Details

analyze226.0ms (3.6%)

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
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 30 to 26 computations (13.3% saved)

sample66.0ms (1%)

Algorithm

1×

intervals

Results

29.0ms	63×	body	1024	valid
11.0ms	139×	body	128	valid
8.0ms	31×	body	512	valid
6.0ms	5×	body	2048	valid
3.0ms	18×	body	256	valid
0.0ms	5×	body	128	invalid
0.0ms	4×	body	128	overflowed

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify223.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4908	41
1	4908	41

prune5.0ms (0.1%)

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

Merged error: 28.6b

Counts

2 → 1

Compiler

Compiled 56 to 48 computations (14.3% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
2.3b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite88.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64_760`
78×	`exp-neg_binary64_795`
76×	`frac-times_binary64_761`
59×	`exp-diff_binary64_796` `neg-sub0_binary64_746`
38×	`associate-r/_binary64_695` `associate-l/_binary64_696`
31×	`flip--_binary64_726` `flip3--_binary64_755`
27×	`flip3-+_binary64_754` `flip-+_binary64_725`
25×	`add-sqr-sqrt_binary64_772`
19×	`un-div-inv_binary64_749`
17×	`*-un-lft-identity_binary64_751`
14×	`associate-l_binary64_694`
12×	`exp-prod_binary64_800`
10×	`add-log-exp_binary64_787`
8×	`add-cube-cbrt_binary64_783`
6×	`pow1_binary64_809` `times-frac_binary64_757` `add-cbrt-cube_binary64_784` `difference-of-squares_binary64_720`
5×	`add-exp-log_binary64_786`
4×	`rem-exp-log_binary64_788`
3×	`difference-of-sqr-1_binary64_721` `associate-r_binary64_693`
2×	`distribute-lft-out--_binary64_705` `distribute-rgt-neg-in_binary64_711` `neg-log_binary64_841` `neg-mul-1_binary64_747` `distribute-lft-neg-in_binary64_710`
1×	`prod-exp_binary64_797` `unswap-sqr_binary64_719` `pow-prod-down_binary64_819` `*-commutative_binary64_684` `div-inv_binary64_748` `diff-log_binary64_840` `cbrt-unprod_binary64_781` `sub-neg_binary64_744`

Counts

4 → 164

Calls

4 calls:

22.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
18.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
4.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

series393.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

253.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
71.0ms	(.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x))))
37.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
31.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))

simplify125.0ms (2%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4966	8717
1	4966	8717

prune486.0ms (7.6%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	173	3	176
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	174	3	177

Merged error: 0.4b

Counts

177 → 3

Compiler

Compiled 8176 to 6347 computations (22.4% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 2/3 (pow.f64 x 3))
6.8b	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_772`
12×	`associate-r_binary64_693`
7×	`add-log-exp_binary64_787` `add-exp-log_binary64_786`
6×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
4×	`unswap-sqr_binary64_719` `unpow-prod-down_binary64_827` `add-cbrt-cube_binary64_784` `cube-prod_binary64_776`
3×	`prod-exp_binary64_797` `associate-l_binary64_694`
2×	`sqr-pow_binary64_723` `pow1_binary64_809` `diff-log_binary64_840`
1×	`cube-mult_binary64_778` `pow-to-exp_binary64_817` `pow-exp_binary64_816` `associate--l+_binary64_690` `flip--_binary64_726` `*-commutative_binary64_684` `sum-log_binary64_839` `cbrt-unprod_binary64_781` `unpow3_binary64_814` `sub-neg_binary64_744` `flip3--_binary64_755` `difference-of-squares_binary64_720`

Counts

2 → 45

Calls

2 calls:

9.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))
7.0ms	(*.f64 2/3 (pow.f64 x 3))

series79.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

45.0ms	(*.f64 2/3 (pow.f64 x 3))
34.0ms	(-.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (.f64 x x))

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4948	664
1	4948	664

prune59.0ms (0.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	50	1	51
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	51	3	54

Merged error: 0.4b

Counts

54 → 3

Compiler

Compiled 1067 to 792 computations (25.8% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 2/3 (pow.f64 x 3))
0.1b	(*.f64 2/3 (pow.f64 x 3))
11.2b	(-.f64 (pow.f64 (+.f64 (*.f64 2/3 (pow.f64 x 3)) 2) 3) (pow.f64 x 6))
13.4b	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) 3) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (+.f64 (.f64 x x) (+.f64 (*.f64 2/3 (pow.f64 x 3)) 2)))))

rewrite86.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

132×	`add-sqr-sqrt_binary64_772`
60×	`difference-of-squares_binary64_720`
48×	`times-frac_binary64_757`
43×	`unpow-prod-down_binary64_827` `*-un-lft-identity_binary64_751`
39×	`sqr-pow_binary64_723`
33×	`add-cube-cbrt_binary64_783`
24×	`associate-r_binary64_693`
23×	`cube-prod_binary64_776`
16×	`add-exp-log_binary64_786` `associate-/l*_binary64_698`
10×	`add-cbrt-cube_binary64_784`
8×	`unswap-sqr_binary64_719`
6×	`prod-exp_binary64_797` `add-log-exp_binary64_787` `associate-l_binary64_694`
5×	`distribute-lft-out--_binary64_705`
4×	`pow1_binary64_809`
3×	`associate-/r*_binary64_697`
2×	`cube-mult_binary64_778` `pow-to-exp_binary64_817` `pow-exp_binary64_816` `associate-/l/_binary64_700` `flip--_binary64_726` `*-commutative_binary64_684` `associate-/r/_binary64_699` `cbrt-unprod_binary64_781` `unpow3_binary64_814` `flip3--_binary64_755`
1×	`flip3-+_binary64_754` `div-sub_binary64_756` `div-inv_binary64_748` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `sub-neg_binary64_744` `flip-+_binary64_725` `div-exp_binary64_799`

Counts

4 → 170

Calls

4 calls:

24.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) 3) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (+.f64 (.f64 x x) (+.f64 (*.f64 2/3 (pow.f64 x 3)) 2)))))
16.0ms	(-.f64 (pow.f64 (+.f64 (*.f64 2/3 (pow.f64 x 3)) 2) 3) (pow.f64 x 6))
7.0ms	(*.f64 2/3 (pow.f64 x 3))
7.0ms	(*.f64 2/3 (pow.f64 x 3))

series309.0ms (4.9%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(/.f64 (-.f64 (pow.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) 3) (pow.f64 x 6)) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (+.f64 (.f64 x x) (+.f64 (*.f64 2/3 (pow.f64 x 3)) 2)))))
106.0ms	(-.f64 (pow.f64 (+.f64 (*.f64 2/3 (pow.f64 x 3)) 2) 3) (pow.f64 x 6))
48.0ms	(*.f64 2/3 (pow.f64 x 3))
47.0ms	(*.f64 2/3 (pow.f64 x 3))

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5854	9303

prune804.0ms (12.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	181	1	182
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	181	4	185

Merged error: 0.4b

Counts

185 → 4

Compiler

Compiled 10411 to 8315 computations (20.1% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 x 6) 5/3)
0.1b	(*.f64 2/3 (pow.f64 x 3))
0.1b	(*.f64 2/3 (pow.f64 x 3))
13.6b	(/.f64 (+.f64 8 (+.f64 (.f64 (pow.f64 x 6) 5/3) (.f64 (pow.f64 x 3) 8))) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (+.f64 (.f64 x x) (+.f64 (.f64 2/3 (pow.f64 x 3)) 2)))))

rewrite55.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`add-sqr-sqrt_binary64_772`
32×	`*-un-lft-identity_binary64_751`
27×	`associate-r_binary64_693`
24×	`add-cube-cbrt_binary64_783`
21×	`add-exp-log_binary64_786`
13×	`associate-l_binary64_694`
12×	`unpow-prod-down_binary64_827` `times-frac_binary64_757` `add-cbrt-cube_binary64_784`
11×	`unswap-sqr_binary64_719`
9×	`prod-exp_binary64_797`
8×	`cube-prod_binary64_776`
6×	`sqr-pow_binary64_723`
4×	`distribute-lft-out_binary64_704` `pow1_binary64_809` `add-log-exp_binary64_787` `associate-/l*_binary64_698`
3×	`pow-to-exp_binary64_817` `pow-exp_binary64_816` `associate-/r_binary64_697` `-commutative_binary64_684` `cbrt-unprod_binary64_781`
2×	`cube-mult_binary64_778` `flip3-+_binary64_754` `associate-/l/_binary64_700` `associate-/r/_binary64_699` `unpow3_binary64_814` `flip-+_binary64_725`
1×	`div-inv_binary64_748` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `div-exp_binary64_799`

Counts

4 → 122

Calls

4 calls:

13.0ms	(/.f64 (+.f64 8 (+.f64 (.f64 (pow.f64 x 6) 5/3) (.f64 (pow.f64 x 3) 8))) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (+.f64 (.f64 x x) (+.f64 (.f64 2/3 (pow.f64 x 3)) 2)))))
7.0ms	(*.f64 2/3 (pow.f64 x 3))
7.0ms	(*.f64 2/3 (pow.f64 x 3))
6.0ms	(*.f64 (pow.f64 x 6) 5/3)

series249.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

97.0ms	(/.f64 (+.f64 8 (+.f64 (.f64 (pow.f64 x 6) 5/3) (.f64 (pow.f64 x 3) 8))) (+.f64 (pow.f64 x 4) (.f64 (+.f64 (.f64 2/3 (pow.f64 x 3)) 2) (+.f64 (.f64 x x) (+.f64 (.f64 2/3 (pow.f64 x 3)) 2)))))
58.0ms	(*.f64 (pow.f64 x 6) 5/3)
47.0ms	(*.f64 2/3 (pow.f64 x 3))
46.0ms	(*.f64 2/3 (pow.f64 x 3))

simplify52.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5057	3664

prune382.0ms (6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	134	4	138

Merged error: 0.4b

Counts

138 → 4

Compiler

Compiled 6443 to 5104 computations (20.8% saved)

regimes61.0ms (1%)

Compiler: Compiled 516 to 432 computations (16.3% saved)

bsearch79.0ms (1.2%)

Steps

Iters	Range		Point
8	0.1393614513910683	496.2217663479898	62.70095631767314

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	208	129
1	208	129

end0.0ms (0%)

sample2.3s (35.5%)

Algorithm

1×

intervals

Results

865.0ms	1990×	body	1024	valid
358.0ms	4321×	body	128	valid
246.0ms	979×	body	512	valid
160.0ms	218×	body	2048	valid
79.0ms	492×	body	256	valid
20.0ms	204×	body	128	invalid
15.0ms	197×	body	128	overflowed
7.0ms	16×	body	1024	invalid
3.0ms	10×	body	512	invalid
1.0ms	6×	body	256	invalid

Compiler

Compiled 371 to 311 computations (16.2% saved)

Details

analyze226.0ms (3.6%)

sample66.0ms (1%)

simplify223.0ms (3.5%)

prune5.0ms (0.1%)

localize20.0ms (0.3%)

rewrite88.0ms (1.4%)

series393.0ms (6.2%)

simplify125.0ms (2%)

prune486.0ms (7.6%)

localize10.0ms (0.2%)

rewrite20.0ms (0.3%)

series79.0ms (1.2%)

simplify82.0ms (1.3%)

prune59.0ms (0.9%)

localize20.0ms (0.3%)

rewrite86.0ms (1.4%)

series309.0ms (4.9%)

simplify94.0ms (1.5%)

prune804.0ms (12.7%)

localize19.0ms (0.3%)

rewrite55.0ms (0.9%)

series249.0ms (3.9%)

simplify52.0ms (0.8%)

prune382.0ms (6%)

regimes61.0ms (1%)

bsearch79.0ms (1.2%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.3s (35.5%)

Profiling