Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
50%	12.5%	37.5%	5
50%	6.2%	43.8%	6
50%	3.1%	46.9%	7
50%	1.6%	48.5%	8
50%	0.8%	49.2%	9
50.4%	0.4%	49.2%	10
50.4%	0.2%	49.4%	11
50.4%	0.1%	49.5%	12
50.4%	0%	49.6%	13
50.4%	0%	49.6%	14

Compiler

Compiled 9 to 8 computations (11.1% saved)

sample108.0ms (1.6%)

Algorithm

1×

intervals

Results

78.0ms	131×	body	2048	valid
17.0ms	67×	body	1024	valid
4.0ms	31×	body	512	valid
1.0ms	13×	body	256	valid
1.0ms	14×	body	128	valid

Compiler

Compiled 17 to 16 computations (5.9% saved)

simplify239.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (115.0ms)

Iter	Nodes	Cost
0	4809	13
1	4809	13

prune4.0ms (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

30.3b

Counts

2 → 1

Compiler

Compiled 16 to 14 computations (12.5% saved)

localize11.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 (exp.f64 x) 2)
3.3b	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_419`
9×	`add-log-exp_binary64_458`
6×	`add-sqr-sqrt_binary64_441` `cancel-sign-sub-inv_binary64_385`
4×	`frac-add_binary64_427` `add-cube-cbrt_binary64_454` `associate-+l+_binary64_352`
3×	`flip3--_binary64_423` `flip--_binary64_394`
2×	`sub-neg_binary64_412` `exp-diff_binary64_467` `exp-neg_binary64_466` `sum-log_binary64_510` `distribute-lft-out_binary64_370` `distribute-lft-out--_binary64_371` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `diff-log_binary64_511` `pow1_binary64_480` `neg-sub0_binary64_414`
1×	`flip3-+_binary64_422` `difference-of-squares_binary64_388` `associate-+l-_binary64_354` `flip-+_binary64_393` `+-commutative_binary64_349`

Counts

2 → 39

Calls

2 calls:

22.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
9.0ms	(-.f64 (exp.f64 x) 2)

series46.0ms (0.7%)

Counts

2 → 6

Calls

2 calls:

38.0ms	(+.f64 (-.f64 (exp.f64 x) 2) (exp.f64 (neg.f64 x)))
8.0ms	(-.f64 (exp.f64 x) 2)

simplify80.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4887	654
1	4887	654

prune59.0ms (0.9%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	43	2	45
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	44	2	46

Error

0.0b

Counts

46 → 2

Compiler

Compiled 606 to 316 computations (47.9% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
0.0b	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
0.0b	(*.f64 1/360 (pow.f64 x 6))
0.1b	(*.f64 1/12 (pow.f64 x 4))

rewrite56.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_441`
14×	`associate-r_binary64_359` `add-exp-log_binary64_457`
11×	`add-log-exp_binary64_458`
10×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454`
8×	`unpow-prod-down_binary64_498` `add-cbrt-cube_binary64_455`
6×	`unswap-sqr_binary64_387` `prod-exp_binary64_468` `associate-l_binary64_360`
4×	`sqr-pow_binary64_391` `sum-log_binary64_510` `pow1_binary64_480`
2×	`flip3-+_binary64_422` `cbrt-unprod_binary64_452` `pow-exp_binary64_487` `pow-to-exp_binary64_488` `*-commutative_binary64_350` `flip-+_binary64_393` `+-commutative_binary64_349`
1×	`associate-+r+_binary64_351`

Counts

4 → 74

Calls

4 calls:

15.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))
11.0ms	(*.f64 1/360 (pow.f64 x 6))
10.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
9.0ms	(*.f64 1/12 (pow.f64 x 4))

series229.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

91.0ms	(+.f64 (.f64 1/360 (pow.f64 x 6)) (.f64 1/12 (pow.f64 x 4)))
57.0ms	(*.f64 1/360 (pow.f64 x 6))
51.0ms	(*.f64 1/12 (pow.f64 x 4))
30.0ms	(+.f64 (.f64 x x) (+.f64 (.f64 1/360 (pow.f64 x 6)) (*.f64 1/12 (pow.f64 x 4))))

simplify121.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	5006	1259

prune132.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	85	3	88

Error

Counts

88 → 3

Compiler

Compiled 1773 to 1249 computations (29.6% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(-.f64 2 (exp.f64 (neg.f64 x)))
3.5b	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`*-un-lft-identity_binary64_419`
11×	`add-sqr-sqrt_binary64_441` `cancel-sign-sub-inv_binary64_385`
9×	`add-log-exp_binary64_458`
5×	`add-cube-cbrt_binary64_454` `distribute-lft-out--_binary64_371`
4×	`diff-log_binary64_511` `associate--r+_binary64_355`
3×	`sub-neg_binary64_412` `difference-of-squares_binary64_388`
2×	`flip3--_binary64_423` `add-cbrt-cube_binary64_455` `add-exp-log_binary64_457` `flip--_binary64_394` `pow1_binary64_480`
1×	`associate--r-_binary64_358`

Counts

2 → 41

Calls

2 calls:

8.0ms	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
4.0ms	(-.f64 2 (exp.f64 (neg.f64 x)))

series40.0ms (0.6%)

Counts

2 → 6

Calls

2 calls:

28.0ms	(-.f64 (exp.f64 x) (-.f64 2 (exp.f64 (neg.f64 x))))
11.0ms	(-.f64 2 (exp.f64 (neg.f64 x)))

simplify91.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4832	659
1	4832	659

prune40.0ms (0.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	47	0	47
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	47	3	50

Error

Counts

50 → 3

Compiler

Compiled 631 to 323 computations (48.8% saved)

localize35.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/12 (pow.f64 x 4))
0.2b	(.f64 (.f64 x x) 1/360)
0.2b	(.f64 (.f64 x x) 1/360)
44.1b	(/.f64 (-.f64 (pow.f64 x 4) (.f64 (pow.f64 x 8) (.f64 (+.f64 1/12 (.f64 (.f64 x x) 1/360)) (+.f64 1/12 (.f64 (.f64 x x) 1/360))))) (-.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))

rewrite63.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_441`
21×	`add-exp-log_binary64_457`
18×	`*-un-lft-identity_binary64_419` `add-cube-cbrt_binary64_454` `add-cbrt-cube_binary64_455`
14×	`pow1_binary64_480`
13×	`associate-r_binary64_359`
12×	`times-frac_binary64_425`
9×	`prod-exp_binary64_468`
7×	`cbrt-unprod_binary64_452`
6×	`pow-prod-down_binary64_490`
5×	`unswap-sqr_binary64_387` `associate-l_binary64_360`
4×	`difference-of-squares_binary64_388` `unpow-prod-down_binary64_498` `add-log-exp_binary64_458` `associate-/r*_binary64_363`
3×	`-commutative_binary64_350` `associate-/l_binary64_364`
2×	`sqr-pow_binary64_391` `flip3--_binary64_423` `associate-/r/_binary64_365` `flip--_binary64_394` `associate-/l/_binary64_366`
1×	`clear-num_binary64_418` `div-inv_binary64_416` `pow-exp_binary64_487` `pow-to-exp_binary64_488` `frac-2neg_binary64_430` `div-exp_binary64_470` `cbrt-undiv_binary64_453` `div-sub_binary64_424`

Counts

4 → 99

Calls

4 calls:

27.0ms	(/.f64 (-.f64 (pow.f64 x 4) (.f64 (pow.f64 x 8) (.f64 (+.f64 1/12 (.f64 (.f64 x x) 1/360)) (+.f64 1/12 (.f64 (.f64 x x) 1/360))))) (-.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
6.0ms	(.f64 (.f64 x x) 1/360)
6.0ms	(.f64 (.f64 x x) 1/360)
6.0ms	(*.f64 1/12 (pow.f64 x 4))

series190.0ms (2.8%)

Counts

4 → 12

Calls

4 calls:

107.0ms	(/.f64 (-.f64 (pow.f64 x 4) (.f64 (pow.f64 x 8) (.f64 (+.f64 1/12 (.f64 (.f64 x x) 1/360)) (+.f64 1/12 (.f64 (.f64 x x) 1/360))))) (-.f64 (.f64 x x) (+.f64 (.f64 1/12 (pow.f64 x 4)) (*.f64 1/360 (pow.f64 x 6)))))
39.0ms	(*.f64 1/12 (pow.f64 x 4))
26.0ms	(.f64 (.f64 x x) 1/360)
18.0ms	(.f64 (.f64 x x) 1/360)

simplify103.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5378	3683

prune421.0ms (6.1%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	111	0	111
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	111	3	114

Error

Counts

114 → 3

Compiler

Compiled 5482 to 3758 computations (31.4% saved)

regimes92.0ms (1.3%)

Accuracy

Total 0.6b remaining (97.7%)

Threshold costs 0.6b (97.7%)

Compiler

Compiled 712 to 538 computations (24.4% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	22
1	17	22

end0.0ms (0%)

sample4.6s (67.4%)

Algorithm

1×

intervals

Results

3.0s	4191×	body	2048	valid
620.0ms	1985×	body	1024	valid
162.0ms	997×	body	512	valid
48.0ms	475×	body	256	valid
19.0ms	352×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 379 to 290 computations (23.5% saved)

Details

analyze6.0ms (0.1%)

sample108.0ms (1.6%)

simplify239.0ms (3.5%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

rewrite36.0ms (0.5%)

series46.0ms (0.7%)

simplify80.0ms (1.2%)

prune59.0ms (0.9%)

localize9.0ms (0.1%)

rewrite56.0ms (0.8%)

series229.0ms (3.3%)

simplify121.0ms (1.8%)

prune132.0ms (1.9%)

localize6.0ms (0.1%)

rewrite15.0ms (0.2%)

series40.0ms (0.6%)

simplify91.0ms (1.3%)

prune40.0ms (0.6%)

localize35.0ms (0.5%)

rewrite63.0ms (0.9%)

series190.0ms (2.8%)

simplify103.0ms (1.5%)

prune421.0ms (6.1%)

regimes92.0ms (1.3%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample4.6s (67.4%)

Profiling