 (neg.f64 a) b)))))
(+.f64 (/.f64 (pow.f64 a #s(literal 4 binary64)) (.f64 (fma.f64 b b (.f64 a a)) (-.f64 b a))) (/.f64 (pow.f64 b #s(literal 4 binary64)) (.f64 (fma.f64 b b (.f64 a a)) (-.f64 b a))))
(+.f64 (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (-.f64 b a) b (.f64 a a))) (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 (-.f64 b a) b (.f64 a a))))
(+.f64 (/.f64 (pow.f64 b #s(literal 3 binary64)) (fma.f64 (-.f64 b a) b (.f64 a a))) (/.f64 (pow.f64 a #s(literal 3 binary64)) (fma.f64 (-.f64 b a) b (.f64 a a))))
(+.f64 (/.f64 (.f64 (-.f64 b a) a) (-.f64 b a)) (/.f64 (.f64 (-.f64 b a) b) (-.f64 b a)))
(+.f64 (/.f64 (.f64 (-.f64 b a) b) (-.f64 b a)) (/.f64 (.f64 (-.f64 b a) a) (-.f64 b a)))
(+.f64 (/.f64 (.f64 b b) (-.f64 b a)) (/.f64 (.f64 a a) (-.f64 b a)))
(+.f64 (/.f64 (.f64 a a) (-.f64 b a)) (/.f64 (.f64 b b) (-.f64 b a)))
(+.f64 (neg.f64 a) (neg.f64 b))
(+.f64 (neg.f64 a) b)
(+.f64 (neg.f64 b) (neg.f64 a))
(+.f64 (neg.f64 b) a)
(+.f64 b a)
(+.f64 a (neg.f64 b))
(+.f64 a b)

eval146.0ms (6%)

Memory: 8.0MiB live, 219.7MiB allocated; 61ms collecting garbage
Compiler: Compiled 12 477 to 1 266 computations (89.9% saved)

prune35.0ms (1.4%)

Memory

-11.2MiB live, 52.6MiB allocated; 32ms collecting garbage

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	494	1	495
Fresh	0	0	0
Picked	0	2	2
Done	0	0	0
Total	494	3	497

Accuracy

100.0%

Counts

497 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (-.f64 a b) (+.f64 b a))
✓	54.1%	#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
▶	52.9%	#s(approx (- (* a a) (* b b)) (*.f64 a a))

Compiler

Compiled 30 to 20 computations (33.3% saved)

simplify0.0ms (0%)

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

series2.0ms (0.1%)

Memory

8.8MiB live, 8.8MiB allocated; 0ms collecting garbage

Counts

3 → 7

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
a

Outputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
a
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(+ (* -1 (pow b 2)) (pow a 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))

Calls

6 calls:

Time	Variable		Point	Expression
1.0ms	a	@	-inf	((- (* a a) (* b b)) (* a a) a)
1.0ms	a	@	inf	((- (* a a) (* b b)) (* a a) a)
0.0ms	a	@	0	((- (* a a) (* b b)) (* a a) a)
0.0ms	b	@	inf	((- (* a a) (* b b)) (* a a) a)
0.0ms	b	@	-inf	((- (* a a) (* b b)) (* a a) a)

simplify160.0ms (6.5%)

Memory

-19.1MiB live, 194.5MiB allocated; 106ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	42
1	40	42
2	136	42
3	829	42
4	3437	42
0	8613	41

Stop Event

1×	iter limit
1×	node limit

Counts

7 → 6

Calls

Call 1

Inputs
(* -1 (pow b 2))
(- (pow a 2) (pow b 2))
(pow a 2)
a
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(+ (* -1 (pow b 2)) (pow a 2))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))

Outputs
(* -1 (pow b 2))
(*.f64 (neg.f64 b) b)
(- (pow a 2) (pow b 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(pow a 2)
(*.f64 a a)
a
(* (pow a 2) (+ 1 (* -1 (/ (pow b 2) (pow a 2)))))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(+ (* -1 (pow b 2)) (pow a 2))
(fma.f64 (neg.f64 b) b (*.f64 a a))
(* (pow b 2) (- (/ (pow a 2) (pow b 2)) 1))
(.f64 (fma.f64 (/.f64 (/.f64 a b) b) a #s(literal -1 binary64)) (.f64 b b))

rewrite72.0ms (2.9%)

Memory

-0.5MiB live, 96.5MiB allocated; 13ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	15
0	8	15
1	37	15
2	329	15
3	4477	15
0	8306	14

Stop Event

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

Counts

3 → 25

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
a

Outputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
(*.f64 a a)
(pow.f64 (exp.f64 #s(literal 2 binary64)) (log.f64 a))
(pow.f64 (pow.f64 a #s(literal 4 binary64)) #s(literal 1/2 binary64))
(pow.f64 (*.f64 a a) #s(literal 1 binary64))
(pow.f64 a #s(literal 2 binary64))
(neg.f64 (*.f64 a a))
(sqrt.f64 (pow.f64 a #s(literal 4 binary64)))
(fabs.f64 (*.f64 a a))
(exp.f64 (/.f64 (*.f64 (log.f64 a) #s(literal 4 binary64)) #s(literal 2 binary64)))
(exp.f64 (.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 1 binary64)))
(exp.f64 (*.f64 (log.f64 a) #s(literal 2 binary64)))
(+.f64 (cosh.f64 (.f64 (log.f64 a) #s(literal 2 binary64))) (sinh.f64 (.f64 (log.f64 a) #s(literal 2 binary64))))
(*.f64 (pow.f64 (sqrt.f64 a) #s(literal 1 binary64)) (pow.f64 (sqrt.f64 a) #s(literal 1 binary64)))
(*.f64 (sqrt.f64 a) (sqrt.f64 a))
(pow.f64 (sqrt.f64 a) #s(literal 2 binary64))
(pow.f64 (*.f64 a a) #s(literal 1/2 binary64))
(pow.f64 a #s(literal 1 binary64))
(neg.f64 a)
(sqrt.f64 (*.f64 a a))
(fabs.f64 a)
(exp.f64 (.f64 (.f64 (log.f64 a) #s(literal 2 binary64)) #s(literal 1/2 binary64)))
(exp.f64 (log.f64 a))
(+.f64 (cosh.f64 (log.f64 a)) (sinh.f64 (log.f64 a)))
a

eval4.0ms (0.2%)

Memory: 12.5MiB live, 12.5MiB allocated; 0ms collecting garbage
Compiler: Compiled 576 to 116 computations (79.9% saved)

prune21.0ms (0.8%)

Memory

-37.7MiB live, 8.3MiB allocated; 3ms collecting garbage

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	41	0	41
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	41	3	44

Accuracy

100.0%

Counts

44 → 3

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	100.0%	(*.f64 (-.f64 a b) (+.f64 b a))
✓	54.1%	#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
✓	52.9%	#s(approx (- (* a a) (* b b)) (*.f64 a a))

Compiler

Compiled 67 to 35 computations (47.8% saved)

regimes9.0ms (0.4%)

Memory

22.7MiB live, 22.7MiB allocated; 0ms collecting garbage

Counts

4 → 1

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
(*.f64 (-.f64 a b) (+.f64 b a))
(-.f64 (.f64 a a) (.f64 b b))

Outputs
(*.f64 (-.f64 a b) (+.f64 b a))

Calls

5 calls:

2.0ms	b
2.0ms	(*.f64 b b)
2.0ms	a
2.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
100.0%	1	`(*.f64 b b)`
100.0%	1	`(*.f64 a a)`
100.0%	1	`(-.f64 (.f64 a a) (.f64 b b))`
100.0%	1	`a`
100.0%	1	`b`

Compiler

Compiled 15 to 15 computations (0% saved)

regimes6.0ms (0.3%)

Memory

17.3MiB live, 17.3MiB allocated; 0ms collecting garbage

Counts

2 → 2

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))

Outputs
#s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b))
#s(approx (- (* a a) (* b b)) (*.f64 a a))

Calls

5 calls:

1.0ms	b
1.0ms	a
1.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(*.f64 b b)
1.0ms	(*.f64 a a)

Results

Accuracy	Segments	Branch
79.6%	2	`(*.f64 b b)`
80.5%	2	`(*.f64 a a)`
95.8%	2	`(-.f64 (.f64 a a) (.f64 b b))`
80.5%	2	`a`
79.6%	2	`b`

Compiler

Compiled 15 to 15 computations (0% saved)

regimes30.0ms (1.2%)

Memory

-23.5MiB live, 30.4MiB allocated; 4ms collecting garbage

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))

Outputs
#s(approx (- (* a a) (* b b)) (*.f64 a a))

Calls

5 calls:

20.0ms	a
1.0ms	b
1.0ms	(-.f64 (.f64 a a) (.f64 b b))
1.0ms	(*.f64 a a)
1.0ms	(*.f64 b b)

Results

Accuracy	Segments	Branch
52.9%	1	`(*.f64 b b)`
52.9%	1	`b`
52.9%	1	`(*.f64 a a)`
52.9%	1	`a`
52.9%	1	`(-.f64 (.f64 a a) (.f64 b b))`

Compiler

Compiled 15 to 15 computations (0% saved)

bsearch0.0ms (0%)

Memory

1.1MiB live, 1.1MiB allocated; 0ms collecting garbage

Algorithm

1×	left-value

Steps

Time	Left	Right
0.0ms	-2.3707854312578028e-300	0.0

Compiler

Compiled 10 to 10 computations (0% saved)

simplify57.0ms (2.3%)

Memory

-11.9MiB live, 32.4MiB allocated; 6ms collecting garbage

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	51
1	39	51
2	104	51
3	247	51
4	425	51
5	860	51
6	1409	51
7	2093	51
8	2924	51
9	3234	51
10	3296	51
11	3296	51
12	3374	51

Stop Event

1×

saturated

Calls

Call 1

Inputs

(*.f64 (-.f64 a b) (+.f64 b a))

(if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal -6032057205060441/3016028602530220424421062271578867838525126125874252890898307532480811172246863646685486789069132871854112712507200418582406770249989531589552959798883475511096677545853948017425342019529539590198394174553047792145043723038206885734470238620775335376572758801465612196212014773714996912064944617579072807182486470656 binary64)) #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b)) #s(approx (- (* a a) (* b b)) (*.f64 a a)))

#s(approx (- (* a a) (* b b)) (*.f64 a a))

Outputs

(*.f64 (-.f64 a b) (+.f64 b a))

(if (<=.f64 (-.f64 (*.f64 a a) (*.f64 b b)) #s(literal -6032057205060441/3016028602530220424421062271578867838525126125874252890898307532480811172246863646685486789069132871854112712507200418582406770249989531589552959798883475511096677545853948017425342019529539590198394174553047792145043723038206885734470238620775335376572758801465612196212014773714996912064944617579072807182486470656 binary64)) #s(approx (- (* a a) (* b b)) (*.f64 (neg.f64 b) b)) #s(approx (- (* a a) (* b b)) (*.f64 a a)))

#s(approx (- (* a a) (* b b)) (*.f64 a a))

derivations288.0ms (11.7%)

Memory

22.0MiB live, 291.2MiB allocated; 43ms collecting garbage

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5	15
0	8	15
1	37	15
2	329	15
3	4470	15
0	8291	14
0	92	211
1	299	206
2	1084	205
3	4475	205
0	8193	200
0	17	46
1	40	46
2	136	46
3	829	46
4	3437	46
0	8613	45

Stop Event

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

Compiler

Compiled 51 to 18 computations (64.7% saved)

preprocess73.0ms (3%)

Memory

-8.8MiB live, 96.0MiB allocated; 17ms collecting garbage

Remove

(abs a)

(abs b)

Compiler

Compiled 158 to 76 computations (51.9% saved)

end0.0ms (0%)

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

start0.0ms (0%)

analyze0.0ms (0%)

sample819.0ms (33.4%)

explain96.0ms (3.9%)

preprocess123.0ms (5%)

eval5.0ms (0.2%)

prune0.0ms (0%)

simplify0.0ms (0%)

series4.0ms (0.2%)

simplify108.0ms (4.4%)

rewrite94.0ms (3.8%)

eval17.0ms (0.7%)

prune2.0ms (0.1%)

simplify0.0ms (0%)

series7.0ms (0.3%)

simplify138.0ms (5.6%)

rewrite131.0ms (5.4%)

eval146.0ms (6%)

prune35.0ms (1.4%)

simplify0.0ms (0%)

series2.0ms (0.1%)

simplify160.0ms (6.5%)

rewrite72.0ms (2.9%)

eval4.0ms (0.2%)

prune21.0ms (0.8%)

regimes9.0ms (0.4%)

regimes6.0ms (0.3%)

regimes30.0ms (1.2%)

bsearch0.0ms (0%)

simplify57.0ms (2.3%)

derivations288.0ms (11.7%)

preprocess73.0ms (3%)

end0.0ms (0%)

Profiling