Details

analyze1.1s (10.2%)

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
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)

sample75.0ms (0.7%)

Algorithm

1×

intervals

Results

18.0ms	44×	body	2048	valid
15.0ms	163×	body	128	valid
12.0ms	23×	body	1024	valid
4.0ms	16×	body	512	valid
3.0ms	6×	body	4096	valid
2.0ms	30×	body	128	nan
1.0ms	4×	body	256	valid
1.0ms	6×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify331.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	309	18
1	309	18

prune11.0ms (0.1%)

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: 34.0b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize28.0ms (0.3%)

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)
0.4b	(-.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)
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite72.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
16×	`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` `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 → 82

Calls

4 calls:

22.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
16.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
11.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series878.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

334.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
227.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
215.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
102.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify123.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (81.0ms)

Iter	Nodes	Cost
0	4975	2155
1	4975	2155

prune183.0ms (1.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	86	8	94
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	87	8	95

Merged error: 3.8b

Counts

95 → 8

Compiler

Compiled 2043 to 419 computations (79.5% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
2.4b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
10.1b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite125.0ms (1.2%)

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:

29.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
17.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
11.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
8.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series1.6s (14.9%)

Counts

4 → 12

Calls

4 calls:

668.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
507.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
215.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
209.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify205.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	5322	8155

prune375.0ms (3.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	228	1	229
Fresh	1	6	7
Picked	0	1	1
Done	0	0	0
Total	229	8	237

Merged error: 3.7b

Counts

237 → 8

Compiler

Compiled 6652 to 885 computations (86.7% saved)

localize21.0ms (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)))))
0.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.5b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite71.0ms (0.7%)

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` `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 → 108

Calls

4 calls:

20.0ms	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
12.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
9.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
8.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series1.1s (10.3%)

Counts

4 → 12

Calls

4 calls:

609.0ms	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
205.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
198.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
96.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify143.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5173	3058

prune194.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	120	0	120
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	120	8	128

Merged error: 3.7b

Counts

128 → 8

Compiler

Compiled 2893 to 695 computations (76% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
0.4b	(-.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)
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite83.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64`
11×	`times-frac_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`prod-exp_binary64` `difference-of-squares_binary64`
3×	`unswap-sqr_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `rec-exp_binary64` `un-div-inv_binary64` `div-inv_binary64` `-commutative_binary64`

Counts

4 → 83

Calls

4 calls:

33.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
17.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
9.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
9.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series875.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

343.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2) (/.f64 1 a))
225.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
206.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
101.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify177.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	4895	1889
1	4895	1889

prune130.0ms (1.2%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	95	0	95
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	95	8	103

Merged error: 3.7b

Counts

103 → 8

Compiler

Compiled 1896 to 504 computations (73.4% saved)

regimes304.0ms (2.8%)

Compiler: Compiled 444 to 270 computations (39.2% saved)

bsearch168.0ms (1.6%)

Steps

Iters	Range	Point
7	9.873422885001818e+93	2.17248665490453e+95	2.1493120198142702e+95
9	-1.2746591395949632e-154	-8.154822685230029e-160	-8.634825202618674e-160
11	-1.298127322958378e+43	-2.6188810339804265e+22	-1.2794042312211462e+43

Iters

Range

Point

9.873422885001818e+93

2.17248665490453e+95

2.1493120198142702e+95

-1.2746591395949632e-154

-8.154822685230029e-160

-8.634825202618674e-160

-1.298127322958378e+43

-2.6188810339804265e+22

-1.2794042312211462e+43

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	135	82
1	135	82

end0.0ms (0%)

sample2.3s (21.5%)

Algorithm

1×

intervals

Results

469.0ms	1112×	body	2048	valid
441.0ms	5222×	body	128	valid
237.0ms	724×	body	1024	valid
223.0ms	411×	body	4096	valid
90.0ms	361×	body	512	valid
61.0ms	757×	body	128	nan
28.0ms	170×	body	256	valid
20.0ms	241×	body	128	invalid

Compiler

Compiled 215 to 130 computations (39.5% saved)

Details

analyze1.1s (10.2%)

sample75.0ms (0.7%)

simplify331.0ms (3.1%)

prune11.0ms (0.1%)

localize28.0ms (0.3%)

rewrite72.0ms (0.7%)

series878.0ms (8.2%)

simplify123.0ms (1.1%)

prune183.0ms (1.7%)

localize21.0ms (0.2%)

rewrite125.0ms (1.2%)

series1.6s (14.9%)

simplify205.0ms (1.9%)

prune375.0ms (3.5%)

localize21.0ms (0.2%)

rewrite71.0ms (0.7%)

series1.1s (10.3%)

simplify143.0ms (1.3%)

prune194.0ms (1.8%)

localize20.0ms (0.2%)

rewrite83.0ms (0.8%)

series875.0ms (8.2%)

simplify177.0ms (1.7%)

prune130.0ms (1.2%)

regimes304.0ms (2.8%)

bsearch168.0ms (1.6%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample2.3s (21.5%)

Profiling