Details

analyze635.0ms (11.8%)

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)

sample45.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms	38×	body	2048	valid
8.0ms	155×	body	128	valid
5.0ms	27×	body	1024	valid
4.0ms	13×	body	4096	valid
2.0ms	12×	body	512	valid
2.0ms	36×	body	128	nan
1.0ms	11×	body	256	valid
0.0ms	10×	body	128	invalid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify177.0ms (3.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	714	18
1	714	18

prune6.0ms (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

Error

34.8b

Counts

2 → 1

Compiler

Compiled 24 to 18 computations (25% saved)

localize17.0ms (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)
1.0b	(-.f64 (.f64 b_2 b_2) (.f64 a c))
1.6b	(-.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)))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64`
18×	`times-frac_binary64`
17×	`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` `cancel-sign-sub-inv_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 → 86

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))

series240.0ms (4.5%)

Counts

4 → 12

Calls

4 calls:

87.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2) a)
63.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
57.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))) b_2)
32.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify80.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	4916	2170
1	4916	2170

prune100.0ms (1.9%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	7	98
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	91	8	99

Error

4.5b

Counts

99 → 8

Compiler

Compiled 2049 to 404 computations (80.3% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

1.2b	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
3.8b	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
8.2b	(/.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)))

rewrite61.0ms (1.1%)

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:

14.0ms	(/.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)))))
6.0ms	(+.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)))

series434.0ms (8%)

Counts

4 → 12

Calls

4 calls:

185.0ms	(/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c)))))
143.0ms	(/.f64 (/.f64 (neg.f64 (.f64 a c)) (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (*.f64 a c))))) a)
53.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
53.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify116.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5421	8163

prune192.0ms (3.6%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	227	2	229
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	229	8	237

Error

4.4b

Counts

237 → 8

Compiler

Compiled 6657 to 873 computations (86.9% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 c (+.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))
1.2b	(+.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)))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
8×	`add-log-exp_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`pow1_binary64` `distribute-lft-out_binary64`
4×	`associate-/r*_binary64`
3×	`associate-/l*_binary64` `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` `cbrt-undiv_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

4 → 72

Calls

4 calls:

8.0ms	(/.f64 c (+.f64 b_2 (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))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series302.0ms (5.6%)

Counts

4 → 12

Calls

4 calls:

166.0ms	(/.f64 c (+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))))
60.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
51.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
26.0ms	(-.f64 (.f64 b_2 b_2) (.f64 a c))

simplify83.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4968	1696
1	4968	1696

prune65.0ms (1.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	84	8	92

Error

4.4b

Counts

92 → 8

Compiler

Compiled 1777 to 438 computations (75.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(+.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)))
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
22.1b	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`*-un-lft-identity_binary64` `sqrt-prod_binary64`
7×	`pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 57

Calls

4 calls:

6.0ms	(+.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	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
4.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

series206.0ms (3.8%)

Counts

4 → 12

Calls

4 calls:

54.0ms	(+.f64 b_2 (sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c))))
53.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
50.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))
48.0ms	(sqrt.f64 (-.f64 (.f64 b_2 b_2) (.f64 a c)))

simplify66.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5264	1175

prune85.0ms (1.6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	69	8	77

Error

4.4b

Counts

77 → 8

Compiler

Compiled 3162 to 554 computations (82.5% saved)

regimes522.0ms (9.7%)

Accuracy

Total 0.9b remaining (14.5%)

Threshold costs 0.9b (14.5%)

Compiler

Compiled 3248 to 1920 computations (40.9% saved)

bsearch118.0ms (2.2%)

Steps

Iters	Range	Point
9	1.8515760575460165e+108	3.3102593882323454e+115	3.263886109249808e+115
11	3.471655958753961e-308	2.5755835898789858e-287	3.5093565565557947e-308
12	-4.659684812883713e+193	-4.559874932742751e+148	-7.085174189094956e+148

Iters

Range

Point

1.8515760575460165e+108

3.3102593882323454e+115

3.263886109249808e+115

3.471655958753961e-308

2.5755835898789858e-287

3.5093565565557947e-308

-4.659684812883713e+193

-4.559874932742751e+148

-7.085174189094956e+148

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	139	79
1	139	79

end0.0ms (0%)

sample1.7s (31.8%)

Algorithm

1×

intervals

Results

244.0ms	5231×	body	128	valid
237.0ms	1066×	body	2048	valid
127.0ms	732×	body	1024	valid
119.0ms	421×	body	4096	valid
48.0ms	347×	body	512	valid
35.0ms	814×	body	128	nan
17.0ms	203×	body	256	valid
10.0ms	225×	body	128	invalid

Compiler

Compiled 861 to 506 computations (41.2% saved)

Details

analyze635.0ms (11.8%)

sample45.0ms (0.8%)

simplify177.0ms (3.3%)

prune6.0ms (0.1%)

localize17.0ms (0.3%)

rewrite36.0ms (0.7%)

series240.0ms (4.5%)

simplify80.0ms (1.5%)

prune100.0ms (1.9%)

localize11.0ms (0.2%)

rewrite61.0ms (1.1%)

series434.0ms (8%)

simplify116.0ms (2.1%)

prune192.0ms (3.6%)

localize9.0ms (0.2%)

rewrite27.0ms (0.5%)

series302.0ms (5.6%)

simplify83.0ms (1.5%)

prune65.0ms (1.2%)

localize15.0ms (0.3%)

rewrite25.0ms (0.5%)

series206.0ms (3.8%)

simplify66.0ms (1.2%)

prune85.0ms (1.6%)

regimes522.0ms (9.7%)

bsearch118.0ms (2.2%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.7s (31.8%)

Profiling