Details

analyze466.0ms (11%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4949	72
1	4949	72
0	3	3
1	3	3

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%	74.9%	25.1%	6
6.2%	68.6%	25.1%	7
10.1%	64.7%	25.1%	8
17.2%	32.8%	50.1%	9
23%	26.9%	50.1%	10
26.8%	23.1%	50.1%	11
31.6%	18.3%	50.1%	12
35.2%	14.7%	50.1%	13
37.5%	12.4%	50.1%	14

Compiler

Compiled 13 to 11 computations (15.4% saved)

sample21.0ms (0.5%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify166.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (161.0ms)

Iter	Nodes	Cost
0	4948	18
1	4948	18

prune2.0ms (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

Error

0.2b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
0.0b	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))
0.1b	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
0.1b	(*.f64 (+.f64 y 1/2) (log.f64 y))

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-log-exp_binary64_10347` `*-un-lft-identity_binary64_10308`
15×	`add-sqr-sqrt_binary64_10330`
12×	`log-prod_binary64_10394`
11×	`add-cube-cbrt_binary64_10343`
7×	`pow1_binary64_10369`
6×	`distribute-lft-in_binary64_10257` `distribute-rgt-in_binary64_10258` `add-cbrt-cube_binary64_10344` `add-exp-log_binary64_10346` `associate--r+_binary64_10244` `diff-log_binary64_10400`
5×	`cancel-sign-sub-inv_binary64_10274`
4×	`sum-log_binary64_10399` `associate-r_binary64_10248` `associate-l_binary64_10249`
3×	`sub-neg_binary64_10301` `distribute-lft-out_binary64_10259`
2×	`flip--_binary64_10283` `flip-+_binary64_10282` `flip3--_binary64_10312` `associate-*l/_binary64_10251` `flip3-+_binary64_10311` `distribute-lft-out--_binary64_10260` `associate-+l+_binary64_10241` `associate-+l-_binary64_10243`
1×	`cbrt-unprod_binary64_10341` `prod-exp_binary64_10357` `log-pow_binary64_10397` `+-commutative_binary64_10238` `associate--l-_binary64_10246` `pow-prod-down_binary64_10379` `*-commutative_binary64_10239` `unswap-sqr_binary64_10276` `associate--l+_binary64_10245` `difference-of-squares_binary64_10277`

Counts

4 → 83

Calls

4 calls:

10.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
8.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
6.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
4.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

series225.0ms (5.3%)

Counts

4 → 12

Calls

4 calls:

92.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
52.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
42.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
38.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

simplify97.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4902	1632
1	4902	1632

prune105.0ms (2.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	86	9	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	9	96

Error

0.0b

Counts

96 → 9

Compiler

Compiled 1888 to 1067 computations (43.5% saved)

localize12.0ms (0.3%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y) z)
0.1b	(*.f64 (+.f64 y 1/2) (log.f64 y))
0.1b	(-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y)

rewrite31.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`log-prod_binary64_10394`
17×	`*-un-lft-identity_binary64_10308`
15×	`add-sqr-sqrt_binary64_10330`
13×	`add-cube-cbrt_binary64_10343`
12×	`associate--l+_binary64_10245`
10×	`add-log-exp_binary64_10347` `associate-+l+_binary64_10241`
9×	`distribute-lft-in_binary64_10257` `distribute-rgt-in_binary64_10258`
6×	`pow1_binary64_10369` `cancel-sign-sub-inv_binary64_10274`
5×	`add-cbrt-cube_binary64_10344` `add-exp-log_binary64_10346`
4×	`associate-r_binary64_10248` `associate-l_binary64_10249`
2×	`sum-log_binary64_10399` `sub-neg_binary64_10301` `flip-+_binary64_10282` `distribute-lft-out_binary64_10259` `associate-*l/_binary64_10251` `flip3-+_binary64_10311` `diff-log_binary64_10400`
1×	`cbrt-unprod_binary64_10341` `prod-exp_binary64_10357` `flip--_binary64_10283` `log-pow_binary64_10397` `+-commutative_binary64_10238` `flip3--_binary64_10312` `pow-prod-down_binary64_10379` `*-commutative_binary64_10239` `unswap-sqr_binary64_10276` `associate-+l-_binary64_10243`

Counts

3 → 72

Calls

3 calls:

11.0ms	(+.f64 (-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y) z)
8.0ms	(-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y)
7.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))

series291.0ms (6.9%)

Counts

3 → 9

Calls

3 calls:

167.0ms	(-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y)
84.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
40.0ms	(+.f64 (-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y) z)

simplify106.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4948	1213
1	4948	1213

prune84.0ms (2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	79	2	81
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	82	8	90

Error

Counts

90 → 8

Compiler

Compiled 1640 to 928 computations (43.4% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (*.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y))) y)
0.1b	(*.f64 (log.f64 (sqrt.f64 y)) (+.f64 y 1/2))
0.1b	(*.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y)))
0.2b	(+.f64 (.f64 (log.f64 (sqrt.f64 y)) (+.f64 y 1/2)) (-.f64 (.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y))) y))

rewrite57.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`log-prod_binary64_10394`
26×	`add-sqr-sqrt_binary64_10330` `*-un-lft-identity_binary64_10308`
24×	`associate--l+_binary64_10245`
22×	`add-cube-cbrt_binary64_10343`
20×	`distribute-lft-in_binary64_10257` `distribute-rgt-in_binary64_10258`
18×	`sqrt-prod_binary64_10324`
16×	`associate-+r+_binary64_10240`
12×	`pow1_binary64_10369`
11×	`add-log-exp_binary64_10347`
10×	`associate-r_binary64_10248` `associate-l_binary64_10249`
8×	`add-cbrt-cube_binary64_10344` `add-exp-log_binary64_10346`
6×	`associate-*r/_binary64_10250` `log-pow_binary64_10397` `cancel-sign-sub-inv_binary64_10274`
5×	`flip-+_binary64_10282` `flip3-+_binary64_10311`
4×	`frac-add_binary64_10316`
3×	`flip--_binary64_10283` `flip3--_binary64_10312`
2×	`cbrt-unprod_binary64_10341` `sum-log_binary64_10399` `prod-exp_binary64_10357` `sqrt-pow1_binary64_10326` `sub-neg_binary64_10301` `distribute-lft-out_binary64_10259` `associate-l/_binary64_10251` `pow-prod-down_binary64_10379` `diff-log_binary64_10400` `associate-+l+_binary64_10241` `-commutative_binary64_10239` `unswap-sqr_binary64_10276` `pow1/2_binary64_10388`
1×	`associate-+r-_binary64_10242` `+-commutative_binary64_10238`

Counts

4 → 123

Calls

4 calls:

17.0ms	(+.f64 (.f64 (log.f64 (sqrt.f64 y)) (+.f64 y 1/2)) (-.f64 (.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y))) y))
11.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y)))
9.0ms	(-.f64 (*.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y))) y)
7.0ms	(*.f64 (log.f64 (sqrt.f64 y)) (+.f64 y 1/2))

series140.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

46.0ms	(+.f64 (.f64 (log.f64 (sqrt.f64 y)) (+.f64 y 1/2)) (-.f64 (.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y))) y))
43.0ms	(-.f64 (*.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y))) y)
25.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (sqrt.f64 y)))
25.0ms	(*.f64 (log.f64 (sqrt.f64 y)) (+.f64 y 1/2))

simplify81.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5140	2900

prune174.0ms (4.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	135	0	135
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	135	8	143

Error

Counts

143 → 8

Compiler

Compiled 4051 to 2135 computations (47.3% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)

rewrite21.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_10339`
23×	`add-sqr-sqrt_binary64_10330`
15×	`add-cube-cbrt_binary64_10343` `*-un-lft-identity_binary64_10308`
11×	`pow1_binary64_10369`
9×	`pow1/3_binary64_10390`
6×	`swap-sqr_binary64_10275` `associate-r_binary64_10248` `associate-l_binary64_10249` `add-exp-log_binary64_10346`
4×	`add-log-exp_binary64_10347` `add-cbrt-cube_binary64_10344` `unswap-sqr_binary64_10276`
2×	`pow-sqr_binary64_10281` `pow-prod-down_binary64_10379` `pow-prod-up_binary64_10378`
1×	`cbrt-unprod_binary64_10341` `prod-exp_binary64_10357` `pow-plus_binary64_10371` `*-commutative_binary64_10239` `pow2_binary64_10389`

Counts

4 → 73

Calls

4 calls:

7.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series340.0ms (8%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
84.0ms	(cbrt.f64 y)
84.0ms	(cbrt.f64 y)
83.0ms	(cbrt.f64 y)

simplify66.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4892	563
1	4892	563

prune101.0ms (2.4%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	85	8	93

Error

Counts

93 → 8

Compiler

Compiled 2264 to 1155 computations (49% saved)

regimes267.0ms (6.3%)

Accuracy

Total 0.1b remaining (96.4%)

Threshold costs 0.1b (96.4%)

Compiler

Compiled 2735 to 2101 computations (23.2% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	199	18
1	199	18

end0.0ms (0%)

sample1.3s (30.8%)

Algorithm

1×

intervals

Results

569.0ms	8000×	body	128	valid
1.0ms	29×	body	128	invalid

Compiler

Compiled 574 to 443 computations (22.8% saved)

Details

analyze466.0ms (11%)

sample21.0ms (0.5%)

simplify166.0ms (3.9%)

prune2.0ms (0.1%)

localize9.0ms (0.2%)

rewrite34.0ms (0.8%)

series225.0ms (5.3%)

simplify97.0ms (2.3%)

prune105.0ms (2.5%)

localize12.0ms (0.3%)

rewrite31.0ms (0.7%)

series291.0ms (6.9%)

simplify106.0ms (2.5%)

prune84.0ms (2%)

localize13.0ms (0.3%)

rewrite57.0ms (1.3%)

series140.0ms (3.3%)

simplify81.0ms (1.9%)

prune174.0ms (4.1%)

localize16.0ms (0.4%)

rewrite21.0ms (0.5%)

series340.0ms (8%)

simplify66.0ms (1.6%)

prune101.0ms (2.4%)

regimes267.0ms (6.3%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.3s (30.8%)

Profiling