Details

analyze1.7s (8.2%)

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
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.7%	0.3%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample2.1s (10.2%)

Results

997.0ms	6935×	body	128	valid
431.0ms	610×	body	8192	exit
161.0ms	379×	body	1024	valid
160.0ms	500×	body	512	valid
90.0ms	61×	body	2048	valid
85.0ms	381×	body	256	valid
83.0ms	598×	body	128	invalid

Compiler

Compiled 37 to 23 computations (37.8% saved)

simplify86.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

836×	`unsub-neg_binary64`
769×	`fma-def_binary64`
696×	`div-sub_binary64`
646×	`sub-neg_binary64`
478×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	21	19
2	52	17
3	144	17
4	421	17
5	1092	17
6	2657	17
7	3901	17
8	4408	17
9	4807	17
10	4881	17

prune4.0ms (0%)

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

10.9b

Counts

3 → 2

Alt Table

Status	Error	Program
	22.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
▶	13.6b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

Compiler

Compiled 100 to 55 computations (45% saved)

localize8.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	13.6b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series92.0ms (0.4%)

Counts

2 → 108

Calls

2 calls:

63.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
28.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

9.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

simplify128.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

523×	`cancel-sign-sub-inv_binary64`
479×	`sub-neg_binary64`
353×	`associate-+r+_binary64`
286×	`+-commutative_binary64`
272×	`associate-+l+_binary64`

Counts

172 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	6269
1	1045	6192
2	3851	6156
3	5233	6156

prune123.0ms (0.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	130	6	136
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	132	6	138

Error

0.2b

Counts

138 → 6

Alt Table

Status	Error	Program
	32.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	34.5b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	42.5b	(-.f64 (+.f64 (/.f64 (.f64 y (.f64 t (pow.f64 z 2))) (pow.f64 a 3)) (+.f64 (/.f64 (.f64 y (.f64 t z)) (pow.f64 a 2)) (+.f64 (/.f64 (.f64 y t) a) (+.f64 (/.f64 (.f64 (pow.f64 z 2) x) (pow.f64 a 2)) (+.f64 (/.f64 (.f64 z x) a) x))))) (+.f64 (/.f64 (.f64 t (pow.f64 z 2)) (pow.f64 a 2)) (+.f64 (/.f64 (.f64 y (.f64 (pow.f64 z 2) x)) (pow.f64 a 3)) (+.f64 (/.f64 (.f64 y x) a) (+.f64 (/.f64 (.f64 y (.f64 z x)) (pow.f64 a 2)) (/.f64 (.f64 t z) a))))))
▶	13.7b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
	42.9b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	34.8b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)

Compiler

Compiled 4806 to 1520 computations (68.4% saved)

localize10.0ms (0%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	0.3b	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
✓	13.6b	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

series105.0ms (0.5%)

Counts

3 → 132

Calls

3 calls:

64.0ms	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)
33.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
8.0ms	(/.f64 1 (-.f64 a z))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`add-sqr-sqrt_binary64`
40×	`*-un-lft-identity_binary64`
32×	`times-frac_binary64`
23×	`add-cube-cbrt_binary64`
21×	`associate-r_binary64`

Counts

3 → 105

Calls

3 calls:

11.0ms	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
4.0ms	(/.f64 1 (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))) x)

simplify141.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

485×	`sub-neg_binary64`
371×	`associate-+r+_binary64`
307×	`+-commutative_binary64`
285×	`associate-+l+_binary64`
246×	`fma-neg_binary64`

Counts

237 → 220

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	385	7102
1	1097	6803
2	4197	6767
3	5010	6767

prune154.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	219	1	220
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	220	6	226

Error

0.2b

Counts

226 → 6

Alt Table

Status	Error	Program
	42.5b	(-.f64 (+.f64 (/.f64 (.f64 y (.f64 t (pow.f64 z 2))) (pow.f64 a 3)) (+.f64 (/.f64 (.f64 y (.f64 t z)) (pow.f64 a 2)) (+.f64 (/.f64 (.f64 y t) a) (+.f64 (/.f64 (.f64 (pow.f64 z 2) x) (pow.f64 a 2)) (+.f64 (/.f64 (.f64 z x) a) x))))) (+.f64 (/.f64 (.f64 t (pow.f64 z 2)) (pow.f64 a 2)) (+.f64 (/.f64 (.f64 y (.f64 (pow.f64 z 2) x)) (pow.f64 a 3)) (+.f64 (/.f64 (.f64 y x) a) (+.f64 (/.f64 (.f64 y (.f64 z x)) (pow.f64 a 2)) (/.f64 (.f64 t z) a))))))
▶	13.7b	(+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)
	32.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	34.5b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	42.9b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	34.8b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)

Compiler

Compiled 6694 to 2356 computations (64.8% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 1 (-.f64 a z))
	0.3b	(*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))
✓	3.5b	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))
✓	3.7b	(+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)

series187.0ms (0.9%)

Counts

2 → 120

Calls

2 calls:

118.0ms	(+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)
68.0ms	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))

rewrite31.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`frac-times_binary64`
17×	`add-exp-log_binary64`
13×	`flip--_binary64`
13×	`flip3--_binary64`
11×	`add-cbrt-cube_binary64`

Counts

2 → 60

Calls

2 calls:

13.0ms	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))
13.0ms	(+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)

simplify174.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

429×	`associate-+l+_binary64`
308×	`fma-neg_binary64`
256×	`associate-l_binary64`
251×	`associate--l+_binary64`
240×	`associate-r_binary64`

Counts

180 → 186

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	445	8808
1	1381	8767
2	4886	8767
3	5160	8767

prune270.0ms (1.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	333	4	337
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	334	9	343

Error

0.1b

Counts

343 → 9

Alt Table

Status	Error	Program
	42.9b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	38.4b	(+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (+.f64 (+.f64 (/.f64 1 a) (/.f64 z (.f64 a a))) (/.f64 (.f64 z z) (pow.f64 a 3))))) x)
	39.0b	(+.f64 (/.f64 (.f64 (-.f64 y z) (-.f64 (.f64 t t) (.f64 x x))) (.f64 (+.f64 t x) (-.f64 a z))) x)
	32.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	34.5b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
✓	13.7b	(+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)
	22.9b	(+.f64 (.f64 (.f64 (-.f64 y z) (-.f64 t x)) (/.f64 1 (-.f64 a z))) x)
▶	14.6b	(.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)) (cbrt.f64 (+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x))) (cbrt.f64 (+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)))
	34.8b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)

Compiler

Compiled 11494 to 4010 computations (65.1% saved)

localize14.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(.f64 (cbrt.f64 (+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)) (cbrt.f64 (+.f64 (.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)))
✓	0.5b	(cbrt.f64 (+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x))
	3.5b	(.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z))))
	3.7b	(+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)

series9.6s (46.7%)

Counts

2 → 120

Calls

2 calls:

8.1s

(*.f64 (cbrt.f64 (+.f64 (*.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)) (cbrt.f64 (+.f64 (*.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)))

1.5s

(cbrt.f64 (+.f64 (*.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x))

rewrite54.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
14×	`cbrt-div_binary64`
11×	`*-un-lft-identity_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 65

Calls

2 calls:

31.0ms

(*.f64 (cbrt.f64 (+.f64 (*.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)) (cbrt.f64 (+.f64 (*.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)))

14.0ms

(cbrt.f64 (+.f64 (*.f64 (-.f64 y z) (*.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x))

simplify682.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

185 → 171

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5899	119030

prune2.2s (10.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	868	1	869
Fresh	0	7	7
Picked	1	0	1
Done	0	1	1
Total	869	9	878

Error

0.1b

Counts

878 → 9

Alt Table

Status	Error	Program
	34.5b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	16.8b	(.f64 (expm1.f64 (log1p.f64 (.f64 (cbrt.f64 (+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)) (cbrt.f64 (+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x))))) (cbrt.f64 (+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)))
	42.9b	(*.f64 y (-.f64 (/.f64 t (-.f64 a z)) (/.f64 x (-.f64 a z))))
	38.4b	(+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (+.f64 (+.f64 (/.f64 1 a) (/.f64 z (.f64 a a))) (/.f64 (.f64 z z) (pow.f64 a 3))))) x)
	39.0b	(+.f64 (/.f64 (.f64 (-.f64 y z) (-.f64 (.f64 t t) (.f64 x x))) (.f64 (+.f64 t x) (-.f64 a z))) x)
	32.3b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
✓	13.7b	(+.f64 (.f64 (-.f64 y z) (.f64 (-.f64 t x) (/.f64 1 (-.f64 a z)))) x)
	22.9b	(+.f64 (.f64 (.f64 (-.f64 y z) (-.f64 t x)) (/.f64 1 (-.f64 a z))) x)
	34.8b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)

Compiler

Compiled 168091 to 77303 computations (54% saved)

regimes2.5s (12.2%)

Accuracy

Total 6.2b remaining (87.2%)

Threshold costs 0b (0%)

Counts

137 → 5

Compiler

Compiled 22788 to 13074 computations (42.6% saved)

bsearch6.0ms (0%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify13.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`+-commutative_binary64`
24×	`*-commutative_binary64`
20×	`sub-neg_binary64`
15×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	270
1	82	270
2	104	270
3	132	270
4	171	270
5	189	270
6	199	270
7	202	270
8	201	270

end150.0ms (0.7%)

Compiler: Compiled 615 to 244 computations (60.3% saved)

Iter	Nodes	Cost
0	55	270
1	82	270
2	104	270
3	132	270
4	171	270
5	189	270
6	199	270
7	202	270
8	201	270

Iter	Nodes	Cost
0	55	270
1	82	270
2	104	270
3	132	270
4	171	270
5	189	270
6	199	270
7	202	270
8	201	270

Details

analyze1.7s (8.2%)

sample2.1s (10.2%)

simplify86.0ms (0.4%)

prune4.0ms (0%)

localize8.0ms (0%)

series92.0ms (0.4%)

rewrite14.0ms (0.1%)

simplify128.0ms (0.6%)

prune123.0ms (0.6%)

localize10.0ms (0%)

series105.0ms (0.5%)

rewrite21.0ms (0.1%)

simplify141.0ms (0.7%)

prune154.0ms (0.8%)

localize11.0ms (0.1%)

series187.0ms (0.9%)

rewrite31.0ms (0.2%)

simplify174.0ms (0.8%)

prune270.0ms (1.3%)

localize14.0ms (0.1%)

series9.6s (46.7%)

rewrite54.0ms (0.3%)

simplify682.0ms (3.3%)

prune2.2s (10.7%)

regimes2.5s (12.2%)

bsearch6.0ms (0%)

simplify13.0ms (0.1%)

end150.0ms (0.7%)

Profiling

Iter	Nodes	Cost
0	55	270
1	82	270
2	104	270
3	132	270
4	171	270
5	189	270
6	199	270
7	202	270
8	201	270