Details

analyze4.0ms (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)

sample56.0ms (1.1%)

Algorithm

1×

intervals

Results

35.0ms	143×	body	1024	valid
7.0ms	52×	body	512	valid
3.0ms	12×	body	2048	valid
2.0ms	32×	body	256	valid
1.0ms	17×	body	128	valid

Compiler

Compiled 22 to 19 computations (13.6% saved)

simplify285.0ms (5.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (280.0ms)

Iter	Nodes	Cost
0	7544	20

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

62.5b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize9.0ms (0.2%)

Local error

Found 8 expressions with local error:

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

rewrite48.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64_78`
37×	`times-frac_binary64_84`
36×	`add-sqr-sqrt_binary64_100`
28×	`sqrt-prod_binary64_94`
26×	`add-cube-cbrt_binary64_113`
12×	`difference-of-squares_binary64_47`
8×	`add-log-exp_binary64_117` `associate-/l*_binary64_23` `distribute-lft-out_binary64_29`
7×	`div-inv_binary64_75`
6×	`add-cbrt-cube_binary64_114` `add-exp-log_binary64_116`
5×	`pow1_binary64_139`
4×	`sqrt-div_binary64_95`
3×	`flip3--_binary64_82` `distribute-rgt-out_binary64_31` `flip--_binary64_53` `associate-/r*_binary64_22`
2×	`associate-/l/_binary64_25`
1×	`+-commutative_binary64_8` `frac-add_binary64_86` `sqrt-pow1_binary64_96` `cbrt-undiv_binary64_112` `div-exp_binary64_129` `flip-+_binary64_52` `rem-sqrt-square_binary64_91` `diff-log_binary64_170` `frac-2neg_binary64_89` `clear-num_binary64_77` `cancel-sign-sub-inv_binary64_44` `pow1/2_binary64_158` `distribute-rgt1-in_binary64_34` `sub-neg_binary64_71` `sum-log_binary64_169` `flip3-+_binary64_81`

Counts

4 → 104

Calls

8 calls:

26.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
6.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
3.0ms	(-.f64 1 (*.f64 x x))
3.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0ms	(-.f64 1 (*.f64 x x))

series137.0ms (2.8%)

Counts

4 → 21

Calls

4 calls:

39.0ms	(-.f64 1 (*.f64 x x))
35.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
33.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
30.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

Compiler

Compiled 435 to 382 computations (12.2% saved)

simplify74.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5023	2004

prune147.0ms (3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	3	126

Error

62.5b

Counts

126 → 3

Compiler

Compiled 2299 to 1480 computations (35.6% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 2 x) (+.f64 (.f64 x 1/2) (.f64 (pow.f64 x 3) 1/8)))
0.0b	(log.f64 (-.f64 (/.f64 2 x) (+.f64 (.f64 x 1/2) (.f64 (pow.f64 x 3) 1/8))))
0.0b	(log.f64 (-.f64 (/.f64 2 x) (+.f64 (.f64 x 1/2) (.f64 (pow.f64 x 3) 1/8))))
0.0b	(-.f64 (/.f64 2 x) (+.f64 (.f64 x 1/2) (.f64 (pow.f64 x 3) 1/8)))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64_100`
8×	`*-un-lft-identity_binary64_78`
7×	`add-log-exp_binary64_117`
6×	`log-prod_binary64_164`
4×	`frac-sub_binary64_87` `add-cube-cbrt_binary64_113` `log-div_binary64_165` `difference-of-squares_binary64_47`
3×	`add-exp-log_binary64_116` `cancel-sign-sub-inv_binary64_44` `pow1_binary64_139`
2×	`add-cbrt-cube_binary64_114` `flip-+_binary64_52` `distribute-lft-out--_binary64_30` `flip3--_binary64_82` `diff-log_binary64_170` `times-frac_binary64_84` `flip--_binary64_53` `flip3-+_binary64_81`
1×	`associate--r+_binary64_14` `rem-log-exp_binary64_119` `log-pow_binary64_167` `sub-neg_binary64_71` `sum-log_binary64_169`

Counts

2 → 40

Calls

4 calls:

11.0ms	(-.f64 (/.f64 2 x) (+.f64 (.f64 x 1/2) (.f64 (pow.f64 x 3) 1/8)))
9.0ms	(log.f64 (-.f64 (/.f64 2 x) (+.f64 (.f64 x 1/2) (.f64 (pow.f64 x 3) 1/8))))
0.0ms	(log.f64 (-.f64 (/.f64 2 x) (+.f64 (.f64 x 1/2) (.f64 (pow.f64 x 3) 1/8))))
0.0ms	(-.f64 (/.f64 2 x) (+.f64 (.f64 x 1/2) (.f64 (pow.f64 x 3) 1/8)))

series177.0ms (3.6%)

Counts

2 → 15

Calls

2 calls:

129.0ms	(-.f64 (/.f64 2 x) (+.f64 (.f64 x 1/2) (.f64 (pow.f64 x 3) 1/8)))
47.0ms	(log.f64 (-.f64 (/.f64 2 x) (+.f64 (.f64 x 1/2) (.f64 (pow.f64 x 3) 1/8))))

Compiler

Compiled 252 to 229 computations (9.1% saved)

simplify56.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

55 → 55

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4973	1559
1	4973	1559

prune143.0ms (2.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	44	11	55
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	45	13	58

Error

60.6b

Counts

58 → 13

Compiler

Compiled 1574 to 1276 computations (18.9% saved)

localize7.0ms (0.1%)

rewrite0.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms (0%)

Counts: 0 → 0

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune21.0ms (0.4%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Kept	Total
New	0	0
Fresh	12	12
Picked	1	1
Done	0	0
Total	13	13

Error

60.6b

Counts

13 → 13

Compiler

Compiled 369 to 309 computations (16.3% saved)

localize16.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.1b	(*.f64 3/32 (pow.f64 x 4))
0.1b	(*.f64 1/48 (pow.f64 x 6))
0.0b	(+.f64 (.f64 3/32 (pow.f64 x 4)) (+.f64 (pow.f64 (.f64 x 1/2) 2) (+.f64 (log.f64 x) (*.f64 1/48 (pow.f64 x 6)))))
0.0b	(+.f64 (pow.f64 (.f64 x 1/2) 2) (+.f64 (log.f64 x) (.f64 1/48 (pow.f64 x 6))))
0.0b	(+.f64 (pow.f64 (.f64 x 1/2) 2) (+.f64 (log.f64 x) (.f64 1/48 (pow.f64 x 6))))
0.1b	(*.f64 1/48 (pow.f64 x 6))
0.1b	(*.f64 3/32 (pow.f64 x 4))
0.1b	(-.f64 (log.f64 2) (+.f64 (.f64 3/32 (pow.f64 x 4)) (+.f64 (pow.f64 (.f64 x 1/2) 2) (+.f64 (log.f64 x) (*.f64 1/48 (pow.f64 x 6))))))

rewrite45.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`add-sqr-sqrt_binary64_100`
17×	`add-log-exp_binary64_117` `*-un-lft-identity_binary64_78`
14×	`associate-r_binary64_18` `add-exp-log_binary64_116`
12×	`add-cube-cbrt_binary64_113`
9×	`sum-log_binary64_169`
8×	`add-cbrt-cube_binary64_114` `unpow-prod-down_binary64_157`
6×	`associate-l_binary64_19` `prod-exp_binary64_127` `unswap-sqr_binary64_46`
5×	`pow1_binary64_139`
4×	`diff-log_binary64_170` `sqr-pow_binary64_50`
3×	`associate--l+_binary64_15` `log-prod_binary64_164` `cancel-sign-sub-inv_binary64_44`
2×	`*-commutative_binary64_9` `pow-exp_binary64_146` `pow-to-exp_binary64_147` `cbrt-unprod_binary64_111` `distribute-lft-out--_binary64_30`
1×	`+-commutative_binary64_8` `flip-+_binary64_52` `flip3--_binary64_82` `associate-+r+_binary64_10` `associate--r+_binary64_14` `flip--_binary64_53` `difference-of-squares_binary64_47` `distribute-lft-out_binary64_29` `log-pow_binary64_167` `sub-neg_binary64_71` `flip3-+_binary64_81`

Counts

4 → 88

Calls

8 calls:

18.0ms	(-.f64 (log.f64 2) (+.f64 (.f64 3/32 (pow.f64 x 4)) (+.f64 (pow.f64 (.f64 x 1/2) 2) (+.f64 (log.f64 x) (*.f64 1/48 (pow.f64 x 6))))))
8.0ms	(+.f64 (pow.f64 (.f64 x 1/2) 2) (+.f64 (log.f64 x) (.f64 1/48 (pow.f64 x 6))))
6.0ms	(*.f64 1/48 (pow.f64 x 6))
6.0ms	(*.f64 3/32 (pow.f64 x 4))
0.0ms	(+.f64 (pow.f64 (.f64 x 1/2) 2) (+.f64 (log.f64 x) (.f64 1/48 (pow.f64 x 6))))

series298.0ms (6.1%)

Counts

4 → 17

Calls

4 calls:

164.0ms	(+.f64 (pow.f64 (.f64 x 1/2) 2) (+.f64 (log.f64 x) (.f64 1/48 (pow.f64 x 6))))
55.0ms	(-.f64 (log.f64 2) (+.f64 (.f64 3/32 (pow.f64 x 4)) (+.f64 (pow.f64 (.f64 x 1/2) 2) (+.f64 (log.f64 x) (*.f64 1/48 (pow.f64 x 6))))))
42.0ms	(*.f64 1/48 (pow.f64 x 6))
37.0ms	(*.f64 3/32 (pow.f64 x 4))

Compiler

Compiled 508 to 449 computations (11.6% saved)

simplify66.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4980	2106
1	4980	2106

prune180.0ms (3.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	102	3	105
Fresh	11	0	11
Picked	1	0	1
Done	0	1	1
Total	114	4	118

Error

59.6b

Counts

118 → 4

Compiler

Compiled 2894 to 2295 computations (20.7% saved)

regimes310.0ms (6.3%)

Accuracy

Total -59.5b remaining (-835407.4%)

Threshold costs -59.5b (-835407.4%)

Compiler

Compiled 2833 to 2362 computations (16.6% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	7	7
1	7	7

end4.0ms (0.1%)

Compiler: Compiled 36 to 31 computations (13.9% saved)

sample2.8s (56.5%)

Algorithm

1×

intervals

Results

1.0s	4017×	body	1024	valid
246.0ms	1933×	body	512	valid
118.0ms	412×	body	2048	valid
75.0ms	976×	body	256	valid
26.0ms	662×	body	128	valid
0.0ms	1×	body	128	invalid

Compiler

Compiled 1008 to 845 computations (16.2% saved)

Pareto

-0.3090138553893239

Details

analyze4.0ms (0.1%)

sample56.0ms (1.1%)

simplify285.0ms (5.8%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite48.0ms (1%)

series137.0ms (2.8%)

simplify74.0ms (1.5%)

prune147.0ms (3%)

localize9.0ms (0.2%)

rewrite24.0ms (0.5%)

series177.0ms (3.6%)

simplify56.0ms (1.1%)

prune143.0ms (2.9%)

localize7.0ms (0.1%)

rewrite0.0ms (0%)

series0.0ms (0%)

simplify7.0ms (0.1%)

prune21.0ms (0.4%)

localize16.0ms (0.3%)

rewrite45.0ms (0.9%)

series298.0ms (6.1%)

simplify66.0ms (1.3%)

prune180.0ms (3.7%)

regimes310.0ms (6.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end4.0ms (0.1%)

sample2.8s (56.5%)

Profiling