Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample46.0ms (0.8%)

Algorithm

1×

intervals

Results

22.0ms	82×	body	1024	valid
7.0ms	47×	body	512	valid
4.0ms	96×	body	128	valid
3.0ms	26×	body	256	valid
2.0ms	5×	body	2048	valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify167.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	168	9
1	168	9

prune9.0ms (0.1%)

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

40.2b

Counts

2 → 1

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
4.7b	(-.f64 (exp.f64 x) 1)

rewrite28.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_2487`
30×	`*-un-lft-identity_binary64_2465`
21×	`times-frac_binary64_2471`
15×	`add-cube-cbrt_binary64_2500`
10×	`difference-of-squares_binary64_2434`
7×	`associate-/l*_binary64_2410`
5×	`difference-of-sqr-1_binary64_2435` `distribute-lft-out--_binary64_2417`
4×	`add-log-exp_binary64_2504` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501`
3×	`associate-/r*_binary64_2409` `cancel-sign-sub-inv_binary64_2431`
2×	`flip--_binary64_2440` `associate-/l/_binary64_2412` `pow1_binary64_2526` `flip3--_binary64_2469`
1×	`clear-num_binary64_2464` `cbrt-undiv_binary64_2499` `div-sub_binary64_2470` `sub-neg_binary64_2458` `div-exp_binary64_2516` `div-inv_binary64_2462` `diff-log_binary64_2557` `frac-2neg_binary64_2476`

Counts

2 → 64

Calls

2 calls:

12.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
8.0ms	(-.f64 (exp.f64 x) 1)

series84.0ms (1.4%)

Counts

2 → 12

Calls

2 calls:

54.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
29.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 134 to 114 computations (14.9% saved)

simplify117.0ms (2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (91.0ms)

Iter	Nodes	Cost
0	4961	1076
1	4961	1076

prune128.0ms (2.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	2	77

Error

0.0b

Counts

77 → 2

Compiler

Compiled 924 to 507 computations (45.1% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 1/6 (*.f64 x 1/24))
0.0b	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
0.2b	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
0.3b	(*.f64 x 1/24)

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_2487`
10×	`*-un-lft-identity_binary64_2465` `add-cube-cbrt_binary64_2500` `add-exp-log_binary64_2503` `add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
9×	`associate-r_binary64_2405` `associate-l_binary64_2406`
6×	`add-log-exp_binary64_2504`
4×	`associate-*r/_binary64_2407`
3×	`flip3-+_binary64_2468` `*-commutative_binary64_2396` `flip-+_binary64_2439` `unswap-sqr_binary64_2433` `prod-exp_binary64_2514` `pow-prod-down_binary64_2536` `cbrt-unprod_binary64_2498`
2×	`distribute-lft-in_binary64_2414` `distribute-rgt-in_binary64_2415`
1×	`+-commutative_binary64_2395` `sum-log_binary64_2556`

Counts

4 → 73

Calls

4 calls:

10.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
10.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
7.0ms	(*.f64 x 1/24)
6.0ms	(+.f64 1/6 (*.f64 x 1/24))

series221.0ms (3.8%)

Counts

4 → 20

Calls

4 calls:

88.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
55.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
47.0ms	(+.f64 1/6 (*.f64 x 1/24))
31.0ms	(*.f64 x 1/24)

Compiler

Compiled 398 to 347 computations (12.8% saved)

simplify167.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (139.0ms)

Iter	Nodes	Cost
0	4884	1083
1	4884	1083

prune157.0ms (2.7%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	93	0	93
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	93	2	95

Error

0.0b

Counts

95 → 2

Compiler

Compiled 1612 to 1249 computations (22.5% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (exp.f64 x) (exp.f64 x))
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(/.f64 (-.f64 (.f64 (exp.f64 x) (exp.f64 x)) (.f64 1 1)) (*.f64 x (+.f64 (exp.f64 x) 1)))
4.7b	(-.f64 (.f64 (exp.f64 x) (exp.f64 x)) (.f64 1 1))

rewrite69.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64_2465` `add-sqr-sqrt_binary64_2487` `exp-prod_binary64_2517`
16×	`add-cube-cbrt_binary64_2500`
11×	`add-cbrt-cube_binary64_2501` `pow1_binary64_2526`
9×	`add-exp-log_binary64_2503`
8×	`add-log-exp_binary64_2504`
4×	`times-frac_binary64_2471` `pow-prod-down_binary64_2536` `associate-/l*_binary64_2410` `pow-sqr_binary64_2438` `pow-prod-up_binary64_2535`
3×	`difference-of-squares_binary64_2434` `swap-sqr_binary64_2432` `associate-r_binary64_2405` `associate-l_binary64_2406`
2×	`flip3-+_binary64_2468` `flip--_binary64_2440` `associate-/l/_binary64_2412` `flip-+_binary64_2439` `associate-*r/_binary64_2407` `cbrt-undiv_binary64_2499` `div-exp_binary64_2516` `associate-/r/_binary64_2411` `prod-exp_binary64_2514` `flip3--_binary64_2469` `cbrt-unprod_binary64_2498`
1×	`-commutative_binary64_2396` `+-commutative_binary64_2395` `pow-plus_binary64_2528` `associate-/r_binary64_2409` `sum-log_binary64_2556` `clear-num_binary64_2464` `div-sub_binary64_2470` `sub-neg_binary64_2458` `unswap-sqr_binary64_2433` `cancel-sign-sub-inv_binary64_2431` `div-inv_binary64_2462` `diff-log_binary64_2557` `pow2_binary64_2546` `frac-2neg_binary64_2476` `distribute-lft-out_binary64_2416`

Counts

4 → 87

Calls

4 calls:

24.0ms	(/.f64 (-.f64 (.f64 (exp.f64 x) (exp.f64 x)) (.f64 1 1)) (*.f64 x (+.f64 (exp.f64 x) 1)))
13.0ms	(*.f64 (exp.f64 x) (exp.f64 x))
12.0ms	(-.f64 (.f64 (exp.f64 x) (exp.f64 x)) (.f64 1 1))
7.0ms	(+.f64 (exp.f64 x) 1)

series292.0ms (5%)

Counts

4 → 24

Calls

4 calls:

150.0ms	(/.f64 (-.f64 (.f64 (exp.f64 x) (exp.f64 x)) (.f64 1 1)) (*.f64 x (+.f64 (exp.f64 x) 1)))
64.0ms	(-.f64 (.f64 (exp.f64 x) (exp.f64 x)) (.f64 1 1))
49.0ms	(*.f64 (exp.f64 x) (exp.f64 x))
29.0ms	(+.f64 (exp.f64 x) 1)

Compiler

Compiled 492 to 392 computations (20.3% saved)

simplify162.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (127.0ms)

Iter	Nodes	Cost
0	4968	1218
1	4968	1218

prune186.0ms (3.2%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	111	2	113

Error

0.0b

Counts

113 → 2

Compiler

Compiled 1954 to 1180 computations (39.6% saved)

localize30.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1)) (cbrt.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1)))
4.7b	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
4.7b	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
4.7b	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

rewrite104.0ms (1.8%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`cbrt-prod_binary64_2496`
34×	`add-sqr-sqrt_binary64_2487`
32×	`*-un-lft-identity_binary64_2465`
28×	`difference-of-sqr--1_binary64_2436`
13×	`swap-sqr_binary64_2432`
12×	`add-cube-cbrt_binary64_2500` `cbrt-div_binary64_2497`
11×	`pow1_binary64_2526` `associate-r_binary64_2405` `associate-l_binary64_2406`
10×	`add-log-exp_binary64_2504`
9×	`flip3-+_binary64_2468` `flip-+_binary64_2439` `distribute-lft-out_binary64_2416`
7×	`unpow2_binary64_2530` `unpow-prod-down_binary64_2544` `sqr-pow_binary64_2437`
6×	`add-exp-log_binary64_2503` `pow1/3_binary64_2547`
4×	`frac-times_binary64_2475` `unswap-sqr_binary64_2433` `add-cbrt-cube_binary64_2501`
3×	`+-commutative_binary64_2395` `sum-log_binary64_2556`
2×	`associate-l/_binary64_2408` `associate-r/_binary64_2407` `pow-prod-down_binary64_2536` `pow-sqr_binary64_2438` `pow-prod-up_binary64_2535`
1×	`*-commutative_binary64_2396` `pow-plus_binary64_2528` `pow2_binary64_2546` `prod-exp_binary64_2514` `cbrt-unprod_binary64_2498`

Counts

4 → 113

Calls

4 calls:

39.0ms	(*.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1)) (cbrt.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1)))
13.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
13.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
12.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

series468.0ms (8%)

Counts

4 → 22

Calls

4 calls:

257.0ms	(*.f64 (cbrt.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1)) (cbrt.f64 (+.f64 (pow.f64 (exp.f64 x) 2) -1)))
74.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
70.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)
67.0ms	(+.f64 (pow.f64 (exp.f64 x) 2) -1)

Compiler

Compiled 1014 to 799 computations (21.2% saved)

simplify191.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (136.0ms)

Iter	Nodes	Cost
0	5076	2411

prune540.0ms (9.3%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	135	2	137

Error

0.0b

Counts

137 → 2

Compiler

Compiled 4636 to 3277 computations (29.3% saved)

regimes187.0ms (3.2%)

Accuracy

Total 0.3b remaining (93.9%)

Threshold costs 0.3b (93.9%)

Compiler

Compiled 670 to 506 computations (24.5% saved)

bsearch36.0ms (0.6%)

Steps

Iters	Range		Point
7	-0.021320333442052152	-0.0003320818424067879	-0.0013678994670240129

Compiler

Compiled 1 to 1 computations (0% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	73
1	37	73

end0.0ms (0%)

sample2.3s (40.2%)

Algorithm

1×

intervals

Results

782.0ms	2615×	body	1024	valid
222.0ms	1330×	body	512	valid
141.0ms	3070×	body	128	valid
112.0ms	291×	body	2048	valid
73.0ms	694×	body	256	valid

Compiler

Compiled 387 to 291 computations (24.8% saved)

Details

analyze6.0ms (0.1%)

sample46.0ms (0.8%)

simplify167.0ms (2.9%)

prune9.0ms (0.1%)

localize8.0ms (0.1%)

rewrite28.0ms (0.5%)

series84.0ms (1.4%)

simplify117.0ms (2%)

prune128.0ms (2.2%)

localize17.0ms (0.3%)

rewrite42.0ms (0.7%)

series221.0ms (3.8%)

simplify167.0ms (2.9%)

prune157.0ms (2.7%)

localize18.0ms (0.3%)

rewrite69.0ms (1.2%)

series292.0ms (5%)

simplify162.0ms (2.8%)

prune186.0ms (3.2%)

localize30.0ms (0.5%)

rewrite104.0ms (1.8%)

series468.0ms (8%)

simplify191.0ms (3.3%)

prune540.0ms (9.3%)

regimes187.0ms (3.2%)

bsearch36.0ms (0.6%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.3s (40.2%)

Profiling