Details

analyze602.0ms (10.6%)

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)

sample42.0ms (0.7%)

Algorithm

1×

intervals

Results

13.0ms	47×	body	2048	valid
8.0ms	159×	body	128	valid
3.0ms	11×	body	4096	valid
3.0ms	16×	body	1024	valid
2.0ms	20×	body	512	valid
1.0ms	25×	body	128	nan
1.0ms	11×	body	128	invalid
0.0ms	3×	body	256	valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify192.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	309	20
1	309	20

prune4.0ms (0.1%)

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: 36.6b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
0.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
26.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite44.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
17×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
8×	`sqrt-prod_binary64`
7×	`associate-/l*_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`associate-/r*_binary64` `diff-log_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 89

Calls

4 calls:

13.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
10.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series465.0ms (8.2%)

Counts

4 → 12

Calls

4 calls:

160.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
124.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
121.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
61.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify78.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4922	2470
1	4922	2470

prune116.0ms (2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	95	6	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	96	6	102

Merged error: 4.3b

Counts

102 → 6

Compiler

Compiled 2210 to 421 computations (81% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
2.7b	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
8.0b	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
26.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite55.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
42×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64`
13×	`associate-/l*_binary64`
10×	`associate-/r/_binary64` `sqrt-prod_binary64`
9×	`associate-/r*_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `flip--_binary64`
6×	`add-log-exp_binary64` `div-inv_binary64`
5×	`pow1_binary64`
2×	`cbrt-unprod_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_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 → 126

Calls

4 calls:

15.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
12.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series886.0ms (15.6%)

Counts

4 → 12

Calls

4 calls:

372.0ms	(/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2))
293.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)) a)
112.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
110.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify89.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4936	4018
1	4936	4018

prune120.0ms (2.1%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	137	7	144

Merged error: 4.3b

Counts

144 → 7

Compiler

Compiled 3569 to 581 computations (83.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
2.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
26.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite50.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
121×	`add-sqr-sqrt_binary64`
94×	`*-un-lft-identity_binary64`
68×	`add-cube-cbrt_binary64`
26×	`difference-of-squares_binary64`
22×	`associate-/r*_binary64`
16×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-lft-out--_binary64`
9×	`add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`div-exp_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`flip3--_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64` `flip--_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate-/r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 152

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series507.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

223.0ms	(/.f64 1 (/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) c))
126.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
106.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
51.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify80.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4895	4846
1	4895	4846

prune133.0ms (2.3%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	164	7	171

Merged error: 4.3b

Counts

171 → 7

Compiler

Compiled 4050 to 809 computations (80% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.0b	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
2.7b	(/.f64 (.f64 (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))) (/.f64 c (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))) a)
26.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
26.7b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite58.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`add-sqr-sqrt_binary64`
10×	`*-un-lft-identity_binary64`
9×	`cbrt-undiv_binary64` `div-exp_binary64`
8×	`add-cube-cbrt_binary64`
7×	`sqrt-prod_binary64`
6×	`add-log-exp_binary64` `pow1_binary64`
4×	`cbrt-unprod_binary64` `prod-exp_binary64` `sqrt-div_binary64`
3×	`associate-/l/_binary64` `associate-/r*_binary64` `flip3--_binary64` `times-frac_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `associate-r/_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `frac-times_binary64` `associate-*l/_binary64`

Counts

4 → 74

Calls

4 calls:

29.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))) (/.f64 c (sqrt.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)
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series613.0ms (10.8%)

Counts

4 → 12

Calls

4 calls:

289.0ms	(/.f64 (.f64 (/.f64 a (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2))) (/.f64 c (sqrt.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))) b_2)))) a)
109.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
108.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
106.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify42.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (21.0ms)

Iter	Nodes	Cost
0	5078	1740

prune73.0ms (1.3%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	86	7	93

Merged error: 4.3b

Counts

93 → 7

Compiler

Compiled 2543 to 460 computations (81.9% saved)

regimes144.0ms (2.5%)

Compiler: Compiled 291 to 222 computations (23.7% saved)

bsearch88.0ms (1.5%)

Steps

Iters	Range	Point
7	3.00461679681557e+143	9.635373291754905e+144	7.36932297436956e+143
6	9.105102607579136e-258	5.273070030902596e-257	1.4772792552103187e-257
10	-1.0417483379886019e+160	-1.140147330439728e+149	-2.746806209943982e+150

Iters

Range

Point

3.00461679681557e+143

9.635373291754905e+144

7.36932297436956e+143

9.105102607579136e-258

5.273070030902596e-257

1.4772792552103187e-257

-1.0417483379886019e+160

-1.140147330439728e+149

-2.746806209943982e+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	135	74
1	135	74

end0.0ms (0%)

sample1.2s (20.3%)

Algorithm

1×

intervals

Results

228.0ms	1109×	body	2048	valid
227.0ms	5156×	body	128	valid
126.0ms	758×	body	1024	valid
109.0ms	425×	body	4096	valid
46.0ms	372×	body	512	valid
33.0ms	802×	body	128	nan
14.0ms	180×	body	256	valid
11.0ms	266×	body	128	invalid

Compiler

Compiled 159 to 112 computations (29.6% saved)

Details

analyze602.0ms (10.6%)

sample42.0ms (0.7%)

simplify192.0ms (3.4%)

prune4.0ms (0.1%)

localize17.0ms (0.3%)

rewrite44.0ms (0.8%)

series465.0ms (8.2%)

simplify78.0ms (1.4%)

prune116.0ms (2%)

localize10.0ms (0.2%)

rewrite55.0ms (1%)

series886.0ms (15.6%)

simplify89.0ms (1.6%)

prune120.0ms (2.1%)

localize12.0ms (0.2%)

rewrite50.0ms (0.9%)

series507.0ms (8.9%)

simplify80.0ms (1.4%)

prune133.0ms (2.3%)

localize16.0ms (0.3%)

rewrite58.0ms (1%)

series613.0ms (10.8%)

simplify42.0ms (0.7%)

prune73.0ms (1.3%)

regimes144.0ms (2.5%)

bsearch88.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (20.3%)

Profiling