Details

analyze114.0ms (2.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
46.8%	53.1%	0.1%	6
70.2%	29.7%	0.1%	7
76.5%	23.4%	0.1%	8
83.5%	16.4%	0.1%	9
87%	12.9%	0.1%	10
91.1%	8.8%	0.1%	11
93.2%	6.7%	0.1%	12
95.4%	4.5%	0.1%	13
96.5%	3.4%	0.1%	14

Compiler

Compiled 20 to 10 computations (50% saved)

sample965.0ms (18%)

Symmetry

(sort x y)

Results

828.0ms

8256×

body

128

valid

Compiler

Compiled 59 to 29 computations (50.8% saved)

simplify143.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

985×	`associate-/l*_binary64`
659×	`distribute-lft-out_binary64`
601×	`*-commutative_binary64`
469×	`distribute-rgt-out_binary64`
356×	`fma-def_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	25
1	39	25
2	135	23
3	474	23
4	1536	23
5	2122	23
6	2589	23
7	2567	23
8	2620	23
9	2677	23
10	2770	23
11	3956	23
12	4088	23
13	4454	23
14	4983	23
15	4968	23
16	4961	23

prune3.0ms (0.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

19.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	19.3b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
	19.3b	(/.f64 (.f64 x y) (.f64 (*.f64 (+.f64 x y) (+.f64 x y)) (+.f64 (+.f64 x y) 1)))

Compiler

Compiled 109 to 47 computations (56.9% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 x y) 3)
✓	0.0b	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
✓	19.1b	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))

series93.0ms (1.7%)

Counts

3 → 72

Calls

3 calls:

74.0ms	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
11.0ms	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))
8.0ms	(pow.f64 (+.f64 x y) 3)

rewrite9.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 62

Calls

3 calls:

3.0ms	(/.f64 (*.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))
3.0ms	(pow.f64 (+.f64 x y) 3)
0.0ms	(fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3))

simplify153.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

326×	`fma-def_binary64`
301×	`times-frac_binary64`
297×	`associate-+r+_binary64`
257×	`associate-/l*_binary64`
223×	`+-commutative_binary64`

Counts

134 → 162

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	347	4819
1	1047	4272
2	4702	4260
3	4981	4260
4	4996	4260
5	4981	4260

prune191.0ms (3.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	155	7	162
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	157	7	164

Error

4.5b

Counts

164 → 7

Alt Table

Status	Error	Program
	26.7b	(/.f64 (.f64 x y) (+.f64 (fma.f64 y y (fma.f64 3 (fma.f64 x (.f64 y y) (.f64 y (.f64 x x))) (fma.f64 x x (pow.f64 x 3)))) (fma.f64 (*.f64 y x) 2 (pow.f64 y 3))))
▶	19.3b	(/.f64 (.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x))))
	43.3b	(/.f64 x (pow.f64 y 2))
	20.7b	(*.f64 x (/.f64 y (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))))
	35.5b	(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
	31.9b	(*.f64 (/.f64 x (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))) (/.f64 y (sqrt.f64 (fma.f64 (+.f64 x y) (+.f64 x y) (pow.f64 (+.f64 x y) 3)))))
	40.0b	(/.f64 y (pow.f64 x 2))

Compiler

Compiled 5933 to 3148 computations (46.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(pow.f64 (+.f64 y x) 2)
✓	0.0b	(fma.f64 (+.f64 x y) (+.f64 x y) (*.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x)))
✓	0.1b	(*.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x))
✓	19.1b	(/.f64 (.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x))))

series94.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

68.0ms	(/.f64 (.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x))))
13.0ms	(fma.f64 (+.f64 x y) (+.f64 x y) (*.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x)))
8.0ms	(*.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x))
5.0ms	(pow.f64 (+.f64 y x) 2)

rewrite18.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64`
11×	`add-cube-cbrt_binary64`
11×	`add-cbrt-cube_binary64`

Counts

4 → 92

Calls

4 calls:

7.0ms	(*.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x))
4.0ms	(pow.f64 (+.f64 y x) 2)
3.0ms	(/.f64 (.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x))))
0.0ms	(fma.f64 (+.f64 x y) (+.f64 x y) (*.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x)))

simplify92.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

350×	`fma-def_binary64`
301×	`times-frac_binary64`
300×	`associate-+r+_binary64`
257×	`associate-/l*_binary64`
217×	`associate-+l+_binary64`

Counts

188 → 211

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	377	5543
1	1101	4854
2	5009	4854

prune207.0ms (3.9%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	210	1	211
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	211	7	218

Error

4.5b

Counts

218 → 7

Alt Table

Status	Error	Program
	31.9b	(*.f64 (/.f64 x (sqrt.f64 (+.f64 (pow.f64 (+.f64 y x) 2) (pow.f64 (+.f64 y x) 3)))) (/.f64 y (sqrt.f64 (+.f64 (pow.f64 (+.f64 y x) 2) (pow.f64 (+.f64 y x) 3)))))
	26.7b	(/.f64 (.f64 x y) (+.f64 (fma.f64 y y (fma.f64 3 (fma.f64 x (.f64 y y) (.f64 y (.f64 x x))) (fma.f64 x x (pow.f64 x 3)))) (fma.f64 (*.f64 y x) 2 (pow.f64 y 3))))
✓	19.3b	(/.f64 (.f64 x y) (fma.f64 (+.f64 x y) (+.f64 x y) (.f64 (pow.f64 (+.f64 y x) 2) (+.f64 y x))))
	43.3b	(/.f64 x (pow.f64 y 2))
▶	20.7b	(*.f64 x (/.f64 y (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))))
	35.5b	(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
	40.0b	(/.f64 y (pow.f64 x 2))

Compiler

Compiled 7560 to 3622 computations (52.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(pow.f64 (+.f64 y x) 2)
✓	5.2b	(*.f64 x (/.f64 y (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))))
✓	6.4b	(/.f64 y (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2)))
✓	12.3b	(+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))

series150.0ms (2.8%)

Counts

3 → 72

Calls

3 calls:

71.0ms	(*.f64 x (/.f64 y (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))))
63.0ms	(/.f64 y (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2)))
15.0ms	(+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))

rewrite47.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
33×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`
24×	`associate-r_binary64`

Counts

3 → 118

Calls

3 calls:

16.0ms	(*.f64 x (/.f64 y (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))))
12.0ms	(+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))
11.0ms	(/.f64 y (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2)))

simplify119.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

498×	`fma-def_binary64`
419×	`times-frac_binary64`
358×	`associate-/l*_binary64`
306×	`associate-/r*_binary64`
187×	`associate-l_binary64`

Counts

190 → 252

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	515	7975
1	1627	7307
2	5026	7307

prune332.0ms (6.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	282	5	287
Fresh	3	2	5
Picked	0	1	1
Done	1	0	1
Total	286	8	294

Error

2.6b

Counts

294 → 8

Alt Table

Status	Error	Program
	20.7b	(.f64 x (/.f64 y (fma.f64 2 (.f64 x y) (fma.f64 y y (fma.f64 3 (fma.f64 x (.f64 y y) (.f64 x (*.f64 x y))) (fma.f64 x x (pow.f64 x 3)))))))
	35.5b	(*.f64 (/.f64 x (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))) (/.f64 y (hypot.f64 (+.f64 y x) (pow.f64 (+.f64 y x) 3/2))))
	26.7b	(/.f64 (.f64 x y) (+.f64 (fma.f64 y y (fma.f64 3 (fma.f64 x (.f64 y y) (.f64 y (.f64 x x))) (fma.f64 x x (pow.f64 x 3)))) (fma.f64 (*.f64 y x) 2 (pow.f64 y 3))))
	48.3b	(.f64 (.f64 (/.f64 (sqrt.f64 y) (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))) (sqrt.f64 x)) (*.f64 (/.f64 (sqrt.f64 y) (hypot.f64 (+.f64 x y) (pow.f64 (+.f64 x y) 3/2))) (sqrt.f64 x)))
	5.4b	(.f64 x (/.f64 (/.f64 y (+.f64 y x)) (+.f64 (.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x))))
▶	4.0b	(.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x))))
✓	20.7b	(*.f64 x (/.f64 y (+.f64 (pow.f64 (+.f64 y x) 3) (pow.f64 (+.f64 y x) 2))))
	21.7b	(.f64 (.f64 x (/.f64 (sqrt.f64 y) (+.f64 y x))) (/.f64 (sqrt.f64 y) (+.f64 (*.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x))))

Compiler

Compiled 11157 to 6474 computations (42% saved)

localize8.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (+.f64 y x) (+.f64 y x))
✓	0.0b	(/.f64 x (+.f64 x y))
✓	0.1b	(.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x))))
✓	14.4b	(/.f64 y (+.f64 (*.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x)))

series176.0ms (3.3%)

Counts

4 → 96

Calls

4 calls:

78.0ms	(.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x))))
47.0ms	(/.f64 x (+.f64 x y))
46.0ms	(/.f64 y (+.f64 (*.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x)))
6.0ms	(*.f64 (+.f64 y x) (+.f64 y x))

rewrite69.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`*-un-lft-identity_binary64`
64×	`times-frac_binary64`
60×	`add-sqr-sqrt_binary64`
50×	`flip-+_binary64`
50×	`flip3-+_binary64`

Counts

4 → 220

Calls

4 calls:

24.0ms	(.f64 (/.f64 x (+.f64 x y)) (/.f64 y (+.f64 (.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x))))
9.0ms	(/.f64 y (+.f64 (*.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x)))
6.0ms	(*.f64 (+.f64 y x) (+.f64 y x))
5.0ms	(/.f64 x (+.f64 x y))

simplify198.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

516×	`times-frac_binary64`
514×	`fma-def_binary64`
294×	`distribute-rgt-in_binary64`
282×	`distribute-lft-in_binary64`
183×	`*-commutative_binary64`

Counts

316 → 416

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	655	10722
1	1997	9531
2	4929	9531
3	4993	9531

prune786.0ms (14.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	409	7	416
Fresh	4	2	6
Picked	1	0	1
Done	1	0	1
Total	415	9	424

Error

0.0b

Counts

424 → 9

Alt Table

Status	Error	Program
	0.7b	(.f64 (.f64 (/.f64 x (+.f64 x y)) (/.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (+.f64 (+.f64 y x) 1))) (/.f64 (cbrt.f64 y) (+.f64 y x)))
	0.1b	(*.f64 (/.f64 x (+.f64 x y)) (/.f64 (/.f64 y (+.f64 y x)) (+.f64 (+.f64 y x) 1)))
	19.1b	(cbrt.f64 (.f64 (pow.f64 (/.f64 y (.f64 (+.f64 y x) (+.f64 1 (+.f64 y x)))) 3) (pow.f64 (/.f64 x (+.f64 y x)) 3)))
	26.7b	(/.f64 (.f64 x y) (+.f64 (fma.f64 y y (fma.f64 3 (fma.f64 x (.f64 y y) (.f64 y (.f64 x x))) (fma.f64 x x (pow.f64 x 3)))) (fma.f64 (*.f64 y x) 2 (pow.f64 y 3))))
	4.0b	(.f64 (.f64 (/.f64 x (+.f64 x y)) y) (/.f64 1 (+.f64 (*.f64 (+.f64 y x) (+.f64 y x)) (+.f64 y x))))
	5.4b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) 1) (.f64 (/.f64 y (.f64 (+.f64 y x) (+.f64 1 (+.f64 y x)))) (/.f64 (cbrt.f64 x) (+.f64 y x))))
	19.2b	(.f64 (/.f64 x (+.f64 x y)) (.f64 (/.f64 (sqrt.f64 y) (+.f64 (+.f64 y x) 1)) (/.f64 (sqrt.f64 y) (+.f64 y x))))
	0.1b	(/.f64 (*.f64 (/.f64 y (+.f64 1 (+.f64 y x))) (/.f64 x (+.f64 y x))) (+.f64 x y))
	20.7b	(.f64 x (/.f64 y (fma.f64 2 (.f64 x y) (fma.f64 y y (fma.f64 3 (fma.f64 x (.f64 y y) (.f64 x (*.f64 x y))) (fma.f64 x x (pow.f64 x 3)))))))

Compiler

Compiled 16521 to 4871 computations (70.5% saved)

regimes1.1s (20.1%)

Accuracy

Total 0.1b remaining (75.7%)

Threshold costs 0.1b (75.7%)

Counts

305 → 1

Compiler

Compiled 20891 to 11060 computations (47.1% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

2×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	25
1	15	25
2	14	25

end280.0ms (5.2%)

Compiler: Compiled 306 to 156 computations (49% saved)

Details

analyze114.0ms (2.1%)

sample965.0ms (18%)

simplify143.0ms (2.7%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series93.0ms (1.7%)

rewrite9.0ms (0.2%)

simplify153.0ms (2.9%)

prune191.0ms (3.6%)

localize11.0ms (0.2%)

series94.0ms (1.8%)

rewrite18.0ms (0.3%)

simplify92.0ms (1.7%)

prune207.0ms (3.9%)

localize7.0ms (0.1%)

series150.0ms (2.8%)

rewrite47.0ms (0.9%)

simplify119.0ms (2.2%)

prune332.0ms (6.2%)

localize8.0ms (0.2%)

series176.0ms (3.3%)

rewrite69.0ms (1.3%)

simplify198.0ms (3.7%)

prune786.0ms (14.7%)

regimes1.1s (20.1%)

simplify2.0ms (0%)

end280.0ms (5.2%)

Profiling