Details

analyze235.0ms (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)

sample67.0ms (1%)

Algorithm

1×

intervals

Results

33.0ms	68×	body	1024	valid
12.0ms	143×	body	128	valid
5.0ms	22×	body	512	valid
3.0ms	4×	body	2048	valid
3.0ms	19×	body	256	valid
1.0ms	2×	body	1024	invalid
1.0ms	7×	body	128	invalid
0.0ms	5×	body	128	overflowed

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify225.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4908	41
1	4908	41

prune7.0ms (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: 27.5b

Counts

2 → 1

Compiler

Compiled 56 to 48 computations (14.3% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(*.f64 (+.f64 1 eps) x)
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
2.4b	(-.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)))))

rewrite71.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64_760`
74×	`exp-neg_binary64_795`
72×	`frac-times_binary64_761`
56×	`exp-diff_binary64_796` `neg-sub0_binary64_746`
38×	`associate-*l/_binary64_696`
36×	`associate-*r/_binary64_695`
28×	`flip3-+_binary64_754` `flip--_binary64_726` `flip3--_binary64_755` `flip-+_binary64_725`
18×	`un-div-inv_binary64_749`
12×	`exp-prod_binary64_800`
10×	`add-log-exp_binary64_787` `*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
8×	`add-cube-cbrt_binary64_783`
6×	`pow1_binary64_809` `add-cbrt-cube_binary64_784` `add-exp-log_binary64_786`
4×	`associate-l_binary64_694` `rem-exp-log_binary64_788`
3×	`associate-r_binary64_693`
2×	`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` `distribute-lft-out_binary64_704` `unswap-sqr_binary64_719` `pow-prod-down_binary64_819` `*-commutative_binary64_684` `diff-log_binary64_840` `cbrt-unprod_binary64_781` `sub-neg_binary64_744`

Counts

4 → 147

Calls

4 calls:

20.0ms	(-.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)))))
7.0ms	(*.f64 (+.f64 1 eps) x)
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
3.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

series366.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

262.0ms	(-.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)))))
40.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
32.0ms	(*.f64 (+.f64 1 eps) x)
31.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))

simplify125.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4987	8061
1	4987	8061

prune496.0ms (7.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	155	4	159
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	156	4	160

Merged error: 0.3b

Counts

160 → 4

Compiler

Compiled 7507 to 5843 computations (22.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64_772`
12×	`associate-l_binary64_694`
10×	`add-log-exp_binary64_787`
8×	`add-exp-log_binary64_786`
7×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
5×	`add-cbrt-cube_binary64_784`
4×	`unswap-sqr_binary64_719` `unpow-prod-down_binary64_827` `cube-prod_binary64_776`
3×	`prod-exp_binary64_797` `pow1_binary64_809` `associate-r_binary64_693`
2×	`sqr-pow_binary64_723` `diff-log_binary64_840` `sum-log_binary64_839`
1×	`cube-mult_binary64_778` `pow-to-exp_binary64_817` `+-commutative_binary64_683` `flip3-+_binary64_754` `pow-exp_binary64_816` `associate--l+_binary64_690` `flip--_binary64_726` `*-commutative_binary64_684` `cbrt-unprod_binary64_781` `unpow3_binary64_814` `sub-neg_binary64_744` `flip3--_binary64_755` `flip-+_binary64_725` `difference-of-squares_binary64_720`

Counts

3 → 56

Calls

3 calls:

9.0ms	(*.f64 (pow.f64 x 3) 2/3)
8.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
6.0ms	(+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)

series188.0ms (2.9%)

Counts

3 → 9

Calls

3 calls:

102.0ms	(+.f64 (*.f64 (pow.f64 x 3) 2/3) 2)
53.0ms	(*.f64 (pow.f64 x 3) 2/3)
33.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify41.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5328	874

prune76.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	63	2	65
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	64	5	69

Merged error: 0.3b

Counts

69 → 5

Compiler

Compiled 1325 to 994 computations (25% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (pow.f64 x 3) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)))
0.1b	(.f64 (.f64 (pow.f64 x 3) (*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3))
1.0b	(*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))
7.4b	(-.f64 (+.f64 (.f64 (.f64 (pow.f64 x 3) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3)) 2) (.f64 x x))

rewrite59.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-exp-log_binary64_786`
29×	`add-sqr-sqrt_binary64_772`
26×	`prod-exp_binary64_797`
19×	`cbrt-prod_binary64_779` `associate-l_binary64_694`
17×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
13×	`pow1_binary64_809` `associate-r_binary64_693`
11×	`add-cbrt-cube_binary64_784`
10×	`cbrt-unprod_binary64_781`
9×	`add-log-exp_binary64_787`
8×	`unswap-sqr_binary64_719`
6×	`pow1/3_binary64_830` `swap-sqr_binary64_718`
4×	`pow-to-exp_binary64_817` `pow-exp_binary64_816` `unpow-prod-down_binary64_827` `cube-prod_binary64_776`
3×	`pow-prod-down_binary64_819` `*-commutative_binary64_684`
2×	`sqr-pow_binary64_723` `pow-sqr_binary64_724` `pow-prod-up_binary64_818` `diff-log_binary64_840`
1×	`cube-mult_binary64_778` `pow-plus_binary64_811` `associate--l+_binary64_690` `flip--_binary64_726` `sum-log_binary64_839` `unpow3_binary64_814` `pow2_binary64_829` `sub-neg_binary64_744` `flip3--_binary64_755` `difference-of-squares_binary64_720`

Counts

4 → 113

Calls

4 calls:

16.0ms	(-.f64 (+.f64 (.f64 (.f64 (pow.f64 x 3) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3)) 2) (.f64 x x))
13.0ms	(.f64 (pow.f64 x 3) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)))
12.0ms	(.f64 (.f64 (pow.f64 x 3) (*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3))
6.0ms	(*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))

series261.0ms (4%)

Counts

4 → 10

Calls

4 calls:

111.0ms	(.f64 (.f64 (pow.f64 x 3) (*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3))
97.0ms	(.f64 (pow.f64 x 3) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3)))
53.0ms	(-.f64 (+.f64 (.f64 (.f64 (pow.f64 x 3) (.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))) (cbrt.f64 2/3)) 2) (.f64 x x))
0.0ms	(*.f64 (cbrt.f64 2/3) (cbrt.f64 2/3))

simplify66.0ms (1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4896	1455
1	4896	1455

prune168.0ms (2.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	123	5	128

Merged error: 0.3b

Counts

128 → 5

Compiler

Compiled 2768 to 2205 computations (20.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 x x) (*.f64 x (pow.f64 (cbrt.f64 2/3) 2)))
0.1b	(.f64 (.f64 (.f64 x x) (.f64 x (pow.f64 (cbrt.f64 2/3) 2))) (cbrt.f64 2/3))
1.0b	(pow.f64 (cbrt.f64 2/3) 2)
7.4b	(-.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (pow.f64 (cbrt.f64 2/3) 2))) (cbrt.f64 2/3)) 2) (*.f64 x x))

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

63×	`add-exp-log_binary64_786`
45×	`prod-exp_binary64_797`
29×	`add-cbrt-cube_binary64_784`
21×	`cbrt-unprod_binary64_781`
19×	`pow1_binary64_809`
10×	`add-sqr-sqrt_binary64_772`
9×	`add-cube-cbrt_binary64_783` `add-log-exp_binary64_787` `pow-prod-down_binary64_819` `*-un-lft-identity_binary64_751`
7×	`associate-r_binary64_693`
6×	`cbrt-prod_binary64_779` `unpow-prod-down_binary64_827`
5×	`pow-to-exp_binary64_817` `pow-exp_binary64_816`
3×	`pow-unpow_binary64_825`
2×	`-commutative_binary64_684` `pow-pow_binary64_820` `diff-log_binary64_840` `associate-l*_binary64_694`
1×	`pow1/3_binary64_830` `unpow2_binary64_813` `sqr-pow_binary64_723` `associate--l+_binary64_690` `flip--_binary64_726` `sum-log_binary64_839` `sub-neg_binary64_744` `flip3--_binary64_755` `difference-of-squares_binary64_720`

Counts

4 → 92

Calls

4 calls:

16.0ms	(-.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (pow.f64 (cbrt.f64 2/3) 2))) (cbrt.f64 2/3)) 2) (*.f64 x x))
13.0ms	(.f64 (.f64 (.f64 x x) (.f64 x (pow.f64 (cbrt.f64 2/3) 2))) (cbrt.f64 2/3))
10.0ms	(.f64 (.f64 x x) (*.f64 x (pow.f64 (cbrt.f64 2/3) 2)))
3.0ms	(pow.f64 (cbrt.f64 2/3) 2)

series285.0ms (4.4%)

Counts

4 → 10

Calls

4 calls:

122.0ms	(.f64 (.f64 (.f64 x x) (.f64 x (pow.f64 (cbrt.f64 2/3) 2))) (cbrt.f64 2/3))
96.0ms	(.f64 (.f64 x x) (*.f64 x (pow.f64 (cbrt.f64 2/3) 2)))
67.0ms	(-.f64 (+.f64 (.f64 (.f64 (.f64 x x) (.f64 x (pow.f64 (cbrt.f64 2/3) 2))) (cbrt.f64 2/3)) 2) (*.f64 x x))
0.0ms	(pow.f64 (cbrt.f64 2/3) 2)

simplify53.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

102 → 102

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5385	1250

prune118.0ms (1.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	102	0	102
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	102	5	107

Merged error: 0.3b

Counts

107 → 5

Compiler

Compiled 2097 to 1566 computations (25.3% saved)

regimes432.0ms (6.6%)

Compiler: Compiled 5104 to 4264 computations (16.5% saved)

bsearch95.0ms (1.5%)

Steps

Iters	Range		Point
10	2.0717416958964465e-05	435548.6755890104	27.34141034853695

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	233	66
1	233	66

end0.0ms (0%)

sample3.0s (45.4%)

Algorithm

1×

intervals

Results

884.0ms	2002×	body	1024	valid
345.0ms	4223×	body	128	valid
263.0ms	1034×	body	512	valid
158.0ms	214×	body	2048	valid
90.0ms	527×	body	256	valid
21.0ms	223×	body	128	invalid
14.0ms	176×	body	128	overflowed
10.0ms	24×	body	1024	invalid
5.0ms	11×	body	512	invalid
1.0ms	7×	body	256	invalid

Compiler

Compiled 1321 to 1104 computations (16.4% saved)

Details

analyze235.0ms (3.6%)

sample67.0ms (1%)

simplify225.0ms (3.4%)

prune7.0ms (0.1%)

localize18.0ms (0.3%)

rewrite71.0ms (1.1%)

series366.0ms (5.6%)

simplify125.0ms (1.9%)

prune496.0ms (7.6%)

localize8.0ms (0.1%)

rewrite27.0ms (0.4%)

series188.0ms (2.9%)

simplify41.0ms (0.6%)

prune76.0ms (1.2%)

localize12.0ms (0.2%)

rewrite59.0ms (0.9%)

series261.0ms (4%)

simplify66.0ms (1%)

prune168.0ms (2.6%)

localize11.0ms (0.2%)

rewrite53.0ms (0.8%)

series285.0ms (4.4%)

simplify53.0ms (0.8%)

prune118.0ms (1.8%)

regimes432.0ms (6.6%)

bsearch95.0ms (1.5%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample3.0s (45.4%)

Profiling