Details

analyze610.0ms (9.5%)

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

8.0ms	169×	body	128	valid
7.0ms	34×	body	2048	valid
4.0ms	24×	body	1024	valid
4.0ms	24×	body	128	nan
3.0ms	10×	body	4096	valid
1.0ms	11×	body	512	valid
1.0ms	8×	body	256	valid
0.0ms	9×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify196.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (18.0ms)

Iter	Nodes	Cost
0	309	18
1	309	18

prune8.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 33.4b

Counts

2 → 1

Compiler

Compiled 50 to 38 computations (24% saved)

localize18.0ms (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 (.f64 b_2 b_2) (.f64 a c))
1.4b	(+.f64 (neg.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)))

rewrite41.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64` `times-frac_binary64`
10×	`add-log-exp_binary64` `distribute-lft-out_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64` `associate-/l*_binary64`
3×	`associate-/r*_binary64` `sqrt-prod_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `neg-sub0_binary64` `associate-+l-_binary64` `flip--_binary64` `flip-+_binary64` `sqrt-div_binary64` `sum-log_binary64`
1×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `cancel-sign-sub-inv_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` `+-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

12.0ms	(/.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))

series494.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

182.0ms	(/.f64 (+.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))) a)
125.0ms	(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))))
61.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify109.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (86.0ms)

Iter	Nodes	Cost
0	4828	1903
1	4828	1903

prune488.0ms (7.6%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	84	8	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	84	9	93

Merged error: 5.4b

Counts

93 → 9

Compiler

Compiled 9999 to 4915 computations (50.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
3.7b	(/.f64 (/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
10.2b	(/.f64 (.f64 a c) (-.f64 (neg.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)))

rewrite60.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

74×	`times-frac_binary64`
60×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
31×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`difference-of-squares_binary64` `associate-/l*_binary64` `distribute-lft-out--_binary64`
13×	`sqrt-prod_binary64`
10×	`associate-/r*_binary64` `associate-/r/_binary64`
8×	`add-log-exp_binary64`
7×	`flip3--_binary64` `cbrt-undiv_binary64` `distribute-rgt-neg-in_binary64` `div-exp_binary64` `flip--_binary64`
6×	`cancel-sign-sub-inv_binary64` `div-inv_binary64`
5×	`pow1_binary64`
2×	`diff-log_binary64` `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` `associate--l-_binary64` `neg-sub0_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `neg-log_binary64`

Counts

4 → 141

Calls

4 calls:

16.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
13.0ms	(/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
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)))

series887.0ms (13.8%)

Counts

4 → 12

Calls

4 calls:

357.0ms	(/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
295.0ms	(/.f64 (/.f64 (.f64 a c) (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
122.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
113.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify104.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4921	4513
1	4921	4513

prune239.0ms (3.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	150	3	153
Fresh	4	3	7
Picked	1	0	1
Done	0	1	1
Total	155	7	162

Merged error: 5.3b

Counts

162 → 7

Compiler

Compiled 6048 to 1922 computations (68.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (-.f64 (neg.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 (neg.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)))

rewrite41.0ms (0.6%)

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×	`associate-/r*_binary64` `cancel-sign-sub-inv_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-rgt-neg-in_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`diff-log_binary64` `associate-/l*_binary64`
2×	`sub-neg_binary64` `associate-/r/_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `associate--l-_binary64` `neg-sub0_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `neg-log_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 95

Calls

4 calls:

12.0ms	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
10.0ms	(-.f64 (neg.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))

series598.0ms (9.3%)

Counts

4 → 12

Calls

4 calls:

327.0ms	(/.f64 c (-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
119.0ms	(-.f64 (neg.f64 b_2) (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
101.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
51.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify82.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

107 → 107

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5148	2471

prune96.0ms (1.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	107	0	107
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	107	7	114

Merged error: 5.3b

Counts

114 → 7

Compiler

Compiled 2677 to 820 computations (69.4% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

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

rewrite53.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 164

Calls

4 calls:

15.0ms	(/.f64 1 (/.f64 a (-.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)))
4.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

series494.0ms (7.7%)

Counts

4 → 12

Calls

4 calls:

221.0ms	(/.f64 1 (/.f64 a (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)))
117.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
104.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
52.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify106.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

176 → 176

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5062	5163

prune156.0ms (2.4%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	176	7	183

Merged error: 5.3b

Counts

183 → 7

Compiler

Compiled 4534 to 999 computations (78% saved)

regimes140.0ms (2.2%)

Compiler: Compiled 412 to 338 computations (18% saved)

bsearch99.0ms (1.5%)

Steps

Iters	Range	Point
9	2.5625574591512168e+61	6.424909099132833e+66	6.130147387831541e+66
8	1.3928820362951154e-302	3.5058117198365836e-298	1.4262394756477407e-302
9	-9.111974499129428e+158	-1.5423413135631464e+150	-2.5165680982392387e+152

Iters

Range

Point

2.5625574591512168e+61

6.424909099132833e+66

6.130147387831541e+66

1.3928820362951154e-302

3.5058117198365836e-298

1.4262394756477407e-302

-9.111974499129428e+158

-1.5423413135631464e+150

-2.5165680982392387e+152

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	114	79
1	114	79

end0.0ms (0%)

sample1.2s (18.9%)

Algorithm

1×

intervals

Results

254.0ms	1179×	body	2048	valid
233.0ms	5044×	body	128	valid
139.0ms	796×	body	1024	valid
110.0ms	416×	body	4096	valid
53.0ms	394×	body	512	valid
34.0ms	766×	body	128	nan
14.0ms	171×	body	256	valid
11.0ms	246×	body	128	invalid

Compiler

Compiled 162 to 119 computations (26.5% saved)

Details

analyze610.0ms (9.5%)

sample40.0ms (0.6%)

simplify196.0ms (3.1%)

prune8.0ms (0.1%)

localize18.0ms (0.3%)

rewrite41.0ms (0.6%)

series494.0ms (7.7%)

simplify109.0ms (1.7%)

prune488.0ms (7.6%)

localize10.0ms (0.2%)

rewrite60.0ms (0.9%)

series887.0ms (13.8%)

simplify104.0ms (1.6%)

prune239.0ms (3.7%)

localize11.0ms (0.2%)

rewrite41.0ms (0.6%)

series598.0ms (9.3%)

simplify82.0ms (1.3%)

prune96.0ms (1.5%)

localize9.0ms (0.1%)

rewrite53.0ms (0.8%)

series494.0ms (7.7%)

simplify106.0ms (1.6%)

prune156.0ms (2.4%)

regimes140.0ms (2.2%)

bsearch99.0ms (1.5%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.2s (18.9%)

Profiling