Details

analyze737.0ms (7.8%)

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

11.0ms	43×	body	1024	valid
10.0ms	150×	body	128	valid
7.0ms	36×	body	512	valid
4.0ms	58×	body	128	nan
3.0ms	14×	body	1024	nan
3.0ms	18×	body	512	nan
3.0ms	24×	body	256	valid
1.0ms	10×	body	256	nan
1.0ms	3×	body	2048	valid

Compiler

Compiled 55 to 44 computations (20% saved)

simplify222.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5009	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: 43.4b

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))))
0.5b	(*.f64 (sqrt.f64 2) t)
16.2b	(-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l))
16.7b	(sqrt.f64 (-.f64 (.f64 (/.f64 (+.f64 x 1) (-.f64 x 1)) (+.f64 (.f64 l l) (.f64 2 (.f64 t t)))) (*.f64 l l)))

rewrite75.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64_101`
13×	`sqrt-prod_binary64_95`
12×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
11×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
7×	`pow1_binary64_140`
6×	`associate-/r_binary64_23` `associate-l*_binary64_20` `times-frac_binary64_85` `add-log-exp_binary64_118`
4×	`sqrt-div_binary64_96`
3×	`flip--_binary64_54` `flip3--_binary64_83` `associate-r_binary64_19`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `associate--l+_binary64_16` `unswap-sqr_binary64_47` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `associate-/r/_binary64_25`
1×	`div-inv_binary64_76` `distribute-lft-in_binary64_28` `associate-/l_binary64_24` `rem-sqrt-square_binary64_92` `-commutative_binary64_10` `pow-prod-down_binary64_150` `sqrt-pow1_binary64_97` `diff-log_binary64_171` `clear-num_binary64_78` `pow1/2_binary64_159` `cancel-sign-sub-inv_binary64_45` `distribute-rgt-in_binary64_29` `sub-neg_binary64_72` `frac-2neg_binary64_90`

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))))
20.0ms	(-.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 (29.9%)

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)))
835.0ms	(/.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))
50.0ms	(*.f64 (sqrt.f64 2) t)

simplify76.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4955	3058
1	4955	3058

prune639.0ms (6.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	86	6	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	6	93

Merged error: 9.6b

Counts

93 → 6

Compiler

Compiled 14850 to 9821 computations (33.9% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

3.4b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 (*.f64 l l) x))))
7.2b	(/.f64 (*.f64 t t) x)
8.5b	(/.f64 (*.f64 l l) x)
23.2b	(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_117` `add-cbrt-cube_binary64_115`
10×	`add-sqr-sqrt_binary64_101`
9×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
8×	`associate-*r/_binary64_21`
6×	`associate-/r*_binary64_23` `times-frac_binary64_85` `add-log-exp_binary64_118`
5×	`pow1_binary64_140`
4×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `flip-+_binary64_53` `frac-add_binary64_87` `sqrt-div_binary64_96` `flip3-+_binary64_82`
3×	`sqrt-prod_binary64_95`
2×	`div-inv_binary64_76` `associate-/l*_binary64_24` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `associate-+r+_binary64_11` `clear-num_binary64_78` `frac-2neg_binary64_90`
1×	`sum-log_binary64_170` `distribute-lft-in_binary64_28` `+-commutative_binary64_9` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29`

Counts

4 → 74

Calls

4 calls:

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

series320.0ms (3.4%)

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)))))
94.0ms	(+.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)

simplify61.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5003	1976

prune424.0ms (4.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	79	7	86
Fresh	0	5	5
Picked	1	0	1
Done	0	0	0
Total	80	12	92

Merged error: 4.9b

Counts

92 → 12

Compiler

Compiled 9944 to 6093 computations (38.7% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
3.4b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
7.2b	(/.f64 (*.f64 t t) x)
23.2b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))

rewrite38.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
8×	`add-sqr-sqrt_binary64_101` `associate-*r/_binary64_21` `add-log-exp_binary64_118`
7×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
5×	`flip-+_binary64_53` `flip3-+_binary64_82` `pow1_binary64_140`
4×	`frac-add_binary64_87` `sqrt-div_binary64_96`
3×	`sqrt-prod_binary64_95` `associate-/r*_binary64_23` `times-frac_binary64_85`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `sum-log_binary64_170` `+-commutative_binary64_9` `associate-+r+_binary64_11`
1×	`div-inv_binary64_76` `distribute-lft-in_binary64_28` `associate-/l*_binary64_24` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

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

series353.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

181.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x))))))
90.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (*.f64 l (/.f64 l x)))))
55.0ms	(+.f64 (.f64 t t) (.f64 l (/.f64 l x)))
26.0ms	(/.f64 (*.f64 t t) x)

simplify41.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5242	2011

prune263.0ms (2.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	72	4	76
Fresh	3	8	11
Picked	0	1	1
Done	0	0	0
Total	75	13	88

Merged error: 4.9b

Counts

88 → 13

Compiler

Compiled 5129 to 2847 computations (44.5% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
3.4b	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
7.2b	(/.f64 (*.f64 t t) x)
23.2b	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))

rewrite71.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-exp-log_binary64_117` `add-cbrt-cube_binary64_115`
8×	`add-sqr-sqrt_binary64_101` `associate-*r/_binary64_21` `add-log-exp_binary64_118`
7×	`add-cube-cbrt_binary64_114` `*-un-lft-identity_binary64_79`
5×	`flip-+_binary64_53` `flip3-+_binary64_82` `pow1_binary64_140`
4×	`frac-add_binary64_87` `sqrt-div_binary64_96`
3×	`sqrt-prod_binary64_95` `associate-/r*_binary64_23` `times-frac_binary64_85`
2×	`cbrt-undiv_binary64_113` `div-exp_binary64_130` `sum-log_binary64_170` `+-commutative_binary64_9` `associate-+r+_binary64_11`
1×	`div-inv_binary64_76` `distribute-lft-in_binary64_28` `associate-/l*_binary64_24` `cbrt-unprod_binary64_112` `prod-exp_binary64_128` `rem-sqrt-square_binary64_92` `sqrt-pow1_binary64_97` `clear-num_binary64_78` `pow1/2_binary64_159` `distribute-rgt-in_binary64_29` `frac-2neg_binary64_90`

Counts

4 → 64

Calls

4 calls:

20.0ms	(+.f64 (*.f64 t t) (/.f64 l (/.f64 x l)))
17.0ms	(+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l)))))
14.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
8.0ms	(/.f64 (*.f64 t t) x)

series474.0ms (5%)

Counts

4 → 12

Calls

4 calls:

277.0ms	(sqrt.f64 (+.f64 (.f64 4 (/.f64 (.f64 t t) x)) (.f64 2 (+.f64 (.f64 t t) (/.f64 l (/.f64 x l))))))
105.0ms	(+.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)))
36.0ms	(/.f64 (*.f64 t t) x)

simplify44.0ms (0.5%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5206	2011

prune117.0ms (1.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	76	13	89

Merged error: 4.9b

Counts

89 → 13

Compiler

Compiled 3013 to 1386 computations (54% saved)

regimes256.0ms (2.7%)

Compiler: Compiled 2546 to 1762 computations (30.8% saved)

bsearch82.0ms (0.9%)

Steps

Iters	Range		Point
4	1.4239405721242226e+91	2.2103175997378023e+91	2.1793155610953975e+91
7	-1.9261537276910763e+137	-1.651013309403966e+135	-3.76396911624431e+135

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	142	152
1	142	152

end0.0ms (0%)

sample2.1s (22.6%)

Algorithm

1×

intervals

Results

364.0ms	5309×	body	128	valid
303.0ms	1182×	body	1024	valid
194.0ms	775×	body	1024	nan
165.0ms	881×	body	512	valid
101.0ms	1567×	body	128	nan
95.0ms	514×	body	512	nan
70.0ms	553×	body	256	valid
31.0ms	251×	body	256	nan
24.0ms	75×	body	2048	valid

Compiler

Compiled 567 to 383 computations (32.5% saved)

Details

analyze737.0ms (7.8%)

sample55.0ms (0.6%)

simplify222.0ms (2.4%)

prune3.0ms (0%)

localize17.0ms (0.2%)

rewrite75.0ms (0.8%)

series2.8s (29.9%)

simplify76.0ms (0.8%)

prune639.0ms (6.8%)

localize15.0ms (0.2%)

rewrite37.0ms (0.4%)

series320.0ms (3.4%)

simplify61.0ms (0.6%)

prune424.0ms (4.5%)

localize15.0ms (0.2%)

rewrite38.0ms (0.4%)

series353.0ms (3.8%)

simplify41.0ms (0.4%)

prune263.0ms (2.8%)

localize25.0ms (0.3%)

rewrite71.0ms (0.8%)

series474.0ms (5%)

simplify44.0ms (0.5%)

prune117.0ms (1.2%)

regimes256.0ms (2.7%)

bsearch82.0ms (0.9%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.1s (22.6%)

Profiling