Details

analyze790.0ms (13.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
15.6%	84.2%	0.2%	8
28.1%	71.7%	0.2%	9
37.4%	62.4%	0.2%	10
41.7%	58.1%	0.2%	11
53%	46.8%	0.2%	12
64.1%	35.6%	0.3%	13
66.7%	32.8%	0.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.2s (19.8%)

Symmetry

(sort y t)

Results

1.0s	8256×	body	128	valid
51.0ms	437×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify79.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

961×	`fma-neg_binary64`
750×	`fma-def_binary64`
246×	`distribute-rgt-in_binary64`
204×	`unsub-neg_binary64`
135×	`cancel-sign-sub-inv_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	35	13
3	88	13
4	231	13
5	568	13
6	1029	13
7	1474	13
8	1787	13
9	1744	13
10	1744	13
11	1905	13
12	1905	13
13	1862	13

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

8.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	8.9b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) (-.f64 t z))
✓	8.8b	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

series137.0ms (2.3%)

Counts

2 → 84

Calls

2 calls:

126.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))
10.0ms	(*.f64 (-.f64 y z) (-.f64 t z))

rewrite22.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 89

Calls

2 calls:

9.0ms	(*.f64 (-.f64 y z) (-.f64 t z))
7.0ms	(/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))

simplify125.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

545×	`times-frac_binary64`
452×	`associate-/l*_binary64`
442×	`associate-/r*_binary64`
280×	`associate-l_binary64`
188×	`fma-def_binary64`

Counts

173 → 193

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	423	5441
1	1244	5124
2	4955	5124
3	5000	5124

prune203.0ms (3.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	184	9	193
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	185	9	194

Error

0.0b

Counts

194 → 9

Alt Table

Status	Error	Program
	21.2b	(.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 (.f64 t t) (.f64 z z)))) (+.f64 t z))
	2.4b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	1.5b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	2.8b	(/.f64 1 (/.f64 (-.f64 y z) (/.f64 x (-.f64 t z))))
	9.4b	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) x))
	9.4b	(.f64 (.f64 (cbrt.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 t z)))) (cbrt.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 t z))))) (cbrt.f64 (/.f64 x (*.f64 (-.f64 y z) (-.f64 t z)))))
	21.7b	(.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 t z))) (+.f64 y z))
	12.4b	(/.f64 x (-.f64 (fma.f64 t y (.f64 z z)) (.f64 z (+.f64 y t))))
▶	1.1b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))

Compiler

Compiled 5830 to 2159 computations (63% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z))
✓	0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.5b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
✓	0.6b	(cbrt.f64 x)

series290.0ms (5%)

Counts

4 → 108

Calls

4 calls:

135.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
81.0ms	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z))
38.0ms	(cbrt.f64 x)
35.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))

rewrite52.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
47×	`times-frac_binary64`
42×	`associate-r_binary64`
36×	`cbrt-prod_binary64`

Counts

4 → 163

Calls

4 calls:

20.0ms	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
9.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
6.0ms	(/.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z))
1.0ms	(cbrt.f64 x)

simplify130.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

742×	`times-frac_binary64`
678×	`associate-/l*_binary64`
491×	`associate-/r*_binary64`
190×	`fma-def_binary64`
138×	`*-commutative_binary64`

Counts

271 → 313

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	494	7735
1	1554	6690
2	5178	6690

prune286.0ms (4.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	345	2	347
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	347	9	356

Error

0.0b

Counts

356 → 9

Alt Table

Status	Error	Program
	21.2b	(.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 (.f64 t t) (.f64 z z)))) (+.f64 t z))
	2.4b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	2.3b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
	1.5b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	9.4b	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) x))
▶	1.2b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 x))) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	21.7b	(.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 t z))) (+.f64 y z))
	12.4b	(/.f64 x (-.f64 (fma.f64 t y (.f64 z z)) (.f64 z (+.f64 y t))))
✓	1.1b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))

Compiler

Compiled 9979 to 3024 computations (69.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 x))) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
✓	0.6b	(cbrt.f64 (cbrt.f64 x))
✓	0.6b	(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))
	0.6b	(cbrt.f64 x)

series764.0ms (13.1%)

Counts

3 → 72

Calls

3 calls:

309.0ms

(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))

267.0ms

(cbrt.f64 (cbrt.f64 x))

189.0ms

(*.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 x))) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
38×	`*-un-lft-identity_binary64`
37×	`times-frac_binary64`
36×	`associate-r_binary64`
35×	`add-exp-log_binary64`

Counts

3 → 107

Calls

3 calls:

22.0ms

(*.f64 (/.f64 (*.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 x))) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))

3.0ms

(cbrt.f64 (*.f64 (cbrt.f64 x) (cbrt.f64 x)))

1.0ms

(cbrt.f64 (cbrt.f64 x))

simplify134.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

597×	`times-frac_binary64`
569×	`associate-/l*_binary64`
413×	`associate-/r*_binary64`
284×	`associate-*r/_binary64`
245×	`associate-*l/_binary64`

Counts

179 → 215

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	449	7432
1	1446	6805
2	5137	6805

prune254.0ms (4.4%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	300	0	300
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	300	9	309

Error

0.0b

Counts

309 → 9

Alt Table

Status	Error	Program
	21.2b	(.f64 (/.f64 x (.f64 (-.f64 y z) (-.f64 (.f64 t t) (.f64 z z)))) (+.f64 t z))
	2.4b	(*.f64 (/.f64 1 (-.f64 y z)) (/.f64 x (-.f64 t z)))
	2.3b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
▶	1.5b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	9.4b	(/.f64 1 (/.f64 (*.f64 (-.f64 y z) (-.f64 t z)) x))
✓	1.2b	(.f64 (/.f64 (.f64 (.f64 (cbrt.f64 x) (cbrt.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)))) (cbrt.f64 (cbrt.f64 x))) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))
	21.7b	(.f64 (/.f64 x (.f64 (-.f64 (.f64 y y) (.f64 z z)) (-.f64 t z))) (+.f64 y z))
	12.4b	(/.f64 x (-.f64 (fma.f64 t y (.f64 z z)) (.f64 z (+.f64 y t))))
✓	1.1b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))

Compiler

Compiled 11093 to 2681 computations (75.8% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 x (-.f64 y z))
✓	1.5b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))

series144.0ms (2.5%)

Counts

2 → 72

Calls

2 calls:

126.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
18.0ms	(/.f64 x (-.f64 y z))

rewrite39.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
176×	`*-un-lft-identity_binary64`
176×	`add-sqr-sqrt_binary64`
88×	`add-cube-cbrt_binary64`
44×	`distribute-lft-out--_binary64`

Counts

2 → 189

Calls

2 calls:

11.0ms	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
4.0ms	(/.f64 x (-.f64 y z))

simplify151.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

540×	`times-frac_binary64`
486×	`associate-/r*_binary64`
474×	`associate-/l*_binary64`
312×	`associate-/l/_binary64`
154×	`fma-def_binary64`

Counts

261 → 270

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	526	8754
1	1583	8488
2	5002	8488

prune188.0ms (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	267	3	270
Fresh	4	2	6
Picked	0	1	1
Done	1	1	2
Total	272	7	279

Error

Counts

279 → 7

Alt Table

Status	Error	Program
	43.6b	(*.f64 (/.f64 1 (sqrt.f64 (-.f64 y z))) (/.f64 (/.f64 x (sqrt.f64 (-.f64 y z))) (-.f64 t z)))
	8.6b	(*.f64 (/.f64 x 1) (/.f64 (/.f64 1 (-.f64 y z)) (-.f64 t z)))
	2.3b	(/.f64 (/.f64 x (-.f64 t z)) (-.f64 y z))
✓	1.5b	(/.f64 (/.f64 x (-.f64 y z)) (-.f64 t z))
	1.5b	(/.f64 (*.f64 x (/.f64 1 (-.f64 y z))) (-.f64 t z))
	12.4b	(/.f64 x (-.f64 (fma.f64 t y (.f64 z z)) (.f64 z (+.f64 y t))))
✓	1.1b	(.f64 (/.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (-.f64 y z)) (/.f64 (cbrt.f64 x) (-.f64 t z)))

Compiler

Compiled 7582 to 2294 computations (69.7% saved)

regimes582.0ms (10%)

Accuracy

Total 1.7b remaining (99%)

Threshold costs 0b (0%)

Counts

97 → 1

Compiler

Compiled 11643 to 6842 computations (41.2% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
3×	`sub-neg_binary64`
2×	`*-commutative_binary64`
1×	`neg-sub0_binary64`
1×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	23
1	17	23
2	23	23
3	25	23
4	26	23
5	26	23

end226.0ms (3.9%)

Compiler: Compiled 193 to 119 computations (38.3% saved)

Details

analyze790.0ms (13.5%)

sample1.2s (19.8%)

simplify79.0ms (1.3%)

prune2.0ms (0%)

localize6.0ms (0.1%)

series137.0ms (2.3%)

rewrite22.0ms (0.4%)

simplify125.0ms (2.1%)

prune203.0ms (3.5%)

localize10.0ms (0.2%)

series290.0ms (5%)

rewrite52.0ms (0.9%)

simplify130.0ms (2.2%)

prune286.0ms (4.9%)

localize17.0ms (0.3%)

series764.0ms (13.1%)

rewrite40.0ms (0.7%)

simplify134.0ms (2.3%)

prune254.0ms (4.4%)

localize7.0ms (0.1%)

series144.0ms (2.5%)

rewrite39.0ms (0.7%)

simplify151.0ms (2.6%)

prune188.0ms (3.2%)

regimes582.0ms (10%)

simplify3.0ms (0%)

end226.0ms (3.9%)

Profiling