Details

analyze623.0ms (9.8%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
18.7%	76.5%	4.8%	7
28.1%	66.3%	5.6%	8
35.1%	55%	9.9%	9
36.3%	50.9%	12.8%	10
42.1%	42.4%	15.5%	11
47.5%	33.8%	18.7%	12
48.8%	30.7%	20.6%	13
51.8%	25.6%	22.5%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample40.0ms (0.6%)

Algorithm

1×

intervals

Results

11.0ms	169×	body	128	valid
7.0ms	34×	body	2048	valid
4.0ms	24×	body	1024	valid
3.0ms	10×	body	4096	valid
1.0ms	11×	body	512	valid
1.0ms	24×	body	128	nan
1.0ms	8×	body	256	valid
1.0ms	9×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify193.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	309	18
1	309	18

prune15.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 33.4b

Counts

2 → 1

Compiler

Compiled 49 to 37 computations (24.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.4b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`difference-of-squares_binary64`
8×	`add-log-exp_binary64` `sqrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`pow1_binary64` `distribute-lft-out--_binary64`
4×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `flip--_binary64`
3×	`associate-/r*_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 86

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series486.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

186.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
133.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
114.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
52.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify71.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4877	2170
1	4877	2170

prune491.0ms (7.7%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	89	9	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	10	99

Merged error: 5.4b

Counts

99 → 10

Compiler

Compiled 10155 to 4750 computations (53.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
3.7b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
10.4b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
21.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite66.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
156×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
32×	`distribute-lft-out_binary64`
21×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
10×	`associate-/r/_binary64`
7×	`associate-/r*_binary64`
6×	`flip3-+_binary64` `add-log-exp_binary64` `div-inv_binary64` `flip-+_binary64`
5×	`pow1_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`neg-sub0_binary64` `clear-num_binary64` `frac-2neg_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip--_binary64` `sum-log_binary64`

Counts

4 → 217

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
10.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
6.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series890.0ms (14%)

Counts

4 → 12

Calls

4 calls:

367.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
296.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
115.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
112.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))

simplify114.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5042	8155

prune318.0ms (5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	226	3	229
Fresh	4	4	8
Picked	1	0	1
Done	0	1	1
Total	231	8	239

Merged error: 5.3b

Counts

239 → 8

Compiler

Compiled 8791 to 2210 computations (74.9% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
21.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite37.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

55×	`*-un-lft-identity_binary64`
40×	`times-frac_binary64`
32×	`add-sqr-sqrt_binary64`
31×	`add-cube-cbrt_binary64`
15×	`distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64`
12×	`distribute-lft-out_binary64`
10×	`associate-/l*_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `neg-mul-1_binary64`
4×	`associate-/r*_binary64`
3×	`sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `associate-/r/_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `distribute-frac-neg_binary64` `sum-log_binary64`

Counts

4 → 109

Calls

4 calls:

11.0ms	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
6.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series626.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

342.0ms	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
116.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
114.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
55.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify78.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

121 → 121

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4961	3067
1	4961	3067

prune110.0ms (1.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	121	0	121
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	121	8	129

Merged error: 5.3b

Counts

129 → 8

Compiler

Compiled 2990 to 794 computations (73.4% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 c)))
0.8b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.0b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
21.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite51.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`associate-r_binary64` `add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
31×	`*-un-lft-identity_binary64`
26×	`add-cube-cbrt_binary64`
13×	`add-exp-log_binary64`
9×	`distribute-lft-neg-in_binary64` `add-cbrt-cube_binary64` `distribute-rgt-neg-in_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
4×	`associate-l_binary64` `prod-exp_binary64`
3×	`flip3-+_binary64` `neg-mul-1_binary64` `unswap-sqr_binary64` `sqrt-prod_binary64` `flip-+_binary64`
2×	`flip3--_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `div-exp_binary64` `flip--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `+-commutative_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 101

Calls

4 calls:

22.0ms	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 c)))
7.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series418.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

147.0ms	(.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))) (/.f64 1 (neg.f64 c)))
111.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
108.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
53.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify63.0ms (1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	4951	2354
1	4951	2354

prune125.0ms (2%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	111	2	113
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	112	9	121

Merged error: 5.2b

Counts

121 → 9

Compiler

Compiled 2917 to 1143 computations (60.8% saved)

regimes116.0ms (1.8%)

Compiler: Compiled 345 to 303 computations (12.2% saved)

bsearch83.0ms (1.3%)

Steps

Iters	Range		Point
7	9.84126100473518e+145	1.2545292449045911e+148	1.836614570390093e+147
6	1.064714154488364e-267	7.6429869058367e-267	1.0864668519398205e-267
8	-1.0755933949851465e+51	-4.612260599031594e+47	-1.059261012864539e+51

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	165	91
1	165	91

end0.0ms (0%)

sample1.2s (19.5%)

Algorithm

1×

intervals

Results

248.0ms	1179×	body	2048	valid
240.0ms	5044×	body	128	valid
134.0ms	796×	body	1024	valid
109.0ms	416×	body	4096	valid
51.0ms	394×	body	512	valid
33.0ms	766×	body	128	nan
14.0ms	171×	body	256	valid
13.0ms	246×	body	128	invalid

Compiler

Compiled 188 to 146 computations (22.3% saved)

Details

analyze623.0ms (9.8%)

sample40.0ms (0.6%)

simplify193.0ms (3%)

prune15.0ms (0.2%)

localize11.0ms (0.2%)

rewrite41.0ms (0.6%)

series486.0ms (7.7%)

simplify71.0ms (1.1%)

prune491.0ms (7.7%)

localize12.0ms (0.2%)

rewrite66.0ms (1%)

series890.0ms (14%)

simplify114.0ms (1.8%)

prune318.0ms (5%)

localize11.0ms (0.2%)

rewrite37.0ms (0.6%)

series626.0ms (9.9%)

simplify78.0ms (1.2%)

prune110.0ms (1.7%)

localize13.0ms (0.2%)

rewrite51.0ms (0.8%)

series418.0ms (6.6%)

simplify63.0ms (1%)

prune125.0ms (2%)

regimes116.0ms (1.8%)

bsearch83.0ms (1.3%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.2s (19.5%)

Profiling