Details

analyze305.0ms (3.9%)

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
18.7%	68.7%	12.6%	6
28.1%	59.3%	12.6%	7
32.8%	48.4%	18.8%	8
38.2%	42.9%	18.8%	9
41%	37.1%	22%	10
43.9%	34.1%	22%	11
45.5%	31%	23.5%	12
46.9%	29.6%	23.5%	13
47.7%	28%	24.3%	14

Compiler

Compiled 17 to 9 computations (47.1% saved)

sample50.0ms (0.6%)

Algorithm

1×

intervals

Results

23.0ms	114×	body	8192	exit
10.0ms	212×	body	128	valid
2.0ms	20×	body	512	valid
2.0ms	24×	body	256	valid
0.0ms	4×	body	128	invalid

Compiler

Compiled 33 to 19 computations (42.4% saved)

simplify227.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (130.0ms)

Iter	Nodes	Cost
0	4887	18
1	4887	18

prune5.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

12.4b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize8.0ms (0.1%)

Local error

Found 6 expressions with local error:

4.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
0.0b	(/.f64 x (exp.f64 wj))
0.0b	(/.f64 x (exp.f64 wj))
0.0b	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
4.3b	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))

rewrite48.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`*-un-lft-identity_binary64_4852`
48×	`add-sqr-sqrt_binary64_4874`
38×	`times-frac_binary64_4858`
23×	`add-cube-cbrt_binary64_4887`
10×	`difference-of-squares_binary64_4821`
9×	`associate-/l*_binary64_4797`
8×	`distribute-lft-out_binary64_4803`
7×	`add-cbrt-cube_binary64_4888` `associate-/r*_binary64_4796`
6×	`add-exp-log_binary64_4890`
5×	`distribute-lft-out--_binary64_4804` `add-log-exp_binary64_4891`
3×	`pow1_binary64_4913`
2×	`flip-+_binary64_4826` `div-sub_binary64_4857` `associate-/l/_binary64_4799` `div-inv_binary64_4849` `clear-num_binary64_4851` `associate-/r/_binary64_4798` `cbrt-undiv_binary64_4886` `flip3-+_binary64_4855` `frac-2neg_binary64_4863` `div-exp_binary64_4903`
1×	`+-commutative_binary64_4782` `flip3--_binary64_4856` `associate-+r-_binary64_4786` `flip--_binary64_4827` `sum-log_binary64_4943`

Counts

3 → 91

Calls

6 calls:

22.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
13.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
4.0ms	(/.f64 x (exp.f64 wj))
0.0ms	(/.f64 x (exp.f64 wj))
0.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))

series375.0ms (4.8%)

Counts

3 → 45

Calls

3 calls:

163.0ms	(+.f64 wj (/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1)))
145.0ms	(/.f64 (-.f64 (/.f64 x (exp.f64 wj)) wj) (+.f64 wj 1))
66.0ms	(/.f64 x (exp.f64 wj))

Compiler

Compiled 846 to 635 computations (24.9% saved)

simplify91.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4955	2769
1	4955	2769

prune164.0ms (2.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	133	3	136
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	134	3	137

Error

0.1b

Counts

137 → 3

Compiler

Compiled 2555 to 1063 computations (58.4% saved)

localize16.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 (pow.f64 wj 3) (.f64 x (+.f64 (+.f64 wj wj) (.f64 (pow.f64 wj 3) 8/3))))
0.0b	(+.f64 (+.f64 wj wj) (*.f64 (pow.f64 wj 3) 8/3))
0.0b	(.f64 x (+.f64 (+.f64 wj wj) (.f64 (pow.f64 wj 3) 8/3)))
0.0b	(+.f64 (*.f64 5/2 x) 1)
0.0b	(+.f64 x (-.f64 (.f64 (+.f64 (.f64 5/2 x) 1) (.f64 wj wj)) (+.f64 (pow.f64 wj 3) (.f64 x (+.f64 (+.f64 wj wj) (*.f64 (pow.f64 wj 3) 8/3))))))
0.0b	(-.f64 (.f64 (+.f64 (.f64 5/2 x) 1) (.f64 wj wj)) (+.f64 (pow.f64 wj 3) (.f64 x (+.f64 (+.f64 wj wj) (*.f64 (pow.f64 wj 3) 8/3)))))
0.1b	(*.f64 (pow.f64 wj 3) 8/3)
7.4b	(.f64 (+.f64 (.f64 5/2 x) 1) (*.f64 wj wj))

rewrite72.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`add-sqr-sqrt_binary64_4874`
18×	`add-log-exp_binary64_4891`
15×	`associate-l_binary64_4793`
14×	`add-exp-log_binary64_4890`
13×	`*-un-lft-identity_binary64_4852`
11×	`add-cube-cbrt_binary64_4887` `add-cbrt-cube_binary64_4888`
9×	`pow1_binary64_4913`
6×	`flip-+_binary64_4826` `cancel-sign-sub-inv_binary64_4818` `prod-exp_binary64_4901` `associate-*l/_binary64_4795` `flip3-+_binary64_4855`
5×	`unswap-sqr_binary64_4820` `sum-log_binary64_4943`
4×	`cube-prod_binary64_4880` `cbrt-unprod_binary64_4885` `associate-r_binary64_4792` `frac-sub_binary64_4861` `unpow-prod-down_binary64_4931` `associate-+r+_binary64_4784` `diff-log_binary64_4944`
3×	`pow-prod-down_binary64_4923`
2×	`sub-neg_binary64_4845` `sqr-pow_binary64_4824` `*-commutative_binary64_4783`
1×	`+-commutative_binary64_4782` `flip3--_binary64_4856` `associate--r+_binary64_4788` `cube-mult_binary64_4882` `distribute-lft-out_binary64_4803` `pow-to-exp_binary64_4921` `associate-+r-_binary64_4786` `flip--_binary64_4827` `pow-exp_binary64_4920` `unpow3_binary64_4918`

Counts

4 → 91

Calls

8 calls:

21.0ms	(-.f64 (.f64 (+.f64 (.f64 5/2 x) 1) (.f64 wj wj)) (+.f64 (pow.f64 wj 3) (.f64 x (+.f64 (+.f64 wj wj) (*.f64 (pow.f64 wj 3) 8/3)))))
21.0ms	(+.f64 x (-.f64 (.f64 (+.f64 (.f64 5/2 x) 1) (.f64 wj wj)) (+.f64 (pow.f64 wj 3) (.f64 x (+.f64 (+.f64 wj wj) (*.f64 (pow.f64 wj 3) 8/3))))))
9.0ms	(.f64 (+.f64 (.f64 5/2 x) 1) (*.f64 wj wj))
6.0ms	(*.f64 (pow.f64 wj 3) 8/3)
0.0ms	(+.f64 (*.f64 5/2 x) 1)

series789.0ms (10.1%)

Counts

4 → 45

Calls

4 calls:

377.0ms	(-.f64 (.f64 (+.f64 (.f64 5/2 x) 1) (.f64 wj wj)) (+.f64 (pow.f64 wj 3) (.f64 x (+.f64 (+.f64 wj wj) (*.f64 (pow.f64 wj 3) 8/3)))))
269.0ms	(+.f64 x (-.f64 (.f64 (+.f64 (.f64 5/2 x) 1) (.f64 wj wj)) (+.f64 (pow.f64 wj 3) (.f64 x (+.f64 (+.f64 wj wj) (*.f64 (pow.f64 wj 3) 8/3))))))
106.0ms	(.f64 (+.f64 (.f64 5/2 x) 1) (*.f64 wj wj))
37.0ms	(*.f64 (pow.f64 wj 3) 8/3)

Compiler

Compiled 1571 to 1235 computations (21.4% saved)

simplify92.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	5131	3669

prune239.0ms (3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	1	1	2
Picked	1	0	1
Done	0	0	0
Total	134	5	139

Error

0.0b

Counts

139 → 5

Compiler

Compiled 4591 to 2844 computations (38.1% saved)

localize6.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (*.f64 wj wj) (pow.f64 wj 3))
0.0b	(+.f64 x (-.f64 (*.f64 wj wj) (pow.f64 wj 3)))
0.0b	(+.f64 x (-.f64 (*.f64 wj wj) (pow.f64 wj 3)))
0.0b	(-.f64 (*.f64 wj wj) (pow.f64 wj 3))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`cancel-sign-sub-inv_binary64_4818`
13×	`associate-+r+_binary64_4784`
11×	`add-sqr-sqrt_binary64_4874`
10×	`*-un-lft-identity_binary64_4852`
9×	`add-log-exp_binary64_4891`
8×	`add-cube-cbrt_binary64_4887`
7×	`cube-prod_binary64_4880` `unpow-prod-down_binary64_4931`
4×	`difference-of-squares_binary64_4821`
3×	`cube-mult_binary64_4882` `unpow3_binary64_4918` `sqr-pow_binary64_4824`
2×	`add-exp-log_binary64_4890` `add-cbrt-cube_binary64_4888` `sub-neg_binary64_4845` `pow1_binary64_4913` `diff-log_binary64_4944` `sum-log_binary64_4943`
1×	`distribute-lft-out--_binary64_4804` `+-commutative_binary64_4782` `flip3--_binary64_4856` `flip-+_binary64_4826` `distribute-rgt-out--_binary64_4806` `distribute-lft-out_binary64_4803` `associate-+r-_binary64_4786` `flip--_binary64_4827` `flip3-+_binary64_4855`

Counts

2 → 56

Calls

4 calls:

11.0ms	(+.f64 x (-.f64 (*.f64 wj wj) (pow.f64 wj 3)))
8.0ms	(-.f64 (*.f64 wj wj) (pow.f64 wj 3))
0.0ms	(+.f64 x (-.f64 (*.f64 wj wj) (pow.f64 wj 3)))
0.0ms	(-.f64 (*.f64 wj wj) (pow.f64 wj 3))

series193.0ms (2.5%)

Counts

2 → 21

Calls

2 calls:

133.0ms	(+.f64 x (-.f64 (*.f64 wj wj) (pow.f64 wj 3)))
59.0ms	(-.f64 (*.f64 wj wj) (pow.f64 wj 3))

Compiler

Compiled 220 to 207 computations (5.9% saved)

simplify81.0ms (1%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	5084	841

prune66.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	0	77
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	77	5	82

Error

0.0b

Counts

82 → 5

Compiler

Compiled 1110 to 596 computations (46.3% saved)

localize18.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 x (cbrt.f64 (pow.f64 (-.f64 (.f64 (.f64 wj wj) (-.f64 (+.f64 (.f64 5/2 x) 1) wj)) (.f64 x (+.f64 (*.f64 (pow.f64 wj 3) 8/3) (+.f64 wj wj)))) 3)))
0.0b	(+.f64 (*.f64 (pow.f64 wj 3) 8/3) (+.f64 wj wj))
0.0b	(.f64 x (+.f64 (.f64 (pow.f64 wj 3) 8/3) (+.f64 wj wj)))
0.0b	(+.f64 (*.f64 5/2 x) 1)
0.1b	(*.f64 (pow.f64 wj 3) 8/3)
0.3b	(pow.f64 (-.f64 (.f64 (.f64 wj wj) (-.f64 (+.f64 (.f64 5/2 x) 1) wj)) (.f64 x (+.f64 (*.f64 (pow.f64 wj 3) 8/3) (+.f64 wj wj)))) 3)
7.4b	(.f64 (.f64 wj wj) (-.f64 (+.f64 (*.f64 5/2 x) 1) wj))
26.9b	(cbrt.f64 (pow.f64 (-.f64 (.f64 (.f64 wj wj) (-.f64 (+.f64 (.f64 5/2 x) 1) wj)) (.f64 x (+.f64 (*.f64 (pow.f64 wj 3) 8/3) (+.f64 wj wj)))) 3))

rewrite68.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_4874`
19×	`*-un-lft-identity_binary64_4852`
18×	`associate-*r/_binary64_4794`
17×	`add-cube-cbrt_binary64_4887`
15×	`add-exp-log_binary64_4890`
13×	`associate-l_binary64_4793`
12×	`add-cbrt-cube_binary64_4888` `cbrt-prod_binary64_4883` `cube-div_binary64_4881`
10×	`cube-prod_binary64_4880` `unpow-prod-down_binary64_4931` `pow1_binary64_4913`
8×	`associate-r_binary64_4792` `frac-sub_binary64_4861`
7×	`flip3--_binary64_4856` `flip--_binary64_4827`
6×	`cancel-sign-sub-inv_binary64_4818` `cbrt-div_binary64_4884` `prod-exp_binary64_4901`
5×	`unswap-sqr_binary64_4820` `distribute-lft-in_binary64_4801` `distribute-rgt-in_binary64_4802`
4×	`cbrt-unprod_binary64_4885` `flip-+_binary64_4826` `add-log-exp_binary64_4891` `flip3-+_binary64_4855` `sqr-pow_binary64_4824`
3×	`cube-mult_binary64_4882` `pow-unpow_binary64_4929` `unpow3_binary64_4918` `pow-prod-down_binary64_4923`
2×	`associate--l+_binary64_4789` `sub-neg_binary64_4845` `pow-to-exp_binary64_4921` `pow-exp_binary64_4920` `*-commutative_binary64_4783`
1×	`difference-of-squares_binary64_4821` `distribute-lft-out--_binary64_4804` `pow-pow_binary64_4924` `rem-cube-cbrt_binary64_4875` `pow1/3_binary64_4934` `rem-cbrt-cube_binary64_4876`

Counts

4 → 120

Calls

8 calls:

17.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 (.f64 wj wj) (-.f64 (+.f64 (.f64 5/2 x) 1) wj)) (.f64 x (+.f64 (*.f64 (pow.f64 wj 3) 8/3) (+.f64 wj wj)))) 3))
15.0ms	(pow.f64 (-.f64 (.f64 (.f64 wj wj) (-.f64 (+.f64 (.f64 5/2 x) 1) wj)) (.f64 x (+.f64 (*.f64 (pow.f64 wj 3) 8/3) (+.f64 wj wj)))) 3)
13.0ms	(.f64 (.f64 wj wj) (-.f64 (+.f64 (*.f64 5/2 x) 1) wj))
6.0ms	(*.f64 (pow.f64 wj 3) 8/3)
0.0ms	(+.f64 (*.f64 5/2 x) 1)

series938.0ms (11.9%)

Counts

4 → 51

Calls

4 calls:

389.0ms	(pow.f64 (-.f64 (.f64 (.f64 wj wj) (-.f64 (+.f64 (.f64 5/2 x) 1) wj)) (.f64 x (+.f64 (*.f64 (pow.f64 wj 3) 8/3) (+.f64 wj wj)))) 3)
379.0ms	(cbrt.f64 (pow.f64 (-.f64 (.f64 (.f64 wj wj) (-.f64 (+.f64 (.f64 5/2 x) 1) wj)) (.f64 x (+.f64 (*.f64 (pow.f64 wj 3) 8/3) (+.f64 wj wj)))) 3))
138.0ms	(.f64 (.f64 wj wj) (-.f64 (+.f64 (*.f64 5/2 x) 1) wj))
31.0ms	(*.f64 (pow.f64 wj 3) 8/3)

Compiler

Compiled 3169 to 2532 computations (20.1% saved)

simplify114.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5037	7614

prune417.0ms (5.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	171	5	176

Error

0.0b

Counts

176 → 5

Compiler

Compiled 7489 to 4910 computations (34.4% saved)

simplify115.0ms (1.5%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	2560	1894
1	2560	1894

regimes383.0ms (4.9%)

Compiler: Compiled 3822 to 2541 computations (33.5% saved)

bsearch23.0ms (0.3%)

Steps

Iters	Range		Point
8	4.31388341174523e-16	4.539425139408517e-12	1.4176093501666414e-12

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes73.0ms (0.9%)

Compiler: Compiled 352 to 288 computations (18.2% saved)

bsearch17.0ms (0.2%)

Steps

Iters	Range		Point
8	4.31388341174523e-16	4.539425139408517e-12	4.44488751859428e-12

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes46.0ms (0.6%)

Compiler: Compiled 156 to 148 computations (5.1% saved)

bsearch17.0ms (0.2%)

Steps

Iters	Range		Point
8	0.6400884701246073	3039.6321902875775	0.6520064569069947

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes34.0ms (0.4%)

Compiler: Compiled 56 to 70 computations (-25% saved)

bsearch16.0ms (0.2%)

Steps

Iters	Range		Point
8	0.6400884701246073	3039.6321902875775	0.6520064569069947

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes27.0ms (0.3%)

Compiler: Compiled 28 to 46 computations (-64.3% saved)

bsearch15.0ms (0.2%)

Steps

Iters	Range		Point
8	0.6400884701246073	3039.6321902875775	3.947283906137509

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes25.0ms (0.3%)

Compiler: Compiled 18 to 38 computations (-111.1% saved)

bsearch14.0ms (0.2%)

Steps

Iters	Range		Point
8	0.6400884701246073	3039.6321902875775	1.0190921207572299

Compiler

Compiled 1 to 2 computations (-100% saved)

regimes16.0ms (0.2%)

Compiler: Compiled 12 to 30 computations (-150% saved)

bsearch0.0ms (0%)

regimes17.0ms (0.2%)

Accuracy

Total 0.9b remaining (88.7%)

Threshold costs 0.9b (88.7%)

Compiler

Compiled 10 to 26 computations (-160% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 118 to 83 computations (29.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	85	171
1	85	171

end0.0ms (0%)

sample2.6s (33.1%)

Algorithm

1×

intervals

Results

798.0ms	3624×	body	8192	exit
251.0ms	6589×	body	128	valid
83.0ms	706×	body	512	valid
51.0ms	683×	body	256	valid
4.0ms	22×	body	1024	valid
3.0ms	77×	body	128	invalid
0.0ms	11×	body	128	overflowed

Compiler

Compiled 1397 to 933 computations (33.2% saved)

Pareto

0.9592955707204928

Details

analyze305.0ms (3.9%)

sample50.0ms (0.6%)

simplify227.0ms (2.9%)

prune5.0ms (0.1%)

localize8.0ms (0.1%)

rewrite48.0ms (0.6%)

series375.0ms (4.8%)

simplify91.0ms (1.2%)

prune164.0ms (2.1%)

localize16.0ms (0.2%)

rewrite72.0ms (0.9%)

series789.0ms (10.1%)

simplify92.0ms (1.2%)

prune239.0ms (3%)

localize6.0ms (0.1%)

rewrite22.0ms (0.3%)

series193.0ms (2.5%)

simplify81.0ms (1%)

prune66.0ms (0.8%)

localize18.0ms (0.2%)

rewrite68.0ms (0.9%)

series938.0ms (11.9%)

simplify114.0ms (1.5%)

prune417.0ms (5.3%)

simplify115.0ms (1.5%)

regimes383.0ms (4.9%)

bsearch23.0ms (0.3%)

regimes73.0ms (0.9%)

bsearch17.0ms (0.2%)

regimes46.0ms (0.6%)

bsearch17.0ms (0.2%)

regimes34.0ms (0.4%)

bsearch16.0ms (0.2%)

regimes27.0ms (0.3%)

bsearch15.0ms (0.2%)

regimes25.0ms (0.3%)

bsearch14.0ms (0.2%)

regimes16.0ms (0.2%)

bsearch0.0ms (0%)

regimes17.0ms (0.2%)

bsearch6.0ms (0.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample2.6s (33.1%)

Profiling