Details

analyze1.5s (12.2%)

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)

sample103.0ms (0.8%)

Algorithm

1×

intervals

Results

20.0ms	43×	body	1024	valid
19.0ms	158×	body	128	valid
14.0ms	34×	body	512	valid
12.0ms	27×	body	1024	nan
5.0ms	44×	body	128	nan
4.0ms	13×	body	512	nan
4.0ms	16×	body	256	valid
3.0ms	5×	body	2048	valid
1.0ms	4×	body	256	nan

Compiler

Compiled 55 to 44 computations (20% saved)

simplify198.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5192	41

prune8.0ms (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

42.4b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize35.0ms (0.3%)

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)
14.0b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
16.4b	(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 (0.6%)

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×	`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` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

22.0ms	(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 (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))))
15.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
5.0ms	(*.f64 (sqrt.f64 2) t)

series2.2s (17.7%)

Counts

4 → 12

Calls

4 calls:

1.3s	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))
540.0ms	(/.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))))
284.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
24.0ms	(*.f64 (sqrt.f64 2) t)

simplify95.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5269	3058

prune189.0ms (1.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	5	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Error

6.9b

Counts

93 → 5

Compiler

Compiled 3554 to 2085 computations (41.3% saved)

localize24.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
6.2b	(/.f64 (*.f64 l l) x)
8.0b	(/.f64 (*.f64 t t) x)
25.3b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite47.0ms (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` `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 → 74

Calls

4 calls:

15.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
9.0ms	(/.f64 (*.f64 t t) x)
9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
7.0ms	(/.f64 (*.f64 l l) x)

series210.0ms (1.7%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
64.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
14.0ms	(/.f64 (*.f64 t t) x)
14.0ms	(/.f64 (*.f64 l l) x)

simplify89.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4990	1973
1	4990	1973

prune181.0ms (1.5%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	81	5	86
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	81	10	91

Error

3.5b

Counts

91 → 10

Compiler

Compiled 3088 to 1408 computations (54.4% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
3.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
8.0b	(/.f64 (*.f64 t t) x)
25.3b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite46.0ms (0.4%)

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` `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 → 64

Calls

4 calls:

11.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))
8.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
5.0ms	(/.f64 (*.f64 t t) x)

series288.0ms (2.3%)

Counts

4 → 12

Calls

4 calls:

156.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))
55.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
53.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
24.0ms	(/.f64 (*.f64 t t) x)

simplify116.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4966	2011
1	4966	2011

prune146.0ms (1.2%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	2	6	8
Picked	0	1	1
Done	0	1	1
Total	76	10	86

Error

3.5b

Counts

86 → 10

Compiler

Compiled 2851 to 1273 computations (55.3% saved)

localize30.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 (.f64 t t) (.f64 (/.f64 l (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))
3.0b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
8.0b	(/.f64 (*.f64 t t) x)
25.3b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))

rewrite71.0ms (0.6%)

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` `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 → 64

Calls

4 calls:

17.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
15.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))
13.0ms	(+.f64 (.f64 t t) (.f64 (/.f64 l (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))
9.0ms	(/.f64 (*.f64 t t) x)

series403.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x)))))))
111.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (.f64 (/.f64 l (.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))))
89.0ms	(+.f64 (.f64 t t) (.f64 (/.f64 l (*.f64 (cbrt.f64 x) (cbrt.f64 x))) (/.f64 l (cbrt.f64 x))))
18.0ms	(/.f64 (*.f64 t t) x)

simplify85.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5048	2016

prune130.0ms (1.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	7	7
Picked	0	1	1
Done	0	2	2
Total	76	10	86

Error

3.5b

Counts

86 → 10

Compiler

Compiled 2807 to 1073 computations (61.8% saved)

regimes1.4s (11%)

Accuracy

Total 6.2b remaining (62.1%)

Threshold costs 0b (0%)

Compiler

Compiled 12961 to 8811 computations (32% saved)

bsearch401.0ms (3.2%)

Steps

Iters	Range		Point
9	5.1064302174684727e+73	5.004625811638427e+80	3.958443330902987e+80
3	3.9359558102926e-203	4.6624094454089573e-203	3.9813591624873726e-203
10	-8.618913352334745e-279	-1.4414880970923945e-295	-1.468126820238527e-295
5	-1.5764015290157395e+117	-5.291315311972374e+116	-1.0935259900820818e+117

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify14.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	159	223
1	159	223

end0.0ms (0%)

sample4.3s (34.9%)

Algorithm

1×

intervals

Results

574.0ms	5262×	body	128	valid
484.0ms	1148×	body	1024	valid
352.0ms	872×	body	1024	nan
282.0ms	905×	body	512	valid
155.0ms	1522×	body	128	nan
151.0ms	503×	body	512	nan
132.0ms	609×	body	256	valid
51.0ms	268×	body	256	nan
43.0ms	76×	body	2048	valid

Compiler

Compiled 1951 to 1299 computations (33.4% saved)

Details

analyze1.5s (12.2%)

sample103.0ms (0.8%)

simplify198.0ms (1.6%)

prune8.0ms (0.1%)

localize35.0ms (0.3%)

rewrite71.0ms (0.6%)

series2.2s (17.7%)

simplify95.0ms (0.8%)

prune189.0ms (1.5%)

localize24.0ms (0.2%)

rewrite47.0ms (0.4%)

series210.0ms (1.7%)

simplify89.0ms (0.7%)

prune181.0ms (1.5%)

localize19.0ms (0.2%)

rewrite46.0ms (0.4%)

series288.0ms (2.3%)

simplify116.0ms (0.9%)

prune146.0ms (1.2%)

localize30.0ms (0.2%)

rewrite71.0ms (0.6%)

series403.0ms (3.3%)

simplify85.0ms (0.7%)

prune130.0ms (1.1%)

regimes1.4s (11%)

bsearch401.0ms (3.2%)

simplify14.0ms (0.1%)

end0.0ms (0%)

sample4.3s (34.9%)

Profiling