Details

analyze1.1s (7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	74.8%	25.2%	8
0%	74.8%	25.2%	9
0%	74.8%	25.2%	10
0%	74.8%	25.2%	11
0%	74.8%	25.2%	12
24.9%	49.9%	25.2%	13
24.9%	37.4%	37.7%	14

Compiler

Compiled 20 to 20 computations (0% saved)

sample77.0ms (0.5%)

Algorithm

1×

intervals

Results

22.0ms	63×	body	1024	valid
11.0ms	140×	body	128	valid
9.0ms	18×	body	2048	valid
6.0ms	80×	body	128	nan
5.0ms	22×	body	512	valid
2.0ms	13×	body	256	valid
2.0ms	26×	body	128	invalid

Compiler

Compiled 39 to 45 computations (-15.4% saved)

simplify146.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	757	29
1	757	29

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

17.4b

Counts

2 → 1

Compiler

Compiled 38 to 38 computations (0% saved)

localize16.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
0.2b	(/.f64 a (*.f64 b 3))
0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (.f64 z t) 3)))) (/.f64 a (.f64 b 3)))
0.0b	(-.f64 y (/.f64 (*.f64 z t) 3))
0.2b	(/.f64 a (*.f64 b 3))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
0.4b	(/.f64 (*.f64 z t) 3)
20.9b	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))

rewrite32.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
11×	`add-sqr-sqrt_binary64_20219` `*-un-lft-identity_binary64_20197` `add-cube-cbrt_binary64_20232`
9×	`times-frac_binary64_20203` `pow1_binary64_20258`
8×	`cos-sum_binary64_20331`
7×	`cancel-sign-sub-inv_binary64_20163`
5×	`cbrt-unprod_binary64_20230` `prod-exp_binary64_20246`
4×	`add-log-exp_binary64_20236` `associate-/r_binary64_20141` `div-exp_binary64_20248` `associate-/l_binary64_20142` `cbrt-undiv_binary64_20231`
3×	`div-inv_binary64_20194` `pow-prod-down_binary64_20268` `associate-r_binary64_20137` `cos-diff_binary64_20334`
2×	`frac-2neg_binary64_20208` `clear-num_binary64_20196`
1×	`sub-neg_binary64_20190` `distribute-lft-in_binary64_20146` `-commutative_binary64_20128` `distribute-rgt-in_binary64_20147` `associate-l*_binary64_20138`

Counts

4 → 78

Calls

8 calls:

8.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
7.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
4.0ms	(/.f64 (*.f64 z t) 3)
4.0ms	(/.f64 a (*.f64 b 3))
0.0ms	(-.f64 y (/.f64 (*.f64 z t) 3))

series513.0ms (3.4%)

Counts

4 → 45

Calls

4 calls:

285.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3))))
108.0ms	(cos.f64 (-.f64 y (/.f64 (*.f64 z t) 3)))
62.0ms	(/.f64 a (*.f64 b 3))
58.0ms	(/.f64 (*.f64 z t) 3)

Compiler

Compiled 1893 to 1751 computations (7.5% saved)

simplify82.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4932	1991
1	4932	1991

prune319.0ms (2.1%)

Pruning

24 alts after pruning (24 fresh and 0 done)

	Pruned	Kept	Total
New	99	24	123
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	24	124

Error

13.3b

Counts

124 → 24

Compiler

Compiled 3439 to 2231 computations (35.1% saved)

localize11.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.2b	(/.f64 a (*.f64 b 3))
0.1b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
0.1b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.2b	(/.f64 a (*.f64 b 3))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233`
8×	`add-sqr-sqrt_binary64_20219` `*-un-lft-identity_binary64_20197` `add-cube-cbrt_binary64_20232` `pow1_binary64_20258`
7×	`cancel-sign-sub-inv_binary64_20163`
6×	`times-frac_binary64_20203`
5×	`add-log-exp_binary64_20236`
4×	`cbrt-unprod_binary64_20230` `prod-exp_binary64_20246`
3×	`associate-/l_binary64_20142` `pow-prod-down_binary64_20268` `associate-r*_binary64_20137`
2×	`div-inv_binary64_20194` `div-exp_binary64_20248` `cbrt-undiv_binary64_20231`
1×	`sub-neg_binary64_20190` `flip3--_binary64_20201` `frac-2neg_binary64_20208` `clear-num_binary64_20196` `associate-/r_binary64_20141` `-commutative_binary64_20128` `associate-l_binary64_20138` `flip--_binary64_20172` `diff-log_binary64_20289`

Counts

3 → 57

Calls

6 calls:

8.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
6.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
4.0ms	(/.f64 a (*.f64 b 3))
0.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
0.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))

series474.0ms (3.1%)

Counts

3 → 36

Calls

3 calls:

332.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 a (*.f64 b 3)))
80.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
62.0ms	(/.f64 a (*.f64 b 3))

Compiler

Compiled 828 to 918 computations (-10.9% saved)

simplify75.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4917	1339
1	4917	1339

prune147.0ms (1%)

Pruning

26 alts after pruning (26 fresh and 0 done)

	Pruned	Kept	Total
New	85	8	93
Fresh	5	18	23
Picked	1	0	1
Done	0	0	0
Total	91	26	117

Error

13.2b

Counts

117 → 26

Compiler

Compiled 2079 to 1411 computations (32.1% saved)

localize10.0ms (0.1%)

Local error

Found 6 expressions with local error:

0.2b	(/.f64 (/.f64 a b) 3)
0.1b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (/.f64 a b) 3))
0.0b	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (/.f64 a b) 3))
0.1b	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
0.2b	(/.f64 (/.f64 a b) 3)

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

141×	`times-frac_binary64_20203`
81×	`add-sqr-sqrt_binary64_20219` `*-un-lft-identity_binary64_20197` `add-cube-cbrt_binary64_20232`
43×	`cancel-sign-sub-inv_binary64_20163`
13×	`add-exp-log_binary64_20235` `add-cbrt-cube_binary64_20233` `associate-/l*_binary64_20142`
9×	`div-inv_binary64_20194`
8×	`pow1_binary64_20258`
5×	`add-log-exp_binary64_20236`
3×	`cbrt-unprod_binary64_20230` `associate-/r_binary64_20141` `div-exp_binary64_20248` `prod-exp_binary64_20246` `pow-prod-down_binary64_20268` `cbrt-undiv_binary64_20231` `associate-r*_binary64_20137`
1×	`sub-neg_binary64_20190` `flip3--_binary64_20201` `frac-2neg_binary64_20208` `clear-num_binary64_20196` `associate-/l/_binary64_20144` `-commutative_binary64_20128` `associate-l*_binary64_20138` `flip--_binary64_20172` `diff-log_binary64_20289`

Counts

3 → 142

Calls

6 calls:

19.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (/.f64 a b) 3))
7.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
6.0ms	(/.f64 (/.f64 a b) 3)
0.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (/.f64 a b) 3))
0.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))

series476.0ms (3.1%)

Counts

3 → 36

Calls

3 calls:

332.0ms	(-.f64 (.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y)) (/.f64 (/.f64 a b) 3))
84.0ms	(.f64 (.f64 2 (sqrt.f64 x)) (cos.f64 y))
59.0ms	(/.f64 (/.f64 a b) 3)

Compiler

Compiled 828 to 918 computations (-10.9% saved)

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5257	3070

prune204.0ms (1.3%)

Pruning

27 alts after pruning (26 fresh and 1 done)

	Pruned	Kept	Total
New	176	2	178
Fresh	1	24	25
Picked	0	1	1
Done	0	0	0
Total	177	27	204

Error

13.2b

Counts

204 → 27

Compiler

Compiled 3961 to 2255 computations (43.1% saved)

localize15.0ms (0.1%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 a (*.f64 b 3))
0.2b	(.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y)))
0.2b	(.f64 (.f64 2 (sqrt.f64 x)) (*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y))))
0.0b	(-.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (/.f64 a (*.f64 b 3)))
0.3b	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
0.4b	(cbrt.f64 (cos.f64 y))
0.4b	(cbrt.f64 (cos.f64 y))
0.4b	(cbrt.f64 (cos.f64 y))

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_20228`
23×	`add-sqr-sqrt_binary64_20219`
15×	`*-un-lft-identity_binary64_20197` `add-cube-cbrt_binary64_20232`
11×	`pow1_binary64_20258`
9×	`pow1/3_binary64_20279`
6×	`add-exp-log_binary64_20235` `swap-sqr_binary64_20164` `associate-l_binary64_20138` `associate-r_binary64_20137`
4×	`add-cbrt-cube_binary64_20233` `add-log-exp_binary64_20236` `unswap-sqr_binary64_20165`
2×	`pow-sqr_binary64_20170` `pow-prod-up_binary64_20267` `pow-prod-down_binary64_20268`
1×	`cbrt-unprod_binary64_20230` `pow-plus_binary64_20260` `pow2_binary64_20278` `prod-exp_binary64_20246` `*-commutative_binary64_20128`

Counts

4 → 73

Calls

8 calls:

7.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
1.0ms	(cbrt.f64 (cos.f64 y))
1.0ms	(cbrt.f64 (cos.f64 y))
1.0ms	(cbrt.f64 (cos.f64 y))
0.0ms	(-.f64 (.f64 (.f64 (.f64 2 (sqrt.f64 x)) (.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))) (cbrt.f64 (cos.f64 y))) (/.f64 a (*.f64 b 3)))

series348.0ms (2.3%)

Counts

4 → 23

Calls

4 calls:

112.0ms	(*.f64 (cbrt.f64 (cos.f64 y)) (cbrt.f64 (cos.f64 y)))
83.0ms	(cbrt.f64 (cos.f64 y))
79.0ms	(cbrt.f64 (cos.f64 y))
74.0ms	(cbrt.f64 (cos.f64 y))

Compiler

Compiled 808 to 744 computations (7.9% saved)

simplify70.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4880	900
1	4880	900

prune142.0ms (0.9%)

Pruning

32 alts after pruning (31 fresh and 1 done)

	Pruned	Kept	Total
New	90	6	96
Fresh	0	25	25
Picked	1	0	1
Done	0	1	1
Total	91	32	123

Error

13.1b

Counts

123 → 32

Compiler

Compiled 2399 to 1082 computations (54.9% saved)

simplify50.0ms (0.3%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (16.0ms)

Iter	Nodes	Cost
0	1158	2700
1	1158	2700

regimes2.3s (14.9%)

Compiler: Compiled 24102 to 22817 computations (5.3% saved)

bsearch4.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

regimes1.8s (11.7%)

Compiler: Compiled 17096 to 17510 computations (-2.4% saved)

bsearch3.0ms (0%)

Compiler: Compiled 3 to 7 computations (-133.3% saved)

regimes1.5s (9.8%)

Compiler: Compiled 15010 to 15391 computations (-2.5% saved)

bsearch1.0ms (0%)

Steps

Iters	Range		Point
0	0.999826834748868	0.9999999994010114	0.9999134170749396

Compiler

Compiled 8 to 11 computations (-37.5% saved)

regimes138.0ms (0.9%)

Compiler: Compiled 448 to 832 computations (-85.7% saved)

bsearch0.0ms (0%)

regimes280.0ms (1.8%)

Compiler: Compiled 344 to 712 computations (-107% saved)

bsearch75.0ms (0.5%)

Steps

Iters	Range		Point
5	4.3063789403095224e+68	9.55994978433402e+68	9.41012478605164e+68
3	66415941070007.266	80822087900684.05	66989658255580.19
7	160357.37630121462	6126024.701622862	6040219.589669799

Compiler

Compiled 2 to 7 computations (-250% saved)

regimes116.0ms (0.8%)

Compiler: Compiled 288 to 624 computations (-116.7% saved)

bsearch0.0ms (0%)

regimes106.0ms (0.7%)

Compiler: Compiled 208 to 520 computations (-150% saved)

bsearch0.0ms (0%)

regimes69.0ms (0.5%)

Compiler: Compiled 90 to 306 computations (-240% saved)

bsearch0.0ms (0%)

regimes57.0ms (0.4%)

Accuracy

Total 1.8b remaining (11.2%)

Threshold costs 0b (0%)

Compiler

Compiled 30 to 198 computations (-560% saved)

bsearch12.0ms (0.1%)

Compiler: Compiled 268 to 219 computations (18.3% saved)

simplify7.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	189	404
1	189	404

end0.0ms (0%)

sample4.4s (28.7%)

Algorithm

1×

intervals

Results

535.0ms	1625×	body	1024	valid
375.0ms	4678×	body	128	valid
305.0ms	667×	body	2048	valid
183.0ms	2341×	body	128	nan
174.0ms	717×	body	512	valid
93.0ms	1209×	body	128	invalid
55.0ms	313×	body	256	valid

Compiler

Compiled 2068 to 1908 computations (7.7% saved)

Pareto

0.7270846179194642

Details

analyze1.1s (7%)

sample77.0ms (0.5%)

simplify146.0ms (1%)

prune3.0ms (0%)

localize16.0ms (0.1%)

rewrite32.0ms (0.2%)

series513.0ms (3.4%)

simplify82.0ms (0.5%)

prune319.0ms (2.1%)

localize11.0ms (0.1%)

rewrite23.0ms (0.2%)

series474.0ms (3.1%)

simplify75.0ms (0.5%)

prune147.0ms (1%)

localize10.0ms (0.1%)

rewrite48.0ms (0.3%)

series476.0ms (3.1%)

simplify81.0ms (0.5%)

prune204.0ms (1.3%)

localize15.0ms (0.1%)

rewrite18.0ms (0.1%)

series348.0ms (2.3%)

simplify70.0ms (0.5%)

prune142.0ms (0.9%)

simplify50.0ms (0.3%)

regimes2.3s (14.9%)

bsearch4.0ms (0%)

regimes1.8s (11.7%)

bsearch3.0ms (0%)

regimes1.5s (9.8%)

bsearch1.0ms (0%)

regimes138.0ms (0.9%)

bsearch0.0ms (0%)

regimes280.0ms (1.8%)

bsearch75.0ms (0.5%)

regimes116.0ms (0.8%)

bsearch0.0ms (0%)

regimes106.0ms (0.7%)

bsearch0.0ms (0%)

regimes69.0ms (0.5%)

bsearch0.0ms (0%)

regimes57.0ms (0.4%)

bsearch12.0ms (0.1%)

simplify7.0ms (0%)

end0.0ms (0%)

sample4.4s (28.7%)

Profiling