Details

analyze596.0ms (8.8%)

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	37×	body	2048	valid
7.0ms	163×	body	128	valid
5.0ms	30×	body	1024	valid
3.0ms	11×	body	4096	valid
2.0ms	29×	body	128	nan
1.0ms	9×	body	512	valid
0.0ms	6×	body	256	valid
0.0ms	8×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify196.0ms (2.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (19.0ms)

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: 35.8b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize19.0ms (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))))
1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite47.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
11×	`sqrt-prod_binary64`
10×	`add-log-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
7×	`cancel-sign-sub-inv_binary64` `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 → 96

Calls

4 calls:

14.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
12.0ms	(-.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))

series459.0ms (6.8%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(/.f64 (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
119.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
118.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
59.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify87.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4935	2578
1	4935	2578

prune120.0ms (1.8%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	101	7	108
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	101	8	109

Merged error: 6.8b

Counts

109 → 8

Compiler

Compiled 2350 to 432 computations (81.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
0.8b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite68.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

165×	`times-frac_binary64`
132×	`add-sqr-sqrt_binary64`
131×	`*-un-lft-identity_binary64`
79×	`add-cube-cbrt_binary64`
27×	`associate-/r*_binary64`
26×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
19×	`sqrt-prod_binary64`
15×	`add-exp-log_binary64`
13×	`distribute-rgt-neg-in_binary64`
10×	`add-log-exp_binary64`
9×	`add-cbrt-cube_binary64` `associate-/r/_binary64`
7×	`flip3--_binary64` `cancel-sign-sub-inv_binary64` `div-exp_binary64` `flip--_binary64`
6×	`pow1_binary64`
5×	`div-inv_binary64`
3×	`diff-log_binary64` `cbrt-undiv_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `1-exp_binary64` `rec-exp_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `inv-pow_binary64` `neg-log_binary64` `frac-2neg_binary64` `pow-flip_binary64`

Counts

4 → 182

Calls

4 calls:

18.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
11.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
5.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series490.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(/.f64 1 (/.f64 a (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))))
127.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
104.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
54.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify100.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4998	5933
1	4998	5933

prune176.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	192	2	194
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	195	7	202

Merged error: 6.7b

Counts

202 → 7

Compiler

Compiled 4980 to 959 computations (80.7% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.7b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
15.9b	(/.f64 (*.f64 a c) a)
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite29.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64`
10×	`add-log-exp_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`add-cube-cbrt_binary64`
5×	`pow1_binary64`
3×	`associate-/r*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
2×	`flip3--_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `flip--_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `distribute-rgt-neg-in_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `prod-exp_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64`

Counts

4 → 63

Calls

4 calls:

10.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
5.0ms	(/.f64 (*.f64 a c) a)
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series301.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
105.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
52.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))
18.0ms	(/.f64 (*.f64 a c) a)

simplify68.0ms (1%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5021	973

prune63.0ms (0.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	74	1	75
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	76	6	82

Merged error: 6.7b

Counts

82 → 6

Compiler

Compiled 1588 to 340 computations (78.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (/.f64 1 (/.f64 1 c)) (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
1.4b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.7b	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
24.6b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite115.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

616×	`times-frac_binary64`
444×	`*-un-lft-identity_binary64`
261×	`add-sqr-sqrt_binary64`
260×	`add-cube-cbrt_binary64`
92×	`distribute-lft-out_binary64`
46×	`distribute-rgt-neg-in_binary64`
44×	`associate-/l*_binary64`
37×	`add-exp-log_binary64`
27×	`div-exp_binary64`
25×	`div-inv_binary64`
13×	`add-cbrt-cube_binary64`
10×	`add-log-exp_binary64`
8×	`associate-/r/_binary64`
7×	`1-exp_binary64` `rec-exp_binary64`
6×	`cbrt-undiv_binary64`
5×	`associate-/r*_binary64` `pow1_binary64`
3×	`sqrt-prod_binary64`
2×	`flip3-+_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`associate-/l/_binary64` `sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `+-commutative_binary64`

Counts

4 → 340

Calls

4 calls:

29.0ms	(/.f64 (/.f64 1 (/.f64 1 c)) (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
12.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series667.0ms (9.9%)

Counts

4 → 12

Calls

4 calls:

374.0ms	(/.f64 (/.f64 1 (/.f64 1 c)) (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
125.0ms	(+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
111.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
57.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify155.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

352 → 352

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5191	11330

prune324.0ms (4.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	352	0	352
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	352	6	358

Merged error: 6.7b

Counts

358 → 6

Compiler

Compiled 8711 to 2203 computations (74.7% saved)

regimes792.0ms (11.7%)

Compiler: Compiled 3758 to 2330 computations (38% saved)

bsearch72.0ms (1.1%)

Steps

Iters	Range		Point
6	4.764379510284616e+53	3.589807743545239e+54	3.379496554939468e+54
9	-3.1133531518980485e-306	5.116285427565832e-304	1.2403787709714774e-308
5	-1.1841090536452334e+89	-5.036143154850016e+88	-1.1713988323127373e+89

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	118	79
1	118	79

end0.0ms (0%)

sample1.7s (25.7%)

Algorithm

1×

intervals

Results

246.0ms	1192×	body	2048	valid
224.0ms	5113×	body	128	valid
119.0ms	740×	body	1024	valid
106.0ms	409×	body	4096	valid
43.0ms	364×	body	512	valid
34.0ms	786×	body	128	nan
15.0ms	182×	body	256	valid
11.0ms	253×	body	128	invalid

Compiler

Compiled 959 to 594 computations (38.1% saved)

Details

analyze596.0ms (8.8%)

sample40.0ms (0.6%)

simplify196.0ms (2.9%)

prune4.0ms (0.1%)

localize19.0ms (0.3%)

rewrite47.0ms (0.7%)

series459.0ms (6.8%)

simplify87.0ms (1.3%)

prune120.0ms (1.8%)

localize11.0ms (0.2%)

rewrite68.0ms (1%)

series490.0ms (7.2%)

simplify100.0ms (1.5%)

prune176.0ms (2.6%)

localize11.0ms (0.2%)

rewrite29.0ms (0.4%)

series301.0ms (4.5%)

simplify68.0ms (1%)

prune63.0ms (0.9%)

localize12.0ms (0.2%)

rewrite115.0ms (1.7%)

series667.0ms (9.9%)

simplify155.0ms (2.3%)

prune324.0ms (4.8%)

regimes792.0ms (11.7%)

bsearch72.0ms (1.1%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.7s (25.7%)

Profiling