Details

analyze612.0ms (10.4%)

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)

sample41.0ms (0.7%)

Algorithm

1×

intervals

Results

7.0ms	165×	body	128	valid
7.0ms	34×	body	2048	valid
6.0ms	29×	body	1024	valid
4.0ms	22×	body	128	nan
3.0ms	11×	body	4096	valid
1.0ms	11×	body	512	valid
0.0ms	6×	body	256	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify188.0ms (3.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	309	18
1	309	18

prune13.0ms (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: 33.9b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize10.0ms (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)
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
0.9b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
21.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite38.0ms (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:

11.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
8.0ms	(-.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 (8.3%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
119.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
61.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4975	2155
1	4975	2155

prune101.0ms (1.7%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	89	5	94
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	89	6	95

Merged error: 5.7b

Counts

95 → 6

Compiler

Compiled 1981 to 386 computations (80.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
4.8b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
9.3b	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
21.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite64.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

210×	`times-frac_binary64`
154×	`*-un-lft-identity_binary64`
93×	`add-sqr-sqrt_binary64`
92×	`add-cube-cbrt_binary64`
36×	`associate-/l*_binary64`
31×	`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×	`add-log-exp_binary64` `div-inv_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `flip-+_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`div-sub_binary64` `distribute-frac-neg_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `neg-sub0_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 216

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
9.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.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))

series841.0ms (14.3%)

Counts

4 → 12

Calls

4 calls:

389.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
290.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
108.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
54.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify116.0ms (2%)

Algorithm

1×	egg-herbie

Counts

228 → 228

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5480	8076

prune189.0ms (3.2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	227	1	228
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	227	7	234

Merged error: 5.6b

Counts

234 → 7

Compiler

Compiled 6586 to 867 computations (86.8% saved)

localize13.0ms (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 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
21.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite36.0ms (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` `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:

10.0ms	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a 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))

series638.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

341.0ms	(/.f64 (neg.f64 c) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
126.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
110.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
60.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify82.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5173	3058

prune98.0ms (1.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	1	3	4
Picked	0	1	1
Done	1	1	2
Total	121	6	127

Merged error: 5.6b

Counts

127 → 6

Compiler

Compiled 2836 to 674 computations (76.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 -1 (/.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) c))
0.4b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
0.6b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
21.5b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64`
80×	`*-un-lft-identity_binary64`
55×	`add-sqr-sqrt_binary64`
54×	`add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`
13×	`distribute-lft-out_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
5×	`pow1_binary64` `div-inv_binary64`
3×	`cbrt-undiv_binary64` `associate-/l*_binary64` `div-exp_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `flip--_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 120

Calls

4 calls:

11.0ms	(/.f64 -1 (/.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) c))
7.0ms	(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	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series540.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

258.0ms	(/.f64 -1 (/.f64 (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) c))
120.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
109.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
54.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify125.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4910	3796
1	4910	3796

prune119.0ms (2%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	131	7	138

Merged error: 5.6b

Counts

138 → 7

Compiler

Compiled 3423 to 1018 computations (70.3% saved)

regimes131.0ms (2.2%)

Compiler: Compiled 309 to 243 computations (21.4% saved)

bsearch85.0ms (1.4%)

Steps

Iters	Range	Point
5	8.846219148740613e+88	2.3909174588825904e+89	2.3613108789709727e+89
7	-4.9158897153091035e-293	-8.714771850556617e-295	-8.359529253987899e-294
11	-4.548525246732965e+170	-1.4125252577431923e+147	-1.300493903130599e+150

Iters

Range

Point

8.846219148740613e+88

2.3909174588825904e+89

2.3613108789709727e+89

-4.9158897153091035e-293

-8.714771850556617e-295

-8.359529253987899e-294

-4.548525246732965e+170

-1.4125252577431923e+147

-1.300493903130599e+150

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	133	79
1	133	79

end0.0ms (0%)

sample1.2s (20.1%)

Algorithm

1×

intervals

Results

237.0ms	5191×	body	128	valid
232.0ms	1104×	body	2048	valid
128.0ms	747×	body	1024	valid
103.0ms	392×	body	4096	valid
48.0ms	379×	body	512	valid
32.0ms	758×	body	128	nan
16.0ms	187×	body	256	valid
11.0ms	243×	body	128	invalid

Compiler

Compiled 168 to 119 computations (29.2% saved)

Details

analyze612.0ms (10.4%)

sample41.0ms (0.7%)

simplify188.0ms (3.2%)

prune13.0ms (0.2%)

localize10.0ms (0.2%)

rewrite38.0ms (0.7%)

series486.0ms (8.3%)

simplify71.0ms (1.2%)

prune101.0ms (1.7%)

localize11.0ms (0.2%)

rewrite64.0ms (1.1%)

series841.0ms (14.3%)

simplify116.0ms (2%)

prune189.0ms (3.2%)

localize13.0ms (0.2%)

rewrite36.0ms (0.6%)

series638.0ms (10.8%)

simplify82.0ms (1.4%)

prune98.0ms (1.7%)

localize11.0ms (0.2%)

rewrite42.0ms (0.7%)

series540.0ms (9.2%)

simplify125.0ms (2.1%)

prune119.0ms (2%)

regimes131.0ms (2.2%)

bsearch85.0ms (1.4%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (20.1%)

Profiling