Details

analyze4.0ms (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)

sample33.0ms (1.1%)

Algorithm

1×

intervals

Results

14.0ms	86×	body	1024	valid
6.0ms	28×	body	256	valid
3.0ms	39×	body	512	valid
3.0ms	99×	body	128	valid
1.0ms	4×	body	2048	valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify103.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (9.0ms)

Iter	Nodes	Cost
0	168	9
1	168	9

prune2.0ms (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

40.3b

Counts

2 → 1

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize4.0ms (0.1%)

Local error

Found 4 expressions with local error:

5.5b	(-.f64 (exp.f64 x) 1)
0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
5.5b	(-.f64 (exp.f64 x) 1)

rewrite17.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_441`
30×	`*-un-lft-identity_binary64_419`
21×	`times-frac_binary64_425`
15×	`add-cube-cbrt_binary64_454`
10×	`difference-of-squares_binary64_388`
7×	`associate-/l*_binary64_364`
5×	`difference-of-sqr-1_binary64_389` `distribute-lft-out--_binary64_371`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457`
3×	`cancel-sign-sub-inv_binary64_385` `associate-/r*_binary64_363`
2×	`flip3--_binary64_423` `flip--_binary64_394` `pow1_binary64_480` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `div-inv_binary64_416` `frac-2neg_binary64_430` `diff-log_binary64_511` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-sub_binary64_424`

Counts

2 → 64

Calls

4 calls:

7.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
5.0ms	(-.f64 (exp.f64 x) 1)
0.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
0.0ms	(-.f64 (exp.f64 x) 1)

series54.0ms (1.8%)

Counts

2 → 12

Calls

2 calls:

33.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
21.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 134 to 114 computations (14.9% saved)

simplify65.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4961	1076
1	4961	1076

prune93.0ms (3.1%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	3	77

Error

0.0b

Counts

77 → 3

Compiler

Compiled 932 to 513 computations (45% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(*.f64 x 1/6)
0.1b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.1b	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.3b	(*.f64 x 1/6)

rewrite12.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64_441`
6×	`-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `associate-r_binary64_359` `associate-l*_binary64_360` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `pow1_binary64_480`
2×	`pow-prod-down_binary64_490` `add-log-exp_binary64_458` `unswap-sqr_binary64_387` `prod-exp_binary64_468` `cbrt-unprod_binary64_452` `associate-r/_binary64_361` `-commutative_binary64_350`
1×	`flip3-+_binary64_422` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `flip-+_binary64_393`

Counts

2 → 40

Calls

4 calls:

5.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
4.0ms	(*.f64 x 1/6)
0.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
0.0ms	(*.f64 x 1/6)

series67.0ms (2.2%)

Counts

2 → 9

Calls

2 calls:

51.0ms	(.f64 x (+.f64 1/2 (.f64 x 1/6)))
16.0ms	(*.f64 x 1/6)

Compiler

Compiled 139 to 127 computations (8.6% saved)

simplify79.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4923	458
1	4923	458

prune40.0ms (1.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	49	0	49
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	49	3	52

Error

0.0b

Counts

52 → 3

Compiler

Compiled 655 to 510 computations (22.1% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

5.0b	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
0.0b	(/.f64 (exp.f64 x) x)
0.0b	(/.f64 (exp.f64 x) x)
5.0b	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))

rewrite25.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`add-sqr-sqrt_binary64_441`
33×	`*-un-lft-identity_binary64_419`
32×	`times-frac_binary64_425`
19×	`add-cube-cbrt_binary64_454`
13×	`cancel-sign-sub-inv_binary64_385`
7×	`div-inv_binary64_416`
6×	`difference-of-squares_binary64_388`
5×	`distribute-lft-out--_binary64_371`
4×	`add-log-exp_binary64_458` `add-cbrt-cube_binary64_455`
3×	`distribute-rgt-out--_binary64_373` `add-exp-log_binary64_457` `associate-/r_binary64_363` `associate-/l_binary64_364`
2×	`pow1_binary64_480`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `flip3--_binary64_423` `frac-2neg_binary64_430` `diff-log_binary64_511` `flip--_binary64_394` `sub-div_binary64_426` `div-exp_binary64_470` `frac-sub_binary64_428` `cbrt-undiv_binary64_453`

Counts

2 → 67

Calls

4 calls:

15.0ms	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
4.0ms	(/.f64 (exp.f64 x) x)
0.0ms	(/.f64 (exp.f64 x) x)
0.0ms	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))

series58.0ms (1.9%)

Counts

2 → 12

Calls

2 calls:

32.0ms	(-.f64 (/.f64 (exp.f64 x) x) (/.f64 1 x))
25.0ms	(/.f64 (exp.f64 x) x)

Compiler

Compiled 142 to 121 computations (14.8% saved)

simplify68.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5008	961

prune49.0ms (1.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	79	3	82

Error

0.0b

Counts

82 → 3

Compiler

Compiled 968 to 457 computations (52.8% saved)

localize11.0ms (0.4%)

Local error

Found 8 expressions with local error:

0.0b	(+.f64 x (.f64 x (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
0.0b	(pow.f64 (exp.f64 x) 3)
0.0b	(.f64 x (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1)))
0.0b	(+.f64 (exp.f64 x) 1)
0.0b	(+.f64 x (.f64 x (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
0.0b	(pow.f64 (exp.f64 x) 3)
0.3b	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 1 3)) (+.f64 x (.f64 x (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1)))))
5.4b	(-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 1 3))

rewrite78.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

200×	`add-sqr-sqrt_binary64_441`
145×	`*-un-lft-identity_binary64_419`
120×	`difference-of-squares_binary64_388`
102×	`times-frac_binary64_425`
96×	`unpow-prod-down_binary64_498` `cube-prod_binary64_447`
52×	`sqr-pow_binary64_391`
50×	`add-cube-cbrt_binary64_454`
34×	`associate-/l*_binary64_364`
30×	`distribute-lft-out--_binary64_371`
12×	`cancel-sign-sub-inv_binary64_385`
8×	`add-log-exp_binary64_458`
7×	`cube-mult_binary64_449` `add-cbrt-cube_binary64_455`
6×	`add-exp-log_binary64_457`
5×	`difference-cubes_binary64_421` `pow1_binary64_480`
4×	`associate-+r+_binary64_351` `distribute-rgt-in_binary64_369` `distribute-lft-in_binary64_368` `pow-pow_binary64_491`
3×	`exp-prod_binary64_471` `pow-unpow_binary64_496` `associate-/r*_binary64_363`
2×	`flip3-+_binary64_422` `unpow3_binary64_485` `flip3--_binary64_423` `associate-/r/_binary64_365` `flip-+_binary64_393` `flip--_binary64_394` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `sub-neg_binary64_412` `div-inv_binary64_416` `rem-cube-cbrt_binary64_442` `pow-exp_binary64_487` `sum-log_binary64_510` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `diff-log_binary64_511` `+-commutative_binary64_349` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-sub_binary64_424`

Counts

4 → 251

Calls

8 calls:

25.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 1 3)) (+.f64 x (.f64 x (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1)))))
13.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 1 3))
4.0ms	(+.f64 x (.f64 x (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
3.0ms	(pow.f64 (exp.f64 x) 3)
0.0ms	(+.f64 (exp.f64 x) 1)

series297.0ms (9.8%)

Counts

4 → 24

Calls

4 calls:

154.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 1 3)) (+.f64 x (.f64 x (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1)))))
66.0ms	(+.f64 x (.f64 x (.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
40.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) (pow.f64 1 3))
36.0ms	(pow.f64 (exp.f64 x) 3)

Compiler

Compiled 616 to 468 computations (24% saved)

simplify129.0ms (4.3%)

Algorithm

1×	egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4970	9169
1	4970	9169

prune426.0ms (14.1%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	274	1	275
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	275	3	278

Error

0.0b

Counts

278 → 3

Compiler

Compiled 8169 to 4930 computations (39.6% saved)

regimes143.0ms (4.7%)

Accuracy

Total 0.4b remaining (91.8%)

Threshold costs 0.4b (91.8%)

Compiler

Compiled 493 to 363 computations (26.4% saved)

bsearch18.0ms (0.6%)

Steps

Iters	Range		Point
8	-0.011427994505944315	-6.511678050582778e-06	-0.0001903937319594397

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	51
1	42	51

end2.0ms (0.1%)

Compiler: Compiled 33 to 24 computations (27.3% saved)

sample1.1s (37.4%)

Algorithm

1×

intervals

Results

425.0ms	2658×	body	1024	valid
119.0ms	1283×	body	512	valid
85.0ms	3114×	body	128	valid
54.0ms	287×	body	2048	valid
40.0ms	658×	body	256	valid

Compiler

Compiled 270 to 198 computations (26.7% saved)

Pareto

Details

analyze4.0ms (0.1%)

sample33.0ms (1.1%)

simplify103.0ms (3.4%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite17.0ms (0.6%)

series54.0ms (1.8%)

simplify65.0ms (2.1%)

prune93.0ms (3.1%)

localize6.0ms (0.2%)

rewrite12.0ms (0.4%)

series67.0ms (2.2%)

simplify79.0ms (2.6%)

prune40.0ms (1.3%)

localize5.0ms (0.2%)

rewrite25.0ms (0.8%)

series58.0ms (1.9%)

simplify68.0ms (2.3%)

prune49.0ms (1.6%)

localize11.0ms (0.4%)

rewrite78.0ms (2.6%)

series297.0ms (9.8%)

simplify129.0ms (4.3%)

prune426.0ms (14.1%)

regimes143.0ms (4.7%)

bsearch18.0ms (0.6%)

simplify3.0ms (0.1%)

end2.0ms (0.1%)

sample1.1s (37.4%)

Profiling