Details

analyze752.0ms (7.9%)

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)

sample55.0ms (0.6%)

Algorithm

1×

intervals

Results

12.0ms	176×	body	128	valid
11.0ms	42×	body	1024	valid
5.0ms	20×	body	1024	nan
5.0ms	26×	body	512	valid
3.0ms	42×	body	128	nan
3.0ms	14×	body	512	nan
2.0ms	15×	body	256	nan
1.0ms	10×	body	256	valid
1.0ms	2×	body	2048	valid

Compiler

Compiled 55 to 44 computations (20% saved)

simplify73.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5009	41

prune4.0ms (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: 40.8b

Counts

2 → 1

Compiler

Compiled 54 to 40 computations (25.9% saved)

localize16.0ms (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))))
0.5b	(*.f64 (sqrt.f64 2) t)
11.1b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
19.2b	(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×	`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	(/.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))))
17.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
17.0ms	(sqrt.f64 (-.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)

series2.8s (30%)

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)))
846.0ms	(/.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))))
325.0ms	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
46.0ms	(*.f64 (sqrt.f64 2) t)

simplify70.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4956	3058
1	4956	3058

prune615.0ms (6.5%)

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

Merged error: 4.8b

Counts

93 → 5

Compiler

Compiled 14017 to 9209 computations (34.3% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.4b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
6.4b	(/.f64 (*.f64 t t) x)
6.7b	(/.f64 (*.f64 l l) x)
24.4b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))

rewrite37.0ms (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:

10.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
5.0ms	(/.f64 (*.f64 l l) x)
5.0ms	(/.f64 (*.f64 t t) x)

series296.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x)))))
81.0ms	(+.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)
24.0ms	(/.f64 (*.f64 t t) x)

simplify60.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5003	1976

prune342.0ms (3.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	80	6	86
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	81	10	91

Merged error: 2.6b

Counts

91 → 10

Compiler

Compiled 8472 to 4921 computations (41.9% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
4.4b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
6.4b	(/.f64 (*.f64 t t) x)
24.4b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite43.0ms (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` `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:

13.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
9.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
5.0ms	(/.f64 (*.f64 t t) x)

series336.0ms (3.5%)

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 l (/.f64 x l))))))
82.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
51.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
26.0ms	(/.f64 (*.f64 t t) x)

simplify43.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5206	2011

prune182.0ms (1.9%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	2	76
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	77	9	86

Merged error: 2.6b

Counts

86 → 9

Compiler

Compiled 4590 to 2388 computations (48% saved)

localize19.0ms (0.2%)

Local error

Found 4 expressions with local error:

6.4b	(/.f64 (*.f64 t t) x)
6.4b	(/.f64 (*.f64 t t) x)
24.4b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
24.4b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
8×	`associate-*r/_binary64` `sqrt-div_binary64`
6×	`associate-/r*_binary64` `pow1_binary64` `times-frac_binary64` `sqrt-prod_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `div-exp_binary64` `flip-+_binary64`
2×	`pow1/2_binary64` `cbrt-unprod_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 → 76

Calls

4 calls:

9.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
8.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
5.0ms	(/.f64 (*.f64 t t) x)
5.0ms	(/.f64 (*.f64 t t) x)

series387.0ms (4.1%)

Counts

4 → 12

Calls

4 calls:

170.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
165.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
28.0ms	(/.f64 (*.f64 t t) x)
23.0ms	(/.f64 (*.f64 t t) x)

simplify77.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4960	2090
1	4960	2090

prune173.0ms (1.8%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	87	10	97

Merged error: 2.6b

Counts

97 → 10

Compiler

Compiled 5288 to 2259 computations (57.3% saved)

regimes274.0ms (2.9%)

Compiler: Compiled 2227 to 1516 computations (31.9% saved)

bsearch566.0ms (6%)

Steps

Iters	Range		Point
8	3.6284419505607833e+58	4.4824569522341695e+61	4.430742223517365e+61
7	6.682524137853144e-186	1.4871723549307054e-183	6.794026911200415e-186
10	3.004380604730448e-307	2.2855463754454536e-296	2.2639360950810393e-296
9	-1.1308104757353412e-286	-1.4256942457803158e-293	-1.1072730107488086e-286
8	-2.3317138014209243e-240	-1.0280394764802885e-243	-1.0408412389809283e-243
8	-3.829033292858828e+148	-1.2245979129767736e+145	-6.640054786982412e+146

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	153	354
1	153	354

end0.0ms (0%)

sample2.1s (21.9%)

Algorithm

1×

intervals

Results

375.0ms	5357×	body	128	valid
302.0ms	1149×	body	1024	valid
214.0ms	843×	body	1024	nan
174.0ms	885×	body	512	valid
108.0ms	1556×	body	128	nan
93.0ms	494×	body	512	nan
70.0ms	532×	body	256	valid
40.0ms	309×	body	256	nan
28.0ms	77×	body	2048	valid

Compiler

Compiled 651 to 414 computations (36.4% saved)

Details

analyze752.0ms (7.9%)

sample55.0ms (0.6%)

simplify73.0ms (0.8%)

prune4.0ms (0%)

localize16.0ms (0.2%)

rewrite71.0ms (0.8%)

series2.8s (30%)

simplify70.0ms (0.7%)

prune615.0ms (6.5%)

localize15.0ms (0.2%)

rewrite37.0ms (0.4%)

series296.0ms (3.1%)

simplify60.0ms (0.6%)

prune342.0ms (3.6%)

localize17.0ms (0.2%)

rewrite43.0ms (0.5%)

series336.0ms (3.5%)

simplify43.0ms (0.4%)

prune182.0ms (1.9%)

localize19.0ms (0.2%)

rewrite40.0ms (0.4%)

series387.0ms (4.1%)

simplify77.0ms (0.8%)

prune173.0ms (1.8%)

regimes274.0ms (2.9%)

bsearch566.0ms (6%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample2.1s (21.9%)

Profiling