Metrics for Expression, p14

analyze454.0ms (9%)

Algorithm

1×

Search

Probability	Valid	Unknown	Precondition	Infinite	Domain	Can't	Iter
0%	0%	0%	100%	0%	0%	0%	0
0%	0%	0%	100%	0%	0%	0%	1
0%	0%	0%	100%	0%	0%	0%	2
0%	0%	0%	100%	0%	0%	0%	3
0%	0%	0%	100%	0%	0%	0%	4
25%	0%	0%	100%	0%	0%	0%	5
25%	0%	0%	100%	0%	0%	0%	6
25%	0%	0%	100%	0%	0%	0%	7
37.5%	0%	0%	100%	0%	0%	0%	8
56.3%	0%	0%	100%	0%	0%	0%	9
56.3%	0%	0%	100%	0%	0%	0%	10
56.3%	0%	0%	100%	0%	0%	0%	11
65.6%	0%	0%	100%	0%	0%	0%	12

Compiler

Compiled 42 to 27 computations (35.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 222.0ms

ival-<=: 125.0ms (56.2% of total)

...c/correct-round.rkt:119:19: 37.0ms (16.6% of total)

ival-add: 24.0ms (10.8% of total)

ival-and: 16.0ms (7.2% of total)

ival-mult: 13.0ms (5.8% of total)

const: 7.0ms (3.1% of total)

backward-pass: 1.0ms (0.4% of total)

sample3.2s (62.6%)

Results

2.1s

8256×

valid

Precisions

Click to see histograms. Total time spent on operations: 1.4s

ival-<=: 611.0ms (42.5% of total)

...c/correct-round.rkt:119:19: 362.0ms (25.2% of total)

ival-add: 307.0ms (21.3% of total)

ival-and: 74.0ms (5.1% of total)

ival-mult: 62.0ms (4.3% of total)

const: 19.0ms (1.3% of total)

backward-pass: 3.0ms (0.2% of total)

Bogosity

preprocess106.0ms (2.1%)

Algorithm

2×	egg-herbie

Rules

3456×	`sum4-define`
2016×	`fnmadd-define`
1430×	`sum3-define`
962×	`unsub-neg`
750×	`distribute-lft-in`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	100
1	179	100
2	629	97
3	1993	97
4	6082	97
5	6937	97
6	7378	97
7	7400	97
8	7400	97
0	7	6
1	19	6
2	46	6
3	96	6
4	118	6
5	119	6
0	119	6

Stop Event

1×	iter limit
1×	saturated
1×	node limit

Calls

Call 1

Inputs
(* a (+ (+ b c) d))

Outputs
(* a (+ (+ b c) d))
(*.f64 a (+.f64 b (+.f64 c d)))

Call 2

Inputs
(* a (+ (+ b c) d))
(* (neg a) (+ (+ b c) d))
(* a (+ (+ (neg b) c) d))
(* a (+ (+ b (neg c)) d))
(* a (+ (+ b c) (neg d)))
(neg (* (neg a) (+ (+ b c) d)))
(neg (* a (+ (+ (neg b) c) d)))
(neg (* a (+ (+ b (neg c)) d)))
(neg (* a (+ (+ b c) (neg d))))
(* b (+ (+ a c) d))
(* c (+ (+ b a) d))
(* d (+ (+ b c) a))
(* a (+ (+ c b) d))
(* a (+ (+ d c) b))
(* a (+ (+ b d) c))

Outputs
(* a (+ (+ b c) d))
(* a (sum3 b c d))
(* (neg a) (+ (+ b c) d))
(* (sum3 b c d) (neg a))
(* a (+ (+ (neg b) c) d))
(* a (+ d (- c b)))
(* a (+ (+ b (neg c)) d))
(* a (+ b (- d c)))
(* a (+ (+ b c) (neg d)))
(* a (+ b (- c d)))
(neg (* (neg a) (+ (+ b c) d)))
(* a (sum3 b c d))
(neg (* a (+ (+ (neg b) c) d)))
(* a (- (- b c) d))
(neg (* a (+ (+ b (neg c)) d)))
(* a (- c (+ b d)))
(neg (* a (+ (+ b c) (neg d))))
(* a (- d (+ b c)))
(* b (+ (+ a c) d))
(* b (sum3 a c d))
(* c (+ (+ b a) d))
(* c (sum3 a b d))
(* d (+ (+ b c) a))
(* d (sum3 a b c))
(* a (+ (+ c b) d))
(* a (sum3 b c d))
(* a (+ (+ d c) b))
(* a (sum3 b c d))
(* a (+ (+ b d) c))
(* a (sum3 b c d))

Symmetry

(negabs a)

(sort b c d)

explain122.0ms (2.4%)

FPErrors

Click to see full error table

Example	Example	Subexpression
-	-	`b`
-	-	`(+.f64 (+.f64 b c) d)`
-	-	`d`
-	-	`a`
-	-	`(*.f64 a (+.f64 (+.f64 b c) d))`
-	-	`(+.f64 b c)`
-	-	`c`

Results

87.0ms	508×	0	valid
1.0ms	4×	1	valid

Compiler

Compiled 59 to 23 computations (61% saved)

Precisions

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

ival-add: 6.0ms (58.6% of total)

ival-mult: 4.0ms (39% of total)

const: 1.0ms (9.8% of total)

backward-pass: 0.0ms (0% of total)

eval0.0ms (0%)

Compiler: Compiled 11 to 7 computations (36.4% saved)

prune1.0ms (0%)

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(*.f64 a (+.f64 (+.f64 b c) d))

Compiler

Compiled 11 to 7 computations (36.4% saved)

simplify21.0ms (0.4%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Program
✓	cost-diff	(+.f64 b c)
✓	cost-diff	(+.f64 (+.f64 b c) d)
✓	cost-diff	(*.f64 a (+.f64 (+.f64 b c) d))

Rules

56×	`fma-define`
48×	`fma-lowering-fma.f32`
48×	`+-lowering-+.f64`
48×	`+-lowering-+.f32`
48×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	17
1	19	17
2	46	17
3	96	17
4	118	17
5	119	17
0	119	17

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* a (+ (+ b c) d))
a
(+ (+ b c) d)
(+ b c)
b
c
d

Outputs
(* a (+ (+ b c) d))
(*.f64 a (+.f64 b (+.f64 c d)))
a
(+ (+ b c) d)
(+.f64 b (+.f64 c d))
(+ b c)
(+.f64 b c)
b
c
d

localize31.0ms (0.6%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 b c)
✓	accuracy	100.0%	(+.f64 (+.f64 b c) d)
✓	accuracy	99.9%	(*.f64 a (+.f64 (+.f64 b c) d))

Results

23.0ms	254×	0	valid
0.0ms	2×	1	valid

Compiler

Compiled 24 to 8 computations (66.7% saved)

Precisions

Click to see histograms. Total time spent on operations: 5.0ms

ival-add: 3.0ms (58% of total)

ival-mult: 2.0ms (38.7% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series8.0ms (0.1%)

Counts

3 → 108

Calls

Call 1

Inputs
#<alt (* a (+ (+ b c) d))>
#<alt (+ (+ b c) d)>
#<alt (+ b c)>

Outputs
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ c d))>
#<alt (+ (* a b) (* a (+ c d)))>
#<alt (+ (* a b) (* a (+ c d)))>
#<alt (+ (* a b) (* a (+ c d)))>
#<alt (* a b)>
#<alt (* b (+ a (/ (* a (+ c d)) b)))>
#<alt (* b (+ a (/ (* a (+ c d)) b)))>
#<alt (* b (+ a (/ (* a (+ c d)) b)))>
#<alt (* a b)>
#<alt (* -1 (* b (+ (* -1 a) (* -1 (/ (* a (+ c d)) b)))))>
#<alt (* -1 (* b (+ (* -1 a) (* -1 (/ (* a (+ c d)) b)))))>
#<alt (* -1 (* b (+ (* -1 a) (* -1 (/ (* a (+ c d)) b)))))>
#<alt (* a (+ b d))>
#<alt (+ (* a c) (* a (+ b d)))>
#<alt (+ (* a c) (* a (+ b d)))>
#<alt (+ (* a c) (* a (+ b d)))>
#<alt (* a c)>
#<alt (* c (+ a (/ (* a (+ b d)) c)))>
#<alt (* c (+ a (/ (* a (+ b d)) c)))>
#<alt (* c (+ a (/ (* a (+ b d)) c)))>
#<alt (* a c)>
#<alt (* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))>
#<alt (* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))>
#<alt (* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))>
#<alt (* a (+ b c))>
#<alt (+ (* a d) (* a (+ b c)))>
#<alt (+ (* a d) (* a (+ b c)))>
#<alt (+ (* a d) (* a (+ b c)))>
#<alt (* a d)>
#<alt (* d (+ a (/ (* a (+ b c)) d)))>
#<alt (* d (+ a (/ (* a (+ b c)) d)))>
#<alt (* d (+ a (/ (* a (+ b c)) d)))>
#<alt (* a d)>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (* a (+ b c)) d)))))>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (* a (+ b c)) d)))))>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (* a (+ b c)) d)))))>
#<alt (+ c d)>
#<alt (+ b (+ c d))>
#<alt (+ b (+ c d))>
#<alt (+ b (+ c d))>
#<alt b>
#<alt (* b (+ 1 (+ (/ c b) (/ d b))))>
#<alt (* b (+ 1 (+ (/ c b) (/ d b))))>
#<alt (* b (+ 1 (+ (/ c b) (/ d b))))>
#<alt b>
#<alt (* -1 (* b (- (* -1 (/ (+ c d) b)) 1)))>
#<alt (* -1 (* b (- (* -1 (/ (+ c d) b)) 1)))>
#<alt (* -1 (* b (- (* -1 (/ (+ c d) b)) 1)))>
#<alt (+ b d)>
#<alt (+ b (+ c d))>
#<alt (+ b (+ c d))>
#<alt (+ b (+ c d))>
#<alt c>
#<alt (* c (+ 1 (+ (/ b c) (/ d c))))>
#<alt (* c (+ 1 (+ (/ b c) (/ d c))))>
#<alt (* c (+ 1 (+ (/ b c) (/ d c))))>
#<alt c>
#<alt (* -1 (* c (- (* -1 (/ (+ b d) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (+ b d) c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ (+ b d) c)) 1)))>
#<alt (+ b c)>
#<alt (+ b (+ c d))>
#<alt (+ b (+ c d))>
#<alt (+ b (+ c d))>
#<alt d>
#<alt (* d (+ 1 (+ (/ b d) (/ c d))))>
#<alt (* d (+ 1 (+ (/ b d) (/ c d))))>
#<alt (* d (+ 1 (+ (/ b d) (/ c d))))>
#<alt d>
#<alt (* -1 (* d (- (* -1 (/ (+ b c) d)) 1)))>
#<alt (* -1 (* d (- (* -1 (/ (+ b c) d)) 1)))>
#<alt (* -1 (* d (- (* -1 (/ (+ b c) d)) 1)))>
#<alt c>
#<alt (+ b c)>
#<alt (+ b c)>
#<alt (+ b c)>
#<alt b>
#<alt (* b (+ 1 (/ c b)))>
#<alt (* b (+ 1 (/ c b)))>
#<alt (* b (+ 1 (/ c b)))>
#<alt b>
#<alt (* -1 (* b (- (* -1 (/ c b)) 1)))>
#<alt (* -1 (* b (- (* -1 (/ c b)) 1)))>
#<alt (* -1 (* b (- (* -1 (/ c b)) 1)))>
#<alt b>
#<alt (+ b c)>
#<alt (+ b c)>
#<alt (+ b c)>
#<alt c>
#<alt (* c (+ 1 (/ b c)))>
#<alt (* c (+ 1 (/ b c)))>
#<alt (* c (+ 1 (/ b c)))>
#<alt c>
#<alt (* -1 (* c (- (* -1 (/ b c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ b c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ b c)) 1)))>

Calls

27 calls:

Time	Variable		Point	Expression
2.0ms	a	@	-inf	(* a (+ (+ b c) d))
1.0ms	a	@	0	(* a (+ (+ b c) d))
0.0ms	b	@	-inf	(* a (+ (+ b c) d))
0.0ms	d	@	0	(+ (+ b c) d)
0.0ms	b	@	inf	(* a (+ (+ b c) d))

rewrite34.0ms (0.7%)

Algorithm

1×	batch-egg-rewrite

Rules

56×	`fma-define`
48×	`fma-lowering-fma.f32`
48×	`+-lowering-+.f64`
48×	`+-lowering-+.f32`
48×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	13
1	19	13
2	46	13
3	96	13
4	118	13
5	119	13
0	119	13

Stop Event

1×	iter limit
1×	saturated

Counts

3 → 28

Calls

Call 1

Inputs
(* a (+ (+ b c) d))
(+ (+ b c) d)
(+ b c)

Outputs
(+.f64 (.f64 a (+.f64 b c)) (.f64 a d))
(+.f64 (.f64 a d) (.f64 a (+.f64 b c)))
(+.f64 (.f64 a (+.f64 c d)) (.f64 a b))
(+.f64 (.f64 a b) (.f64 a (+.f64 c d)))
(+.f64 (.f64 a c) (.f64 a (+.f64 b d)))
(+.f64 (.f64 a (+.f64 b d)) (.f64 a c))
(fma.f64 a b (*.f64 a (+.f64 c d)))
(fma.f64 a c (*.f64 a (+.f64 b d)))
(fma.f64 a (+.f64 b c) (*.f64 a d))
(fma.f64 a d (*.f64 a (+.f64 b c)))
(fma.f64 a (+.f64 c d) (*.f64 a b))
(fma.f64 a (+.f64 b d) (*.f64 a c))
(fma.f64 b a (*.f64 a (+.f64 c d)))
(fma.f64 c a (*.f64 a (+.f64 b d)))
(fma.f64 (+.f64 b c) a (*.f64 a d))
(fma.f64 d a (*.f64 a (+.f64 b c)))
(fma.f64 (+.f64 c d) a (*.f64 a b))
(fma.f64 (+.f64 b d) a (*.f64 a c))
(*.f64 a (+.f64 b (+.f64 c d)))
(*.f64 (+.f64 b (+.f64 c d)) a)
(+.f64 b (+.f64 c d))
(+.f64 c (+.f64 b d))
(+.f64 (+.f64 b c) d)
(+.f64 d (+.f64 b c))
(+.f64 (+.f64 c d) b)
(+.f64 (+.f64 b d) c)
(+.f64 b c)
(+.f64 c b)

simplify149.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

2422×	`-lowering-.f32`
2422×	`-lowering-.f64`
1844×	`fnmadd-define`
1184×	`/-lowering-/.f32`
1184×	`/-lowering-/.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	84	516
1	292	450
2	886	450
3	2781	450
0	8007	450

Stop Event

1×	iter limit
1×	node limit

Counts

108 → 108

Calls

Call 1

Inputs
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ c d))
(+ (* a b) (* a (+ c d)))
(+ (* a b) (* a (+ c d)))
(+ (* a b) (* a (+ c d)))
(* a b)
(* b (+ a (/ (* a (+ c d)) b)))
(* b (+ a (/ (* a (+ c d)) b)))
(* b (+ a (/ (* a (+ c d)) b)))
(* a b)
(* -1 (* b (+ (* -1 a) (* -1 (/ (* a (+ c d)) b)))))
(* -1 (* b (+ (* -1 a) (* -1 (/ (* a (+ c d)) b)))))
(* -1 (* b (+ (* -1 a) (* -1 (/ (* a (+ c d)) b)))))
(* a (+ b d))
(+ (* a c) (* a (+ b d)))
(+ (* a c) (* a (+ b d)))
(+ (* a c) (* a (+ b d)))
(* a c)
(* c (+ a (/ (* a (+ b d)) c)))
(* c (+ a (/ (* a (+ b d)) c)))
(* c (+ a (/ (* a (+ b d)) c)))
(* a c)
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))
(* a (+ b c))
(+ (* a d) (* a (+ b c)))
(+ (* a d) (* a (+ b c)))
(+ (* a d) (* a (+ b c)))
(* a d)
(* d (+ a (/ (* a (+ b c)) d)))
(* d (+ a (/ (* a (+ b c)) d)))
(* d (+ a (/ (* a (+ b c)) d)))
(* a d)
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a (+ b c)) d)))))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a (+ b c)) d)))))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a (+ b c)) d)))))
(+ c d)
(+ b (+ c d))
(+ b (+ c d))
(+ b (+ c d))
b
(* b (+ 1 (+ (/ c b) (/ d b))))
(* b (+ 1 (+ (/ c b) (/ d b))))
(* b (+ 1 (+ (/ c b) (/ d b))))
b
(* -1 (* b (- (* -1 (/ (+ c d) b)) 1)))
(* -1 (* b (- (* -1 (/ (+ c d) b)) 1)))
(* -1 (* b (- (* -1 (/ (+ c d) b)) 1)))
(+ b d)
(+ b (+ c d))
(+ b (+ c d))
(+ b (+ c d))
c
(* c (+ 1 (+ (/ b c) (/ d c))))
(* c (+ 1 (+ (/ b c) (/ d c))))
(* c (+ 1 (+ (/ b c) (/ d c))))
c
(* -1 (* c (- (* -1 (/ (+ b d) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ b d) c)) 1)))
(* -1 (* c (- (* -1 (/ (+ b d) c)) 1)))
(+ b c)
(+ b (+ c d))
(+ b (+ c d))
(+ b (+ c d))
d
(* d (+ 1 (+ (/ b d) (/ c d))))
(* d (+ 1 (+ (/ b d) (/ c d))))
(* d (+ 1 (+ (/ b d) (/ c d))))
d
(* -1 (* d (- (* -1 (/ (+ b c) d)) 1)))
(* -1 (* d (- (* -1 (/ (+ b c) d)) 1)))
(* -1 (* d (- (* -1 (/ (+ b c) d)) 1)))
c
(+ b c)
(+ b c)
(+ b c)
b
(* b (+ 1 (/ c b)))
(* b (+ 1 (/ c b)))
(* b (+ 1 (/ c b)))
b
(* -1 (* b (- (* -1 (/ c b)) 1)))
(* -1 (* b (- (* -1 (/ c b)) 1)))
(* -1 (* b (- (* -1 (/ c b)) 1)))
b
(+ b c)
(+ b c)
(+ b c)
c
(* c (+ 1 (/ b c)))
(* c (+ 1 (/ b c)))
(* c (+ 1 (/ b c)))
c
(* -1 (* c (- (* -1 (/ b c)) 1)))
(* -1 (* c (- (* -1 (/ b c)) 1)))
(* -1 (* c (- (* -1 (/ b c)) 1)))

Outputs
(* a (+ b (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ c d))
(*.f64 a (+.f64 c d))
(+ (* a b) (* a (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(+ (* a b) (* a (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(+ (* a b) (* a (+ c d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a b)
(*.f64 a b)
(* b (+ a (/ (* a (+ c d)) b)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* b (+ a (/ (* a (+ c d)) b)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* b (+ a (/ (* a (+ c d)) b)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a b)
(*.f64 a b)
(* -1 (* b (+ (* -1 a) (* -1 (/ (* a (+ c d)) b)))))
(*.f64 a (+.f64 d (+.f64 b c)))
(* -1 (* b (+ (* -1 a) (* -1 (/ (* a (+ c d)) b)))))
(*.f64 a (+.f64 d (+.f64 b c)))
(* -1 (* b (+ (* -1 a) (* -1 (/ (* a (+ c d)) b)))))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b d))
(*.f64 a (+.f64 b d))
(+ (* a c) (* a (+ b d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(+ (* a c) (* a (+ b d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(+ (* a c) (* a (+ b d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a c)
(*.f64 a c)
(* c (+ a (/ (* a (+ b d)) c)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* c (+ a (/ (* a (+ b d)) c)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* c (+ a (/ (* a (+ b d)) c)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a c)
(*.f64 a c)
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))
(*.f64 a (+.f64 d (+.f64 b c)))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))
(*.f64 a (+.f64 d (+.f64 b c)))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a (+ b c))
(*.f64 a (+.f64 b c))
(+ (* a d) (* a (+ b c)))
(*.f64 a (+.f64 d (+.f64 b c)))
(+ (* a d) (* a (+ b c)))
(*.f64 a (+.f64 d (+.f64 b c)))
(+ (* a d) (* a (+ b c)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a d)
(*.f64 a d)
(* d (+ a (/ (* a (+ b c)) d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* d (+ a (/ (* a (+ b c)) d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* d (+ a (/ (* a (+ b c)) d)))
(*.f64 a (+.f64 d (+.f64 b c)))
(* a d)
(*.f64 a d)
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a (+ b c)) d)))))
(*.f64 a (+.f64 d (+.f64 b c)))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a (+ b c)) d)))))
(*.f64 a (+.f64 d (+.f64 b c)))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a (+ b c)) d)))))
(*.f64 a (+.f64 d (+.f64 b c)))
(+ c d)
(+.f64 c d)
(+ b (+ c d))
(+.f64 d (+.f64 b c))
(+ b (+ c d))
(+.f64 d (+.f64 b c))
(+ b (+ c d))
(+.f64 d (+.f64 b c))
b
(* b (+ 1 (+ (/ c b) (/ d b))))
(+.f64 d (+.f64 b c))
(* b (+ 1 (+ (/ c b) (/ d b))))
(+.f64 d (+.f64 b c))
(* b (+ 1 (+ (/ c b) (/ d b))))
(+.f64 d (+.f64 b c))
b
(* -1 (* b (- (* -1 (/ (+ c d) b)) 1)))
(+.f64 d (+.f64 b c))
(* -1 (* b (- (* -1 (/ (+ c d) b)) 1)))
(+.f64 d (+.f64 b c))
(* -1 (* b (- (* -1 (/ (+ c d) b)) 1)))
(+.f64 d (+.f64 b c))
(+ b d)
(+.f64 b d)
(+ b (+ c d))
(+.f64 d (+.f64 b c))
(+ b (+ c d))
(+.f64 d (+.f64 b c))
(+ b (+ c d))
(+.f64 d (+.f64 b c))
c
(* c (+ 1 (+ (/ b c) (/ d c))))
(+.f64 d (+.f64 b c))
(* c (+ 1 (+ (/ b c) (/ d c))))
(+.f64 d (+.f64 b c))
(* c (+ 1 (+ (/ b c) (/ d c))))
(+.f64 d (+.f64 b c))
c
(* -1 (* c (- (* -1 (/ (+ b d) c)) 1)))
(+.f64 d (+.f64 b c))
(* -1 (* c (- (* -1 (/ (+ b d) c)) 1)))
(+.f64 d (+.f64 b c))
(* -1 (* c (- (* -1 (/ (+ b d) c)) 1)))
(+.f64 d (+.f64 b c))
(+ b c)
(+.f64 b c)
(+ b (+ c d))
(+.f64 d (+.f64 b c))
(+ b (+ c d))
(+.f64 d (+.f64 b c))
(+ b (+ c d))
(+.f64 d (+.f64 b c))
d
(* d (+ 1 (+ (/ b d) (/ c d))))
(+.f64 d (+.f64 b c))
(* d (+ 1 (+ (/ b d) (/ c d))))
(+.f64 d (+.f64 b c))
(* d (+ 1 (+ (/ b d) (/ c d))))
(+.f64 d (+.f64 b c))
d
(* -1 (* d (- (* -1 (/ (+ b c) d)) 1)))
(+.f64 d (+.f64 b c))
(* -1 (* d (- (* -1 (/ (+ b c) d)) 1)))
(+.f64 d (+.f64 b c))
(* -1 (* d (- (* -1 (/ (+ b c) d)) 1)))
(+.f64 d (+.f64 b c))
c
(+ b c)
(+.f64 b c)
(+ b c)
(+.f64 b c)
(+ b c)
(+.f64 b c)
b
(* b (+ 1 (/ c b)))
(+.f64 b c)
(* b (+ 1 (/ c b)))
(+.f64 b c)
(* b (+ 1 (/ c b)))
(+.f64 b c)
b
(* -1 (* b (- (* -1 (/ c b)) 1)))
(+.f64 b c)
(* -1 (* b (- (* -1 (/ c b)) 1)))
(+.f64 b c)
(* -1 (* b (- (* -1 (/ c b)) 1)))
(+.f64 b c)
b
(+ b c)
(+.f64 b c)
(+ b c)
(+.f64 b c)
(+ b c)
(+.f64 b c)
c
(* c (+ 1 (/ b c)))
(+.f64 b c)
(* c (+ 1 (/ b c)))
(+.f64 b c)
(* c (+ 1 (/ b c)))
(+.f64 b c)
c
(* -1 (* c (- (* -1 (/ b c)) 1)))
(+.f64 b c)
(* -1 (* c (- (* -1 (/ b c)) 1)))
(+.f64 b c)
(* -1 (* c (- (* -1 (/ b c)) 1)))
(+.f64 b c)

eval13.0ms (0.3%)

Compiler: Compiled 908 to 47 computations (94.8% saved)

prune7.0ms (0.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	133	4	137

Accuracy

100.0%

Counts

137 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	100.0%	(+.f64 (.f64 a (+.f64 b d)) (.f64 a c))
✓	99.9%	(*.f64 a (+.f64 (+.f64 b c) d))
▶	99.9%	(*.f64 a (+.f64 c d))
▶	93.3%	(*.f64 a d)

Compiler

Compiled 40 to 26 computations (35% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 a c)
✓	cost-diff	0	(+.f64 b d)
✓	cost-diff	0	(*.f64 a (+.f64 b d))
✓	cost-diff	128	(+.f64 (.f64 a (+.f64 b d)) (.f64 a c))
✓	cost-diff	0	(+.f64 c d)
✓	cost-diff	0	(*.f64 a (+.f64 c d))
✓	cost-diff	0	(*.f64 a d)

Rules

52×	`fma-define`
48×	`fma-lowering-fma.f32`
48×	`+-lowering-+.f64`
48×	`+-lowering-+.f32`
48×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	38
1	28	37
2	54	37
3	78	37
4	95	37
5	96	37
0	96	37

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(* a d)
a
d
(* a (+ c d))
a
(+ c d)
c
d
(+ (* a (+ b d)) (* a c))
(* a (+ b d))
a
(+ b d)
b
d
(* a c)
c

Outputs
(* a d)
(*.f64 a d)
a
d
(* a (+ c d))
(*.f64 a (+.f64 d c))
a
(+ c d)
(+.f64 d c)
c
d
(+ (* a (+ b d)) (* a c))
(*.f64 a (+.f64 d (+.f64 c b)))
(* a (+ b d))
(*.f64 a (+.f64 d b))
a
(+ b d)
(+.f64 d b)
b
d
(* a c)
(*.f64 a c)
c

localize56.0ms (1.1%)

Localize:

Found 7 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(+.f64 b d)
✓	accuracy	100.0%	(*.f64 a c)
✓	accuracy	100.0%	(*.f64 a (+.f64 b d))
✓	accuracy	100.0%	(+.f64 (.f64 a (+.f64 b d)) (.f64 a c))
✓	accuracy	100.0%	(+.f64 c d)
✓	accuracy	99.9%	(*.f64 a (+.f64 c d))
✓	accuracy	100.0%	(*.f64 a d)

Results

45.0ms

256×

valid

Compiler

Compiled 45 to 12 computations (73.3% saved)

Precisions

Click to see histograms. Total time spent on operations: 12.0ms

ival-mult: 8.0ms (66.3% of total)

ival-add: 4.0ms (33.1% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series13.0ms (0.2%)

Counts

7 → 216

Calls

Call 1

Inputs
#<alt (* a d)>
#<alt (* a (+ c d))>
#<alt (+ c d)>
#<alt (+ (* a (+ b d)) (* a c))>
#<alt (* a (+ b d))>
#<alt (+ b d)>
#<alt (* a c)>

Outputs
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a d)>
#<alt (+ (* a c) (* a d))>
#<alt (+ (* a c) (* a d))>
#<alt (+ (* a c) (* a d))>
#<alt (* a c)>
#<alt (* c (+ a (/ (* a d) c)))>
#<alt (* c (+ a (/ (* a d) c)))>
#<alt (* c (+ a (/ (* a d) c)))>
#<alt (* a c)>
#<alt (* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))>
#<alt (* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))>
#<alt (* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))>
#<alt (* a c)>
#<alt (+ (* a c) (* a d))>
#<alt (+ (* a c) (* a d))>
#<alt (+ (* a c) (* a d))>
#<alt (* a d)>
#<alt (* d (+ a (/ (* a c) d)))>
#<alt (* d (+ a (/ (* a c) d)))>
#<alt (* d (+ a (/ (* a c) d)))>
#<alt (* a d)>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))>
#<alt d>
#<alt (+ c d)>
#<alt (+ c d)>
#<alt (+ c d)>
#<alt c>
#<alt (* c (+ 1 (/ d c)))>
#<alt (* c (+ 1 (/ d c)))>
#<alt (* c (+ 1 (/ d c)))>
#<alt c>
#<alt (* -1 (* c (- (* -1 (/ d c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ d c)) 1)))>
#<alt (* -1 (* c (- (* -1 (/ d c)) 1)))>
#<alt c>
#<alt (+ c d)>
#<alt (+ c d)>
#<alt (+ c d)>
#<alt d>
#<alt (* d (+ 1 (/ c d)))>
#<alt (* d (+ 1 (/ c d)))>
#<alt (* d (+ 1 (/ c d)))>
#<alt d>
#<alt (* -1 (* d (- (* -1 (/ c d)) 1)))>
#<alt (* -1 (* d (- (* -1 (/ c d)) 1)))>
#<alt (* -1 (* d (- (* -1 (/ c d)) 1)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* a (+ b (+ c d)))>
#<alt (* -1 (* a (+ (* -1 c) (* -1 (+ b d)))))>
#<alt (* -1 (* a (+ (* -1 c) (* -1 (+ b d)))))>
#<alt (* -1 (* a (+ (* -1 c) (* -1 (+ b d)))))>
#<alt (* -1 (* a (+ (* -1 c) (* -1 (+ b d)))))>
#<alt (+ (* a c) (* a d))>
#<alt (+ (* a b) (+ (* a c) (* a d)))>
#<alt (+ (* a b) (+ (* a c) (* a d)))>
#<alt (+ (* a b) (+ (* a c) (* a d)))>
#<alt (* a b)>
#<alt (* b (+ a (+ (/ (* a c) b) (/ (* a d) b))))>
#<alt (* b (+ a (+ (/ (* a c) b) (/ (* a d) b))))>
#<alt (* b (+ a (+ (/ (* a c) b) (/ (* a d) b))))>
#<alt (* a b)>
#<alt (* -1 (* b (+ (* -1 a) (* -1 (/ (+ (* a c) (* a d)) b)))))>
#<alt (* -1 (* b (+ (* -1 a) (* -1 (/ (+ (* a c) (* a d)) b)))))>
#<alt (* -1 (* b (+ (* -1 a) (* -1 (/ (+ (* a c) (* a d)) b)))))>
#<alt (+ (* a b) (* a c))>
#<alt (+ (* a b) (+ (* a c) (* a d)))>
#<alt (+ (* a b) (+ (* a c) (* a d)))>
#<alt (+ (* a b) (+ (* a c) (* a d)))>
#<alt (* a d)>
#<alt (* d (+ a (+ (/ (* a b) d) (/ (* a c) d))))>
#<alt (* d (+ a (+ (/ (* a b) d) (/ (* a c) d))))>
#<alt (* d (+ a (+ (/ (* a b) d) (/ (* a c) d))))>
#<alt (* a d)>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (+ (* a b) (* a c)) d)))))>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (+ (* a b) (* a c)) d)))))>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (+ (* a b) (* a c)) d)))))>
#<alt (* a (+ b d))>
#<alt (+ (* a c) (* a (+ b d)))>
#<alt (+ (* a c) (* a (+ b d)))>
#<alt (+ (* a c) (* a (+ b d)))>
#<alt (* a c)>
#<alt (* c (+ a (/ (* a (+ b d)) c)))>
#<alt (* c (+ a (/ (* a (+ b d)) c)))>
#<alt (* c (+ a (/ (* a (+ b d)) c)))>
#<alt (* a c)>
#<alt (* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))>
#<alt (* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))>
#<alt (* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))>
#<alt (* a (+ b d))>
#<alt (* a (+ b d))>
#<alt (* a (+ b d))>
#<alt (* a (+ b d))>
#<alt (* a (+ b d))>
#<alt (* a (+ b d))>
#<alt (* a (+ b d))>
#<alt (* a (+ b d))>
#<alt (* a (+ b d))>
#<alt (* a (+ b d))>
#<alt (* a (+ b d))>
#<alt (* a (+ b d))>
#<alt (* a d)>
#<alt (+ (* a b) (* a d))>
#<alt (+ (* a b) (* a d))>
#<alt (+ (* a b) (* a d))>
#<alt (* a b)>
#<alt (* b (+ a (/ (* a d) b)))>
#<alt (* b (+ a (/ (* a d) b)))>
#<alt (* b (+ a (/ (* a d) b)))>
#<alt (* a b)>
#<alt (* -1 (* b (+ (* -1 a) (* -1 (/ (* a d) b)))))>
#<alt (* -1 (* b (+ (* -1 a) (* -1 (/ (* a d) b)))))>
#<alt (* -1 (* b (+ (* -1 a) (* -1 (/ (* a d) b)))))>
#<alt (* a b)>
#<alt (+ (* a b) (* a d))>
#<alt (+ (* a b) (* a d))>
#<alt (+ (* a b) (* a d))>
#<alt (* a d)>
#<alt (* d (+ a (/ (* a b) d)))>
#<alt (* d (+ a (/ (* a b) d)))>
#<alt (* d (+ a (/ (* a b) d)))>
#<alt (* a d)>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (* a b) d)))))>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (* a b) d)))))>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (* a b) d)))))>
#<alt d>
#<alt (+ b d)>
#<alt (+ b d)>
#<alt (+ b d)>
#<alt b>
#<alt (* b (+ 1 (/ d b)))>
#<alt (* b (+ 1 (/ d b)))>
#<alt (* b (+ 1 (/ d b)))>
#<alt b>
#<alt (* -1 (* b (- (* -1 (/ d b)) 1)))>
#<alt (* -1 (* b (- (* -1 (/ d b)) 1)))>
#<alt (* -1 (* b (- (* -1 (/ d b)) 1)))>
#<alt b>
#<alt (+ b d)>
#<alt (+ b d)>
#<alt (+ b d)>
#<alt d>
#<alt (* d (+ 1 (/ b d)))>
#<alt (* d (+ 1 (/ b d)))>
#<alt (* d (+ 1 (/ b d)))>
#<alt d>
#<alt (* -1 (* d (- (* -1 (/ b d)) 1)))>
#<alt (* -1 (* d (- (* -1 (/ b d)) 1)))>
#<alt (* -1 (* d (- (* -1 (/ b d)) 1)))>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>

Calls

54 calls:

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

rewrite18.0ms (0.4%)

Algorithm

1×	batch-egg-rewrite

Rules

52×	`fma-define`
48×	`fma-lowering-fma.f32`
48×	`+-lowering-+.f64`
48×	`+-lowering-+.f32`
48×	`fma-lowering-fma.f64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	28	28
2	54	28
3	78	28
4	95	28
5	96	28
0	96	28

Stop Event

1×	iter limit
1×	saturated

Counts

7 → 44

Calls

Call 1

Inputs
(* a d)
(* a (+ c d))
(+ c d)
(+ (* a (+ b d)) (* a c))
(* a (+ b d))
(+ b d)
(* a c)

Outputs
(*.f64 a d)
(*.f64 d a)
(+.f64 (.f64 a d) (.f64 a c))
(+.f64 (.f64 a c) (.f64 a d))
(fma.f64 a d (*.f64 a c))
(fma.f64 a c (*.f64 a d))
(fma.f64 d a (*.f64 a c))
(fma.f64 c a (*.f64 a d))
(*.f64 a (+.f64 d c))
(*.f64 (+.f64 d c) a)
(+.f64 d c)
(+.f64 c d)
(+.f64 (.f64 a d) (.f64 a (+.f64 c b)))
(+.f64 (.f64 a (+.f64 d c)) (.f64 a b))
(+.f64 (.f64 a (+.f64 d b)) (.f64 a c))
(+.f64 (.f64 a c) (.f64 a (+.f64 d b)))
(+.f64 (.f64 a b) (.f64 a (+.f64 d c)))
(+.f64 (.f64 a (+.f64 c b)) (.f64 a d))
(fma.f64 a d (*.f64 a (+.f64 c b)))
(fma.f64 a c (*.f64 a (+.f64 d b)))
(fma.f64 a (+.f64 d c) (*.f64 a b))
(fma.f64 a b (*.f64 a (+.f64 d c)))
(fma.f64 a (+.f64 d b) (*.f64 a c))
(fma.f64 a (+.f64 c b) (*.f64 a d))
(fma.f64 d a (*.f64 a (+.f64 c b)))
(fma.f64 c a (*.f64 a (+.f64 d b)))
(fma.f64 (+.f64 d c) a (*.f64 a b))
(fma.f64 b a (*.f64 a (+.f64 d c)))
(fma.f64 (+.f64 d b) a (*.f64 a c))
(fma.f64 (+.f64 c b) a (*.f64 a d))
(*.f64 a (+.f64 d (+.f64 c b)))
(*.f64 (+.f64 d (+.f64 c b)) a)
(+.f64 (.f64 a d) (.f64 a b))
(+.f64 (.f64 a b) (.f64 a d))
(fma.f64 a d (*.f64 a b))
(fma.f64 a b (*.f64 a d))
(fma.f64 d a (*.f64 a b))
(fma.f64 b a (*.f64 a d))
(*.f64 a (+.f64 d b))
(*.f64 (+.f64 d b) a)
(+.f64 d b)
(+.f64 b d)
(*.f64 a c)
(*.f64 c a)

simplify165.0ms (3.3%)

Algorithm

1×	egg-herbie

Rules

2464×	`-lowering-.f32`
2464×	`-lowering-.f64`
1938×	`fmsub-define`
1554×	`fnmsub-define`
1404×	`fmm-def`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	106	906
1	407	867
2	1318	867
3	4240	867
0	8485	867

Stop Event

1×	iter limit
1×	node limit

Counts

216 → 216

Calls

Call 1

Inputs
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a d)
(+ (* a c) (* a d))
(+ (* a c) (* a d))
(+ (* a c) (* a d))
(* a c)
(* c (+ a (/ (* a d) c)))
(* c (+ a (/ (* a d) c)))
(* c (+ a (/ (* a d) c)))
(* a c)
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))
(* a c)
(+ (* a c) (* a d))
(+ (* a c) (* a d))
(+ (* a c) (* a d))
(* a d)
(* d (+ a (/ (* a c) d)))
(* d (+ a (/ (* a c) d)))
(* d (+ a (/ (* a c) d)))
(* a d)
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))
d
(+ c d)
(+ c d)
(+ c d)
c
(* c (+ 1 (/ d c)))
(* c (+ 1 (/ d c)))
(* c (+ 1 (/ d c)))
c
(* -1 (* c (- (* -1 (/ d c)) 1)))
(* -1 (* c (- (* -1 (/ d c)) 1)))
(* -1 (* c (- (* -1 (/ d c)) 1)))
c
(+ c d)
(+ c d)
(+ c d)
d
(* d (+ 1 (/ c d)))
(* d (+ 1 (/ c d)))
(* d (+ 1 (/ c d)))
d
(* -1 (* d (- (* -1 (/ c d)) 1)))
(* -1 (* d (- (* -1 (/ c d)) 1)))
(* -1 (* d (- (* -1 (/ c d)) 1)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* a (+ b (+ c d)))
(* -1 (* a (+ (* -1 c) (* -1 (+ b d)))))
(* -1 (* a (+ (* -1 c) (* -1 (+ b d)))))
(* -1 (* a (+ (* -1 c) (* -1 (+ b d)))))
(* -1 (* a (+ (* -1 c) (* -1 (+ b d)))))
(+ (* a c) (* a d))
(+ (* a b) (+ (* a c) (* a d)))
(+ (* a b) (+ (* a c) (* a d)))
(+ (* a b) (+ (* a c) (* a d)))
(* a b)
(* b (+ a (+ (/ (* a c) b) (/ (* a d) b))))
(* b (+ a (+ (/ (* a c) b) (/ (* a d) b))))
(* b (+ a (+ (/ (* a c) b) (/ (* a d) b))))
(* a b)
(* -1 (* b (+ (* -1 a) (* -1 (/ (+ (* a c) (* a d)) b)))))
(* -1 (* b (+ (* -1 a) (* -1 (/ (+ (* a c) (* a d)) b)))))
(* -1 (* b (+ (* -1 a) (* -1 (/ (+ (* a c) (* a d)) b)))))
(+ (* a b) (* a c))
(+ (* a b) (+ (* a c) (* a d)))
(+ (* a b) (+ (* a c) (* a d)))
(+ (* a b) (+ (* a c) (* a d)))
(* a d)
(* d (+ a (+ (/ (* a b) d) (/ (* a c) d))))
(* d (+ a (+ (/ (* a b) d) (/ (* a c) d))))
(* d (+ a (+ (/ (* a b) d) (/ (* a c) d))))
(* a d)
(* -1 (* d (+ (* -1 a) (* -1 (/ (+ (* a b) (* a c)) d)))))
(* -1 (* d (+ (* -1 a) (* -1 (/ (+ (* a b) (* a c)) d)))))
(* -1 (* d (+ (* -1 a) (* -1 (/ (+ (* a b) (* a c)) d)))))
(* a (+ b d))
(+ (* a c) (* a (+ b d)))
(+ (* a c) (* a (+ b d)))
(+ (* a c) (* a (+ b d)))
(* a c)
(* c (+ a (/ (* a (+ b d)) c)))
(* c (+ a (/ (* a (+ b d)) c)))
(* c (+ a (/ (* a (+ b d)) c)))
(* a c)
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))
(* a (+ b d))
(* a (+ b d))
(* a (+ b d))
(* a (+ b d))
(* a (+ b d))
(* a (+ b d))
(* a (+ b d))
(* a (+ b d))
(* a (+ b d))
(* a (+ b d))
(* a (+ b d))
(* a (+ b d))
(* a d)
(+ (* a b) (* a d))
(+ (* a b) (* a d))
(+ (* a b) (* a d))
(* a b)
(* b (+ a (/ (* a d) b)))
(* b (+ a (/ (* a d) b)))
(* b (+ a (/ (* a d) b)))
(* a b)
(* -1 (* b (+ (* -1 a) (* -1 (/ (* a d) b)))))
(* -1 (* b (+ (* -1 a) (* -1 (/ (* a d) b)))))
(* -1 (* b (+ (* -1 a) (* -1 (/ (* a d) b)))))
(* a b)
(+ (* a b) (* a d))
(+ (* a b) (* a d))
(+ (* a b) (* a d))
(* a d)
(* d (+ a (/ (* a b) d)))
(* d (+ a (/ (* a b) d)))
(* d (+ a (/ (* a b) d)))
(* a d)
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a b) d)))))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a b) d)))))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a b) d)))))
d
(+ b d)
(+ b d)
(+ b d)
b
(* b (+ 1 (/ d b)))
(* b (+ 1 (/ d b)))
(* b (+ 1 (/ d b)))
b
(* -1 (* b (- (* -1 (/ d b)) 1)))
(* -1 (* b (- (* -1 (/ d b)) 1)))
(* -1 (* b (- (* -1 (/ d b)) 1)))
b
(+ b d)
(+ b d)
(+ b d)
d
(* d (+ 1 (/ b d)))
(* d (+ 1 (/ b d)))
(* d (+ 1 (/ b d)))
d
(* -1 (* d (- (* -1 (/ b d)) 1)))
(* -1 (* d (- (* -1 (/ b d)) 1)))
(* -1 (* d (- (* -1 (/ b d)) 1)))
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)

Outputs
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a (+ c d))
(*.f64 a (+.f64 d c))
(* a (+ c d))
(*.f64 a (+.f64 d c))
(* a (+ c d))
(*.f64 a (+.f64 d c))
(* a (+ c d))
(*.f64 a (+.f64 d c))
(* a (+ c d))
(*.f64 a (+.f64 d c))
(* a (+ c d))
(*.f64 a (+.f64 d c))
(* a (+ c d))
(*.f64 a (+.f64 d c))
(* a (+ c d))
(*.f64 a (+.f64 d c))
(* a (+ c d))
(*.f64 a (+.f64 d c))
(* a (+ c d))
(*.f64 a (+.f64 d c))
(* a (+ c d))
(*.f64 a (+.f64 d c))
(* a (+ c d))
(*.f64 a (+.f64 d c))
(* a d)
(*.f64 a d)
(+ (* a c) (* a d))
(*.f64 a (+.f64 d c))
(+ (* a c) (* a d))
(*.f64 a (+.f64 d c))
(+ (* a c) (* a d))
(*.f64 a (+.f64 d c))
(* a c)
(*.f64 a c)
(* c (+ a (/ (* a d) c)))
(*.f64 a (+.f64 d c))
(* c (+ a (/ (* a d) c)))
(*.f64 a (+.f64 d c))
(* c (+ a (/ (* a d) c)))
(*.f64 a (+.f64 d c))
(* a c)
(*.f64 a c)
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))
(*.f64 a (+.f64 d c))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))
(*.f64 a (+.f64 d c))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))
(*.f64 a (+.f64 d c))
(* a c)
(*.f64 a c)
(+ (* a c) (* a d))
(*.f64 a (+.f64 d c))
(+ (* a c) (* a d))
(*.f64 a (+.f64 d c))
(+ (* a c) (* a d))
(*.f64 a (+.f64 d c))
(* a d)
(*.f64 a d)
(* d (+ a (/ (* a c) d)))
(*.f64 a (+.f64 d c))
(* d (+ a (/ (* a c) d)))
(*.f64 a (+.f64 d c))
(* d (+ a (/ (* a c) d)))
(*.f64 a (+.f64 d c))
(* a d)
(*.f64 a d)
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))
(*.f64 a (+.f64 d c))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))
(*.f64 a (+.f64 d c))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))
(*.f64 a (+.f64 d c))
d
(+ c d)
(+.f64 d c)
(+ c d)
(+.f64 d c)
(+ c d)
(+.f64 d c)
c
(* c (+ 1 (/ d c)))
(+.f64 d c)
(* c (+ 1 (/ d c)))
(+.f64 d c)
(* c (+ 1 (/ d c)))
(+.f64 d c)
c
(* -1 (* c (- (* -1 (/ d c)) 1)))
(+.f64 d c)
(* -1 (* c (- (* -1 (/ d c)) 1)))
(+.f64 d c)
(* -1 (* c (- (* -1 (/ d c)) 1)))
(+.f64 d c)
c
(+ c d)
(+.f64 d c)
(+ c d)
(+.f64 d c)
(+ c d)
(+.f64 d c)
d
(* d (+ 1 (/ c d)))
(+.f64 d c)
(* d (+ 1 (/ c d)))
(+.f64 d c)
(* d (+ 1 (/ c d)))
(+.f64 d c)
d
(* -1 (* d (- (* -1 (/ c d)) 1)))
(+.f64 d c)
(* -1 (* d (- (* -1 (/ c d)) 1)))
(+.f64 d c)
(* -1 (* d (- (* -1 (/ c d)) 1)))
(+.f64 d c)
(* a (+ b (+ c d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a (+ b (+ c d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* -1 (* a (+ (* -1 c) (* -1 (+ b d)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* -1 (* a (+ (* -1 c) (* -1 (+ b d)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* -1 (* a (+ (* -1 c) (* -1 (+ b d)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* -1 (* a (+ (* -1 c) (* -1 (+ b d)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(+ (* a c) (* a d))
(*.f64 a (+.f64 d c))
(+ (* a b) (+ (* a c) (* a d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(+ (* a b) (+ (* a c) (* a d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(+ (* a b) (+ (* a c) (* a d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a b)
(*.f64 a b)
(* b (+ a (+ (/ (* a c) b) (/ (* a d) b))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* b (+ a (+ (/ (* a c) b) (/ (* a d) b))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* b (+ a (+ (/ (* a c) b) (/ (* a d) b))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a b)
(*.f64 a b)
(* -1 (* b (+ (* -1 a) (* -1 (/ (+ (* a c) (* a d)) b)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* -1 (* b (+ (* -1 a) (* -1 (/ (+ (* a c) (* a d)) b)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* -1 (* b (+ (* -1 a) (* -1 (/ (+ (* a c) (* a d)) b)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(+ (* a b) (* a c))
(*.f64 a (+.f64 c b))
(+ (* a b) (+ (* a c) (* a d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(+ (* a b) (+ (* a c) (* a d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(+ (* a b) (+ (* a c) (* a d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a d)
(*.f64 a d)
(* d (+ a (+ (/ (* a b) d) (/ (* a c) d))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* d (+ a (+ (/ (* a b) d) (/ (* a c) d))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* d (+ a (+ (/ (* a b) d) (/ (* a c) d))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a d)
(*.f64 a d)
(* -1 (* d (+ (* -1 a) (* -1 (/ (+ (* a b) (* a c)) d)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* -1 (* d (+ (* -1 a) (* -1 (/ (+ (* a b) (* a c)) d)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* -1 (* d (+ (* -1 a) (* -1 (/ (+ (* a b) (* a c)) d)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(+ (* a c) (* a (+ b d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(+ (* a c) (* a (+ b d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(+ (* a c) (* a (+ b d)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a c)
(*.f64 a c)
(* c (+ a (/ (* a (+ b d)) c)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* c (+ a (/ (* a (+ b d)) c)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* c (+ a (/ (* a (+ b d)) c)))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a c)
(*.f64 a c)
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a (+ b d)) c)))))
(*.f64 a (+.f64 c (+.f64 d b)))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(* a (+ b d))
(*.f64 a (+.f64 d b))
(* a d)
(*.f64 a d)
(+ (* a b) (* a d))
(*.f64 a (+.f64 d b))
(+ (* a b) (* a d))
(*.f64 a (+.f64 d b))
(+ (* a b) (* a d))
(*.f64 a (+.f64 d b))
(* a b)
(*.f64 a b)
(* b (+ a (/ (* a d) b)))
(*.f64 a (+.f64 d b))
(* b (+ a (/ (* a d) b)))
(*.f64 a (+.f64 d b))
(* b (+ a (/ (* a d) b)))
(*.f64 a (+.f64 d b))
(* a b)
(*.f64 a b)
(* -1 (* b (+ (* -1 a) (* -1 (/ (* a d) b)))))
(*.f64 a (+.f64 d b))
(* -1 (* b (+ (* -1 a) (* -1 (/ (* a d) b)))))
(*.f64 a (+.f64 d b))
(* -1 (* b (+ (* -1 a) (* -1 (/ (* a d) b)))))
(*.f64 a (+.f64 d b))
(* a b)
(*.f64 a b)
(+ (* a b) (* a d))
(*.f64 a (+.f64 d b))
(+ (* a b) (* a d))
(*.f64 a (+.f64 d b))
(+ (* a b) (* a d))
(*.f64 a (+.f64 d b))
(* a d)
(*.f64 a d)
(* d (+ a (/ (* a b) d)))
(*.f64 a (+.f64 d b))
(* d (+ a (/ (* a b) d)))
(*.f64 a (+.f64 d b))
(* d (+ a (/ (* a b) d)))
(*.f64 a (+.f64 d b))
(* a d)
(*.f64 a d)
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a b) d)))))
(*.f64 a (+.f64 d b))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a b) d)))))
(*.f64 a (+.f64 d b))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a b) d)))))
(*.f64 a (+.f64 d b))
d
(+ b d)
(+.f64 d b)
(+ b d)
(+.f64 d b)
(+ b d)
(+.f64 d b)
b
(* b (+ 1 (/ d b)))
(+.f64 d b)
(* b (+ 1 (/ d b)))
(+.f64 d b)
(* b (+ 1 (/ d b)))
(+.f64 d b)
b
(* -1 (* b (- (* -1 (/ d b)) 1)))
(+.f64 d b)
(* -1 (* b (- (* -1 (/ d b)) 1)))
(+.f64 d b)
(* -1 (* b (- (* -1 (/ d b)) 1)))
(+.f64 d b)
b
(+ b d)
(+.f64 d b)
(+ b d)
(+.f64 d b)
(+ b d)
(+.f64 d b)
d
(* d (+ 1 (/ b d)))
(+.f64 d b)
(* d (+ 1 (/ b d)))
(+.f64 d b)
(* d (+ 1 (/ b d)))
(+.f64 d b)
d
(* -1 (* d (- (* -1 (/ b d)) 1)))
(+.f64 d b)
(* -1 (* d (- (* -1 (/ b d)) 1)))
(+.f64 d b)
(* -1 (* d (- (* -1 (/ b d)) 1)))
(+.f64 d b)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)

eval23.0ms (0.5%)

Compiler: Compiled 1734 to 66 computations (96.2% saved)

prune10.0ms (0.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	0	0	0
Picked	1	2	3
Done	0	1	1
Total	260	4	264

Accuracy

100.0%

Counts

264 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
▶	99.9%	(+.f64 (.f64 a d) (.f64 a c))
✓	99.9%	(*.f64 a (+.f64 (+.f64 b c) d))
✓	99.9%	(*.f64 a (+.f64 c d))
✓	93.3%	(*.f64 a d)

Compiler

Compiled 38 to 25 computations (34.2% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	cost-diff	0	(*.f64 a c)
✓	cost-diff	0	(*.f64 a d)
✓	cost-diff	128	(+.f64 (.f64 a d) (.f64 a c))

Rules

12×	`-lowering-.f32`
12×	`-lowering-.f64`
8×	`fma-lowering-fma.f32`
8×	`fma-define`
8×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	14
1	12	14
2	18	14
0	18	14

Stop Event

1×	iter limit
1×	saturated

Calls

Call 1

Inputs
(+ (* a d) (* a c))
(* a d)
a
d
(* a c)
c

Outputs
(+ (* a d) (* a c))
(*.f64 a (+.f64 d c))
(* a d)
(*.f64 a d)
a
d
(* a c)
(*.f64 a c)
c

localize31.0ms (0.6%)

Localize:

Found 3 expressions of interest:

New	Metric	Score	Program
✓	accuracy	100.0%	(*.f64 a d)
✓	accuracy	100.0%	(*.f64 a c)
✓	accuracy	100.0%	(+.f64 (.f64 a d) (.f64 a c))

Results

22.0ms

256×

valid

Compiler

Compiled 21 to 8 computations (61.9% saved)

Precisions

Click to see histograms. Total time spent on operations: 6.0ms

ival-mult: 4.0ms (71.4% of total)

ival-add: 1.0ms (17.8% of total)

const: 0.0ms (0% of total)

backward-pass: 0.0ms (0% of total)

series1.0ms (0%)

Counts

3 → 84

Calls

Call 1

Inputs
#<alt (+ (* a d) (* a c))>
#<alt (* a d)>
#<alt (* a c)>

Outputs
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* a (+ c d))>
#<alt (* -1 (* a (+ (* -1 c) (* -1 d))))>
#<alt (* -1 (* a (+ (* -1 c) (* -1 d))))>
#<alt (* -1 (* a (+ (* -1 c) (* -1 d))))>
#<alt (* -1 (* a (+ (* -1 c) (* -1 d))))>
#<alt (* a c)>
#<alt (+ (* a c) (* a d))>
#<alt (+ (* a c) (* a d))>
#<alt (+ (* a c) (* a d))>
#<alt (* a d)>
#<alt (* d (+ a (/ (* a c) d)))>
#<alt (* d (+ a (/ (* a c) d)))>
#<alt (* d (+ a (/ (* a c) d)))>
#<alt (* a d)>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))>
#<alt (* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))>
#<alt (* a d)>
#<alt (+ (* a c) (* a d))>
#<alt (+ (* a c) (* a d))>
#<alt (+ (* a c) (* a d))>
#<alt (* a c)>
#<alt (* c (+ a (/ (* a d) c)))>
#<alt (* c (+ a (/ (* a d) c)))>
#<alt (* c (+ a (/ (* a d) c)))>
#<alt (* a c)>
#<alt (* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))>
#<alt (* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))>
#<alt (* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a d)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>
#<alt (* a c)>

Calls

21 calls:

Time	Variable		Point	Expression
0.0ms	c	@	0	(+ (* a d) (* a c))
0.0ms	a	@	-inf	(+ (* a d) (* a c))
0.0ms	a	@	0	(+ (* a d) (* a c))
0.0ms	d	@	inf	(+ (* a d) (* a c))
0.0ms	d	@	-inf	(+ (* a d) (* a c))

rewrite17.0ms (0.3%)

Algorithm

1×	batch-egg-rewrite

Rules

12×	`-lowering-.f32`
12×	`-lowering-.f64`
8×	`fma-lowering-fma.f32`
8×	`fma-define`
8×	`+-lowering-+.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	6	11
1	12	11
2	18	11
0	18	11

Stop Event

1×	iter limit
1×	saturated

Counts

3 → 12

Calls

Call 1

Inputs
(+ (* a d) (* a c))
(* a d)
(* a c)

Outputs
(+.f64 (.f64 a d) (.f64 a c))
(+.f64 (.f64 a c) (.f64 a d))
(fma.f64 a d (*.f64 a c))
(fma.f64 a c (*.f64 a d))
(fma.f64 d a (*.f64 a c))
(fma.f64 c a (*.f64 a d))
(*.f64 a (+.f64 d c))
(*.f64 (+.f64 d c) a)
(*.f64 a d)
(*.f64 d a)
(*.f64 a c)
(*.f64 c a)

simplify107.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1776×	`fnmadd-define`
1712×	`fmsub-define`
1664×	`fnmsub-define`
1504×	`fmm-def`
1410×	`-lowering-.f32`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	312
1	107	312
2	334	312
3	929	312
4	3254	312
0	8366	312

Stop Event

1×	iter limit
1×	node limit

Counts

84 → 84

Calls

Call 1

Inputs
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* a (+ c d))
(* -1 (* a (+ (* -1 c) (* -1 d))))
(* -1 (* a (+ (* -1 c) (* -1 d))))
(* -1 (* a (+ (* -1 c) (* -1 d))))
(* -1 (* a (+ (* -1 c) (* -1 d))))
(* a c)
(+ (* a c) (* a d))
(+ (* a c) (* a d))
(+ (* a c) (* a d))
(* a d)
(* d (+ a (/ (* a c) d)))
(* d (+ a (/ (* a c) d)))
(* d (+ a (/ (* a c) d)))
(* a d)
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))
(* a d)
(+ (* a c) (* a d))
(+ (* a c) (* a d))
(+ (* a c) (* a d))
(* a c)
(* c (+ a (/ (* a d) c)))
(* c (+ a (/ (* a d) c)))
(* c (+ a (/ (* a d) c)))
(* a c)
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a d)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)
(* a c)

Outputs
(* a (+ c d))
(*.f64 a (+.f64 c d))
(* a (+ c d))
(*.f64 a (+.f64 c d))
(* a (+ c d))
(*.f64 a (+.f64 c d))
(* a (+ c d))
(*.f64 a (+.f64 c d))
(* a (+ c d))
(*.f64 a (+.f64 c d))
(* a (+ c d))
(*.f64 a (+.f64 c d))
(* a (+ c d))
(*.f64 a (+.f64 c d))
(* a (+ c d))
(*.f64 a (+.f64 c d))
(* -1 (* a (+ (* -1 c) (* -1 d))))
(*.f64 a (+.f64 c d))
(* -1 (* a (+ (* -1 c) (* -1 d))))
(*.f64 a (+.f64 c d))
(* -1 (* a (+ (* -1 c) (* -1 d))))
(*.f64 a (+.f64 c d))
(* -1 (* a (+ (* -1 c) (* -1 d))))
(*.f64 a (+.f64 c d))
(* a c)
(*.f64 a c)
(+ (* a c) (* a d))
(*.f64 a (+.f64 c d))
(+ (* a c) (* a d))
(*.f64 a (+.f64 c d))
(+ (* a c) (* a d))
(*.f64 a (+.f64 c d))
(* a d)
(*.f64 a d)
(* d (+ a (/ (* a c) d)))
(*.f64 a (+.f64 c d))
(* d (+ a (/ (* a c) d)))
(*.f64 a (+.f64 c d))
(* d (+ a (/ (* a c) d)))
(*.f64 a (+.f64 c d))
(* a d)
(*.f64 a d)
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))
(*.f64 a (+.f64 c d))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))
(*.f64 a (+.f64 c d))
(* -1 (* d (+ (* -1 a) (* -1 (/ (* a c) d)))))
(*.f64 a (+.f64 c d))
(* a d)
(*.f64 a d)
(+ (* a c) (* a d))
(*.f64 a (+.f64 c d))
(+ (* a c) (* a d))
(*.f64 a (+.f64 c d))
(+ (* a c) (* a d))
(*.f64 a (+.f64 c d))
(* a c)
(*.f64 a c)
(* c (+ a (/ (* a d) c)))
(*.f64 a (+.f64 c d))
(* c (+ a (/ (* a d) c)))
(*.f64 a (+.f64 c d))
(* c (+ a (/ (* a d) c)))
(*.f64 a (+.f64 c d))
(* a c)
(*.f64 a c)
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))
(*.f64 a (+.f64 c d))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))
(*.f64 a (+.f64 c d))
(* -1 (* c (+ (* -1 a) (* -1 (/ (* a d) c)))))
(*.f64 a (+.f64 c d))
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a d)
(*.f64 a d)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)
(* a c)
(*.f64 a c)

eval19.0ms (0.4%)

Compiler: Compiled 584 to 21 computations (96.4% saved)

prune4.0ms (0.1%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	96	4	100

Accuracy

100.0%

Counts

100 → 4

Alt Table

Click to see full alt table

Status	Accuracy	Program
✓	99.9%	(+.f64 (.f64 a d) (.f64 a c))
✓	99.9%	(*.f64 a (+.f64 (+.f64 b c) d))
✓	99.9%	(*.f64 a (+.f64 c d))
✓	93.3%	(*.f64 a d)

Compiler

Compiled 73 to 40 computations (45.2% saved)

regimes19.0ms (0.4%)

Counts

5 → 1

Calls

Call 1

Inputs
(*.f64 a d)
(*.f64 a (+.f64 c d))
(*.f64 a (+.f64 (+.f64 b c) d))
(+.f64 (.f64 a d) (.f64 a c))
(+.f64 (.f64 a (+.f64 b d)) (.f64 a c))

Outputs
(+.f64 (.f64 a (+.f64 b d)) (.f64 a c))

Calls

7 calls:

5.0ms	(*.f64 a (+.f64 (+.f64 b c) d))
2.0ms	(+.f64 b c)
2.0ms	(+.f64 (+.f64 b c) d)
2.0ms	d
2.0ms	c

Results

Accuracy	Segments	Branch
100.0%	1	`a`
100.0%	1	`b`
100.0%	1	`c`
100.0%	1	`d`
100.0%	1	`(*.f64 a (+.f64 (+.f64 b c) d))`
100.0%	1	`(+.f64 (+.f64 b c) d)`
100.0%	1	`(+.f64 b c)`

Compiler

Compiled 47 to 34 computations (27.7% saved)

regimes18.0ms (0.3%)

Counts

4 → 1

Calls

Call 1

Inputs
(*.f64 a d)
(*.f64 a (+.f64 c d))
(*.f64 a (+.f64 (+.f64 b c) d))
(+.f64 (.f64 a d) (.f64 a c))

Outputs
(+.f64 (.f64 a d) (.f64 a c))

Calls

7 calls:

5.0ms	c
2.0ms	a
2.0ms	(+.f64 (+.f64 b c) d)
2.0ms	b
2.0ms	(*.f64 a (+.f64 (+.f64 b c) d))

Results

Accuracy	Segments	Branch
99.9%	1	`a`
99.9%	1	`b`
99.9%	1	`c`
99.9%	1	`d`
99.9%	1	`(*.f64 a (+.f64 (+.f64 b c) d))`
99.9%	1	`(+.f64 (+.f64 b c) d)`
99.9%	1	`(+.f64 b c)`

Compiler

Compiled 47 to 34 computations (27.7% saved)

regimes13.0ms (0.3%)

Counts

3 → 1

Calls

Call 1

Inputs
(*.f64 a d)
(*.f64 a (+.f64 c d))
(*.f64 a (+.f64 (+.f64 b c) d))

Outputs
(*.f64 a (+.f64 (+.f64 b c) d))

Calls

7 calls:

2.0ms	(*.f64 a (+.f64 (+.f64 b c) d))
2.0ms	(+.f64 b c)
2.0ms	d
2.0ms	(+.f64 (+.f64 b c) d)
2.0ms	c

Results

Accuracy	Segments	Branch
99.9%	1	`a`
99.9%	1	`b`
99.9%	1	`c`
99.9%	1	`d`
99.9%	1	`(*.f64 a (+.f64 (+.f64 b c) d))`
99.9%	1	`(+.f64 (+.f64 b c) d)`
99.9%	1	`(+.f64 b c)`

Compiler

Compiled 47 to 34 computations (27.7% saved)

regimes9.0ms (0.2%)

Counts

2 → 1

Calls

Call 1

Inputs
(*.f64 a d)
(*.f64 a (+.f64 c d))

Outputs
(*.f64 a (+.f64 c d))

Calls

4 calls:

4.0ms	c
2.0ms	b
2.0ms	a
1.0ms	d

Results

Accuracy	Segments	Branch
99.9%	1	`a`
99.9%	1	`b`
99.9%	1	`c`
99.9%	1	`d`

Compiler

Compiled 20 to 16 computations (20% saved)

regimes5.0ms (0.1%)

Accuracy

Total -0.0b remaining (-0%)

Threshold costs -0b (-0%)

Counts

1 → 1

Calls

Call 1

Inputs
(*.f64 a d)

Outputs
(*.f64 a d)

Calls

4 calls:

1.0ms	d
1.0ms	c
1.0ms	a
1.0ms	b

Results

Accuracy	Segments	Branch
93.3%	1	`a`
93.3%	1	`b`
93.3%	1	`c`
93.3%	1	`d`

Compiler

Compiled 20 to 16 computations (20% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

12×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	31
1	26	31

Stop Event

1×

saturated

Calls

Call 1

Inputs
(+.f64 (.f64 a (+.f64 b d)) (.f64 a c))
(+.f64 (.f64 a d) (.f64 a c))
(*.f64 a (+.f64 (+.f64 b c) d))
(*.f64 a (+.f64 c d))
(*.f64 a d)

Outputs
(+.f64 (.f64 a (+.f64 b d)) (.f64 a c))
(+.f64 (.f64 a d) (.f64 a c))
(+.f64 (.f64 a c) (.f64 a d))
(*.f64 a (+.f64 (+.f64 b c) d))
(*.f64 a (+.f64 d (+.f64 b c)))
(*.f64 a (+.f64 c d))
(*.f64 a (+.f64 d c))
(*.f64 a d)

soundness326.0ms (6.4%)

Rules

2422×	`-lowering-.f32`
2422×	`-lowering-.f64`
1844×	`fnmadd-define`
1184×	`/-lowering-/.f32`
1184×	`/-lowering-/.f64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	29
1	28	28
2	54	28
3	78	28
4	95	28
5	96	28
0	96	28
0	7	13
1	19	13
2	46	13
3	96	13
4	118	13
5	119	13
0	119	13
0	84	516
1	292	450
2	886	450
3	2781	450
0	8007	450

Stop Event

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

Compiler

Compiled 84 to 47 computations (44% saved)

preprocess77.0ms (1.5%)

Remove: (negabs a)
Compiler: Compiled 430 to 252 computations (41.4% saved)

Expression, p14

analyze454.0ms (9%)

sample3.2s (62.6%)

preprocess106.0ms (2.1%)

explain122.0ms (2.4%)

eval0.0ms (0%)

prune1.0ms (0%)

simplify21.0ms (0.4%)

localize31.0ms (0.6%)

series8.0ms (0.1%)

rewrite34.0ms (0.7%)

simplify149.0ms (2.9%)

eval13.0ms (0.3%)

prune7.0ms (0.1%)

simplify7.0ms (0.1%)

localize56.0ms (1.1%)

series13.0ms (0.2%)

rewrite18.0ms (0.4%)

simplify165.0ms (3.3%)

eval23.0ms (0.5%)

prune10.0ms (0.2%)

simplify5.0ms (0.1%)

localize31.0ms (0.6%)

series1.0ms (0%)

rewrite17.0ms (0.3%)

simplify107.0ms (2.1%)

eval19.0ms (0.4%)

prune4.0ms (0.1%)

regimes19.0ms (0.4%)

regimes18.0ms (0.3%)

regimes13.0ms (0.3%)

regimes9.0ms (0.2%)

regimes5.0ms (0.1%)

simplify7.0ms (0.1%)

soundness326.0ms (6.4%)

preprocess77.0ms (1.5%)

end0.0ms (0%)

Profiling