Details

analyze912.0ms (5.3%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	5644	164
0	3	3
1	3	3

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
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Symmetry

Compiler

Compiled 28 to 21 computations (25% saved)

sample58.0ms (0.3%)

Algorithm

1×

intervals

Results

11.0ms	170×	body	128	valid
9.0ms	35×	body	1024	valid
7.0ms	35×	body	512	valid
6.0ms	26×	body	1024	nan
3.0ms	17×	body	512	nan
3.0ms	50×	body	128	nan
2.0ms	16×	body	256	valid
1.0ms	9×	body	256	nan

Compiler

Compiled 55 to 44 computations (20% saved)

simplify71.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	5192	41

prune3.0ms (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

42.0b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize19.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.4b	(*.f64 (sqrt.f64 2) t)
14.5b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
19.7b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite229.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Error

41.8b

Rules

17×	`add-sqr-sqrt_binary64_100`
13×	`sqrt-prod_binary64_94`
12×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
11×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
7×	`pow1_binary64_139`
6×	`add-log-exp_binary64_117` `associate-l_binary64_19` `times-frac_binary64_84` `associate-/r*_binary64_22`
4×	`sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `flip--_binary64_53` `associate-r_binary64_18`
2×	`associate--l+_binary64_15` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `unswap-sqr_binary64_46` `div-exp_binary64_129` `cbrt-undiv_binary64_112` `associate-/r/_binary64_24`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `sub-neg_binary64_71` `cancel-sign-sub-inv_binary64_44` `distribute-rgt-in_binary64_28` `distribute-lft-in_binary64_27` `pow-prod-down_binary64_149` `-commutative_binary64_9` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23`

Counts

4 → 80

Calls

4 calls:

20.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
15.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
15.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
6.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 3564 to 2030 computations (43% saved)

series4.2s (24.5%)

Error

6.4b

Counts

4 → 61

Calls

4 calls:

2.1s	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
1.3s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
679.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
34.0ms	(*.f64 (sqrt.f64 2) t)

Compiler

Compiled 11466 to 9525 computations (16.9% saved)

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (20.0ms)

Iter	Nodes	Cost
0	4978	6801
1	4978	6801

prune296.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	135	6	141
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	136	6	142

Error

6.4b

Counts

142 → 6

Compiler

Compiled 6204 to 3867 computations (37.7% saved)

localize16.0ms (0.1%)

Local error

Found 4 expressions with local error:

2.8b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
5.9b	(/.f64 (*.f64 l l) x)
9.1b	(/.f64 (*.f64 t t) x)
27.8b	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))

rewrite142.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Error

5.0b

Rules

14×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
10×	`add-sqr-sqrt_binary64_100`
9×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
6×	`add-log-exp_binary64_117` `times-frac_binary64_84` `associate-/r*_binary64_22`
5×	`pow1_binary64_139`
4×	`sqrt-div_binary64_95` `div-exp_binary64_129` `cbrt-undiv_binary64_112`
3×	`flip3-+_binary64_81` `flip-+_binary64_52` `sqrt-prod_binary64_94`
2×	`associate-r/_binary64_20` `frac-add_binary64_86` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l_binary64_23`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `sum-log_binary64_169` `+-commutative_binary64_8`

Counts

4 → 70

Calls

4 calls:

12.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
7.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
5.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 2731 to 1340 computations (50.9% saved)

series940.0ms (5.4%)

Error

0.3b

Counts

4 → 45

Calls

4 calls:

596.0ms	(sqrt.f64 (+.f64 (.f64 2 (/.f64 (.f64 l l) x)) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
136.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
70.0ms	(/.f64 (*.f64 l l) x)
65.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 4622 to 3742 computations (19% saved)

simplify78.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5163	2849

prune173.0ms (1%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	110	5	115
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	112	9	121

Error

0.3b

Counts

121 → 9

Compiler

Compiled 4048 to 2247 computations (44.5% saved)

localize23.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x))))
2.8b	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
9.1b	(/.f64 (*.f64 t t) x)
27.8b	(sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x)))))

rewrite202.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

16×	`associate-*r/_binary64_20`
12×	`frac-add_binary64_86`
11×	`add-log-exp_binary64_117`
9×	`add-exp-log_binary64_116` `add-cbrt-cube_binary64_114` `flip3-+_binary64_81` `flip-+_binary64_52`
8×	`add-sqr-sqrt_binary64_100` `sqrt-div_binary64_95`
7×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
5×	`pow1_binary64_139`
4×	`frac-times_binary64_88` `associate-*l/_binary64_21` `sum-log_binary64_169`
3×	`sqrt-prod_binary64_94` `times-frac_binary64_84` `associate-/r*_binary64_22`
2×	`div-exp_binary64_129` `cbrt-undiv_binary64_112` `+-commutative_binary64_8`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91` `prod-exp_binary64_127` `cbrt-unprod_binary64_111` `frac-2neg_binary64_89` `clear-num_binary64_77` `div-inv_binary64_75` `associate-/l*_binary64_23` `associate-+r+_binary64_10`

Counts

4 → 72

Calls

4 calls:

21.0ms	(+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x))))
19.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x)))))
7.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
5.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 4308 to 1743 computations (59.5% saved)

series1.3s (7.6%)

Error

0.3b

Counts

4 → 57

Calls

4 calls:

613.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x)))))
399.0ms	(+.f64 (.f64 2 (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (*.f64 t t) x))))
144.0ms	(+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))
74.0ms	(/.f64 (*.f64 t t) x)

Compiler

Compiled 5510 to 4422 computations (19.7% saved)

simplify80.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5297	4621

prune209.0ms (1.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	129	9	138

Error

0.3b

Counts

138 → 9

Compiler

Compiled 5274 to 2683 computations (49.1% saved)

localize21.0ms (0.1%)

Local error

Found 4 expressions with local error:

27.8b	(sqrt.f64 (+.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 l l) x)) (cbrt.f64 (/.f64 (.f64 l l) x))) (cbrt.f64 (/.f64 (.f64 l l) x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
33.6b	(cbrt.f64 (/.f64 (*.f64 l l) x))
33.6b	(cbrt.f64 (/.f64 (*.f64 l l) x))
33.6b	(cbrt.f64 (/.f64 (*.f64 l l) x))

rewrite205.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

0.3b

Rules

27×	`cbrt-div_binary64_110`
21×	`cbrt-prod_binary64_109`
20×	`associate-*r/_binary64_20`
16×	`sqrt-div_binary64_95`
14×	`frac-add_binary64_86`
12×	`add-sqr-sqrt_binary64_100`
11×	`add-cube-cbrt_binary64_113` `*-un-lft-identity_binary64_78`
10×	`frac-times_binary64_88` `associate-*l/_binary64_21`
9×	`times-frac_binary64_84`
8×	`flip3-+_binary64_81` `flip-+_binary64_52`
5×	`pow1_binary64_139`
4×	`add-log-exp_binary64_117` `add-exp-log_binary64_116` `add-cbrt-cube_binary64_114`
3×	`pow1/3_binary64_160` `div-inv_binary64_75` `sqrt-prod_binary64_94`
1×	`pow1/2_binary64_158` `sqrt-pow1_binary64_96` `rem-sqrt-square_binary64_91`

Counts

4 → 77

Calls

4 calls:

25.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 l l) x)) (cbrt.f64 (/.f64 (.f64 l l) x))) (cbrt.f64 (/.f64 (.f64 l l) x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
3.0ms	(cbrt.f64 (/.f64 (*.f64 l l) x))
3.0ms	(cbrt.f64 (/.f64 (*.f64 l l) x))
3.0ms	(cbrt.f64 (/.f64 (*.f64 l l) x))

Compiler

Compiled 5069 to 1788 computations (64.7% saved)

series1.4s (8.2%)

Error

0.3b

Counts

4 → 42

Calls

4 calls:

650.0ms	(sqrt.f64 (+.f64 (.f64 2 (.f64 (.f64 (cbrt.f64 (/.f64 (.f64 l l) x)) (cbrt.f64 (/.f64 (.f64 l l) x))) (cbrt.f64 (/.f64 (.f64 l l) x)))) (+.f64 (.f64 2 (.f64 t t)) (.f64 4 (/.f64 (.f64 t t) x)))))
234.0ms	(cbrt.f64 (/.f64 (*.f64 l l) x))
223.0ms	(cbrt.f64 (/.f64 (*.f64 l l) x))
221.0ms	(cbrt.f64 (/.f64 (*.f64 l l) x))

Compiler

Compiled 5771 to 4315 computations (25.2% saved)

simplify77.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5025	4491

prune221.0ms (1.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	119	0	119
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	119	9	128

Error

0.3b

Counts

128 → 9

Compiler

Compiled 5894 to 2606 computations (55.8% saved)

regimes1.8s (10.7%)

Accuracy

Total 7.8b remaining (94.6%)

Threshold costs 0b (0%)

Compiler

Compiled 23447 to 16785 computations (28.4% saved)

bsearch403.0ms (2.3%)

Steps

Iters	Range		Point
8	7.549743730319744e+25	7.542780393846487e+28	7.465776635895058e+28
11	1.0706423392090946e-160	2.168381505663483e-141	1.0817817285694105e-160
8	3.1505274549513004e-241	3.0290508047593325e-237	2.9657881463761506e-237
8	-1.466355502600728e+106	-3.472291400289074e+102	-7.925051725780633e+105

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	108	223
1	108	223

Removed

()

end0.0ms (0%)

sample4.0s (23.2%)

Algorithm

1×

intervals

Results

363.0ms	5350×	body	128	valid
307.0ms	1143×	body	1024	valid
201.0ms	786×	body	1024	nan
192.0ms	931×	body	512	valid
101.0ms	1496×	body	128	nan
94.0ms	503×	body	512	nan
67.0ms	514×	body	256	valid
34.0ms	272×	body	256	nan
21.0ms	62×	body	2048	valid

Compiler

Compiled 3426 to 2467 computations (28% saved)

Details

analyze912.0ms (5.3%)

sample58.0ms (0.3%)

simplify71.0ms (0.4%)

prune3.0ms (0%)

localize19.0ms (0.1%)

rewrite229.0ms (1.3%)

series4.2s (24.5%)

simplify75.0ms (0.4%)

prune296.0ms (1.7%)

localize16.0ms (0.1%)

rewrite142.0ms (0.8%)

series940.0ms (5.4%)

simplify78.0ms (0.4%)

prune173.0ms (1%)

localize23.0ms (0.1%)

rewrite202.0ms (1.2%)

series1.3s (7.6%)

simplify80.0ms (0.5%)

prune209.0ms (1.2%)

localize21.0ms (0.1%)

rewrite205.0ms (1.2%)

series1.4s (8.2%)

simplify77.0ms (0.4%)

prune221.0ms (1.3%)

regimes1.8s (10.7%)

bsearch403.0ms (2.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample4.0s (23.2%)

Profiling