Details

analyze235.0ms (4.1%)

Algorithm

1×

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)

sample20.0ms (0.3%)

Algorithm

1×

intervals

Results

12.0ms

256×

body

128

valid

Compiler

Compiled 25 to 24 computations (4% saved)

simplify75.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	1363	18
1	1363	18

prune3.0ms (0%)

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

Merged error: 0.1b

Counts

2 → 1

Compiler

Compiled 24 to 20 computations (16.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
15×	`add-sqr-sqrt_binary64`
12×	`log-prod_binary64`
11×	`add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`associate--r+_binary64` `diff-log_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
5×	`cancel-sign-sub-inv_binary64`
4×	`associate-r_binary64` `associate-l_binary64` `sum-log_binary64`
3×	`sub-neg_binary64` `distribute-lft-out_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `flip-+_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `log-pow_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `+-commutative_binary64` `associate--l+_binary64` `*-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

10.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
8.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
7.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
5.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

series415.0ms (7.3%)

Counts

4 → 12

Calls

4 calls:

183.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
94.0ms	(-.f64 (+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y) z)
76.0ms	(+.f64 (-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y))) y)
62.0ms	(-.f64 x (*.f64 (+.f64 y 1/2) (log.f64 y)))

simplify94.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (74.0ms)

Iter	Nodes	Cost
0	4978	1643
1	4978	1643

prune198.0ms (3.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	89	6	95
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	6	96

Merged error: 0.0b

Counts

96 → 6

Compiler

Compiled 3489 to 2264 computations (35.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite50.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
20×	`add-log-exp_binary64`
18×	`log-prod_binary64`
17×	`add-cube-cbrt_binary64` `associate--l+_binary64`
15×	`cancel-sign-sub-inv_binary64`
10×	`associate--r+_binary64` `diff-log_binary64`
9×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
7×	`pow1_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`sub-neg_binary64`
4×	`associate-r_binary64` `associate-l_binary64` `distribute-lft-out--_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`associate--r-_binary64` `difference-of-squares_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate--l-_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `log-pow_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `flip-+_binary64` `*-commutative_binary64`

Counts

4 → 101

Calls

4 calls:

13.0ms	(-.f64 (-.f64 x (-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y)) z)
11.0ms	(-.f64 x (-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y))
9.0ms	(-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y)
8.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))

series856.0ms (15%)

Counts

4 → 12

Calls

4 calls:

512.0ms	(-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y)
170.0ms	(*.f64 (+.f64 y 1/2) (log.f64 y))
97.0ms	(-.f64 (-.f64 x (-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y)) z)
77.0ms	(-.f64 x (-.f64 (*.f64 (+.f64 y 1/2) (log.f64 y)) y))

simplify99.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4877	1868
1	4877	1868

prune138.0ms (2.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	114	5	119

Merged error: 0.0b

Counts

119 → 5

Compiler

Compiled 2680 to 1581 computations (41% saved)

localize16.0ms (0.3%)

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 (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64`
23×	`add-sqr-sqrt_binary64`
15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`pow1_binary64`
9×	`pow1/3_binary64`
6×	`swap-sqr_binary64` `associate-r_binary64` `add-exp-log_binary64` `associate-l_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-sqr_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

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)

series642.0ms (11.3%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
153.0ms	(cbrt.f64 y)
153.0ms	(cbrt.f64 y)
151.0ms	(cbrt.f64 y)

simplify56.0ms (1%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5244	563

prune125.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	85	5	90

Merged error: 0.0b

Counts

90 → 5

Compiler

Compiled 2602 to 1408 computations (45.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
0.3b	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
0.6b	(cbrt.f64 y)
0.6b	(cbrt.f64 y)

rewrite43.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

48×	`log-prod_binary64`
36×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
30×	`cbrt-prod_binary64`
26×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
24×	`add-cube-cbrt_binary64` `associate-+l+_binary64`
12×	`associate-+r+_binary64`
10×	`associate-*l/_binary64`
7×	`pow1_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip-+_binary64`
5×	`associate-r_binary64`
4×	`frac-add_binary64` `associate-l_binary64`
3×	`pow1/3_binary64`
2×	`distribute-lft-out_binary64` `log-pow_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 109

Calls

4 calls:

17.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
10.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
1.0ms	(cbrt.f64 y)
1.0ms	(cbrt.f64 y)

series1.5s (25.5%)

Counts

4 → 12

Calls

4 calls:

740.0ms	(+.f64 (.f64 (+.f64 y 1/2) (.f64 2 (log.f64 (cbrt.f64 y)))) (*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y))))
398.0ms	(*.f64 (+.f64 y 1/2) (log.f64 (cbrt.f64 y)))
159.0ms	(cbrt.f64 y)
152.0ms	(cbrt.f64 y)

simplify105.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4906	1857
1	4906	1857

prune185.0ms (3.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	120	6	126

Merged error: 0b

Counts

126 → 6

Compiler

Compiled 3883 to 2286 computations (41.1% saved)

regimes51.0ms (0.9%)

Compiler: Compiled 417 to 321 computations (23% saved)

bsearch0.0ms (0%)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	80	18
1	80	18

end0.0ms (0%)

sample742.0ms (13%)

Algorithm

1×

intervals

Results

382.0ms	7998×	body	128	valid
2.0ms	33×	body	128	invalid
0.0ms	2×	body	1024	valid

Compiler

Compiled 174 to 135 computations (22.4% saved)

Details

analyze235.0ms (4.1%)

sample20.0ms (0.3%)

simplify75.0ms (1.3%)

prune3.0ms (0%)

localize12.0ms (0.2%)

rewrite36.0ms (0.6%)

series415.0ms (7.3%)

simplify94.0ms (1.6%)

prune198.0ms (3.5%)

localize10.0ms (0.2%)

rewrite50.0ms (0.9%)

series856.0ms (15%)

simplify99.0ms (1.7%)

prune138.0ms (2.4%)

localize16.0ms (0.3%)

rewrite21.0ms (0.4%)

series642.0ms (11.3%)

simplify56.0ms (1%)

prune125.0ms (2.2%)

localize14.0ms (0.2%)

rewrite43.0ms (0.8%)

series1.5s (25.5%)

simplify105.0ms (1.8%)

prune185.0ms (3.2%)

regimes51.0ms (0.9%)

bsearch0.0ms (0%)

simplify3.0ms (0%)

end0.0ms (0%)

sample742.0ms (13%)

Profiling