Details

analyze766.0ms (8.6%)

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%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	74.9%	25.1%	8
0%	74.9%	25.1%	9
9.4%	65.5%	25.1%	10
9.4%	53%	37.6%	11
14%	48.4%	37.6%	12
16.4%	46%	37.6%	13
16.4%	39.8%	43.8%	14

Compiler

Compiled 28 to 21 computations (25% saved)

sample63.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms	175×	body	80	valid
9.0ms	27×	body	1280	valid
8.0ms	30×	body	640	valid
6.0ms	23×	body	640	nan
5.0ms	17×	body	1280	nan
3.0ms	18×	body	320	valid
3.0ms	45×	body	80	nan
2.0ms	13×	body	320	nan
1.0ms	6×	body	160	valid
1.0ms	5×	body	160	nan

Compiler

Compiled 55 to 44 computations (20% saved)

simplify156.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	5156	41

prune3.0ms (0%)

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

Merged error: 40.6b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
0.4b	(*.f64 (sqrt.f64 2) t)
11.9b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
21.1b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite71.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`sqrt-prod_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`associate-/r_binary64` `add-log-exp_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`insert-posit16` `sqrt-div_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate--l+_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

24.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
19.0ms	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
19.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
6.0ms	(*.f64 (sqrt.f64 2) t)

series2.7s (30.5%)

Counts

4 → 12

Calls

4 calls:

1.6s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
772.0ms	(/.f64 (.f64 (sqrt.f64 2) t) (sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (.f64 l l))))
326.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
50.0ms	(*.f64 (sqrt.f64 2) t)

simplify114.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (76.0ms)

Iter	Nodes	Cost
0	4952	3171
1	4952	3171

prune185.0ms (2.1%)

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: 6.4b

Counts

96 → 6

Compiler

Compiled 3734 to 2192 computations (41.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.8b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
7.3b	(/.f64 (*.f64 l l) x)
11.2b	(/.f64 (*.f64 t t) x)
27.2b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-*r/_binary64`
6×	`associate-/r*_binary64` `add-log-exp_binary64` `times-frac_binary64`
5×	`pow1_binary64`
4×	`flip3-+_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `div-exp_binary64` `insert-posit16` `flip-+_binary64` `sqrt-div_binary64`
3×	`sqrt-prod_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `associate-+r+_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 78

Calls

4 calls:

11.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
10.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
6.0ms	(/.f64 (*.f64 l l) x)
6.0ms	(/.f64 (*.f64 t t) x)

series320.0ms (3.6%)

Counts

4 → 12

Calls

4 calls:

176.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
93.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
25.0ms	(/.f64 (*.f64 l l) x)
25.0ms	(/.f64 (*.f64 t t) x)

simplify66.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5522	2057

prune130.0ms (1.5%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	85	5	90
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	87	9	96

Merged error: 3.2b

Counts

96 → 9

Compiler

Compiled 3232 to 1478 computations (54.3% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (sqrt.f64 2) t)
2.8b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
11.2b	(/.f64 (*.f64 t t) x)
27.2b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite35.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-sqr-sqrt_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-*r/_binary64`
7×	`pow1_binary64` `sqrt-prod_binary64`
6×	`add-log-exp_binary64` `associate-l_binary64`
4×	`flip3-+_binary64` `frac-add_binary64` `insert-posit16` `flip-+_binary64` `sqrt-div_binary64`
3×	`associate-/r_binary64` `associate-r*_binary64` `times-frac_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-exp_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

11.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
10.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
6.0ms	(/.f64 (*.f64 t t) x)
6.0ms	(*.f64 (sqrt.f64 2) t)

series344.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

174.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
87.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
52.0ms	(*.f64 (sqrt.f64 2) t)
30.0ms	(/.f64 (*.f64 t t) x)

simplify67.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	5198	2053

prune131.0ms (1.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	90	1	91
Fresh	2	6	8
Picked	0	1	1
Done	0	0	0
Total	92	8	100

Merged error: 3.2b

Counts

100 → 8

Compiler

Compiled 3224 to 1476 computations (54.2% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
2.8b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
11.2b	(/.f64 (*.f64 t t) x)
27.2b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite44.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64` `associate-*r/_binary64` `add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`frac-add_binary64` `insert-posit16` `sqrt-div_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`cbrt-undiv_binary64` `div-exp_binary64` `+-commutative_binary64` `associate-+r+_binary64` `sum-log_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 68

Calls

4 calls:

14.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
11.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
10.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
6.0ms	(/.f64 (*.f64 t t) x)

series347.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

177.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
86.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
55.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
29.0ms	(/.f64 (*.f64 t t) x)

simplify67.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (33.0ms)

Iter	Nodes	Cost
0	5040	2097

prune126.0ms (1.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	78	10	88

Merged error: 3.2b

Counts

88 → 10

Compiler

Compiled 3053 to 1518 computations (50.3% saved)

regimes311.0ms (3.5%)

Compiler: Compiled 2264 to 1713 computations (24.3% saved)

bsearch445.0ms (5%)

Steps

Iters	Range		Point
5	9.311626355674152e+114	3.4660893286146996e+115	3.4085637128961917e+115
11	3.476711097862903e-209	1.7426821071695204e-187	3.5195377972172254e-209
10	5.810832024238319e-303	3.7516614648686874e-290	3.6984633075944683e-290
9	-4.20182754377471e+38	-4.962878473728418e+33	-4.147584491189506e+38

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	210	204
1	210	204

end0.0ms (0%)

sample2.3s (25.7%)

Algorithm

1×

intervals

Results

379.0ms	5105×	body	80	valid
273.0ms	841×	body	1280	valid
267.0ms	1029×	body	640	valid
204.0ms	635×	body	1280	nan
151.0ms	599×	body	640	nan
131.0ms	663×	body	320	valid
94.0ms	1373×	body	80	nan
72.0ms	366×	body	320	nan
48.0ms	362×	body	160	valid
26.0ms	204×	body	160	nan

Compiler

Compiled 534 to 388 computations (27.3% saved)

Details

analyze766.0ms (8.6%)

sample63.0ms (0.7%)

simplify156.0ms (1.8%)

prune3.0ms (0%)

localize17.0ms (0.2%)

rewrite71.0ms (0.8%)

series2.7s (30.5%)

simplify114.0ms (1.3%)

prune185.0ms (2.1%)

localize15.0ms (0.2%)

rewrite35.0ms (0.4%)

series320.0ms (3.6%)

simplify66.0ms (0.7%)

prune130.0ms (1.5%)

localize18.0ms (0.2%)

rewrite35.0ms (0.4%)

series344.0ms (3.9%)

simplify67.0ms (0.8%)

prune131.0ms (1.5%)

localize17.0ms (0.2%)

rewrite44.0ms (0.5%)

series347.0ms (3.9%)

simplify67.0ms (0.7%)

prune126.0ms (1.4%)

regimes311.0ms (3.5%)

bsearch445.0ms (5%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample2.3s (25.7%)

Profiling