Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0.1%	14

Compiler

Compiled 9 to 5 computations (44.4% saved)

sample11.0ms (0.4%)

Algorithm

1×

intervals

Results

6.0ms

256×

body

128

valid

Compiler

Compiled 17 to 10 computations (41.2% saved)

simplify103.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

prune4.0ms (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

31.2b

Counts

2 → 1

Compiler

Compiled 12 to 8 computations (33.3% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

30.1b	(sqrt.f64 (*.f64 x (+.f64 x x)))
30.1b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow1_binary64_132`
2×	`sqrt-div_binary64_88` `sqrt-pow1_binary64_89` `associate-*r/_binary64_13`
1×	`add-cbrt-cube_binary64_107` `add-log-exp_binary64_110` `*-un-lft-identity_binary64_71` `add-exp-log_binary64_109` `sqrt-prod_binary64_87` `add-cube-cbrt_binary64_106` `flip-+_binary64_45` `pow-prod-down_binary64_142` `add-sqr-sqrt_binary64_93` `flip3-+_binary64_74` `pow1/2_binary64_151`

Counts

1 → 13

Calls

2 calls:

5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
0.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series28.0ms (1%)

Counts

1 → 3

Calls

1 calls:

28.0ms

(sqrt.f64 (*.f64 x (+.f64 x x)))

Compiler

Compiled 28 to 28 computations (0% saved)

simplify70.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5009	140

prune23.0ms (0.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	12	4	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	12	5	17

Error

0.1b

Counts

17 → 5

Compiler

Compiled 173 to 72 computations (58.4% saved)

localize3.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.4b	(*.f64 x (sqrt.f64 2))
0.4b	(*.f64 x (sqrt.f64 2))

rewrite6.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64_93`
6×	`associate-r_binary64_11`
4×	`*-un-lft-identity_binary64_71` `sqrt-prod_binary64_87` `add-cube-cbrt_binary64_106`
3×	`add-cbrt-cube_binary64_107` `associate-l_binary64_12` `add-exp-log_binary64_109` `pow1_binary64_132`
2×	`unswap-sqr_binary64_39`
1×	`add-log-exp_binary64_110` `*-commutative_binary64_2` `prod-exp_binary64_120` `cbrt-unprod_binary64_104` `pow-prod-down_binary64_142`

Counts

1 → 22

Calls

2 calls:

5.0ms	(*.f64 x (sqrt.f64 2))
0.0ms	(*.f64 x (sqrt.f64 2))

series33.0ms (1.2%)

Counts

1 → 3

Calls

1 calls:

33.0ms

(*.f64 x (sqrt.f64 2))

Compiler

Compiled 24 to 24 computations (0% saved)

simplify43.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

25 → 25

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5010	211

prune25.0ms (0.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	23	2	25
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	23	7	30

Error

0.1b

Counts

30 → 7

Compiler

Compiled 250 to 191 computations (23.6% saved)

localize5.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
0.2b	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
0.2b	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
0.3b	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

rewrite22.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`sqrt-prod_binary64_87`
18×	`associate-r_binary64_11`
15×	`add-sqr-sqrt_binary64_93`
9×	`add-cbrt-cube_binary64_107` `*-un-lft-identity_binary64_71` `add-exp-log_binary64_109` `add-cube-cbrt_binary64_106` `pow1_binary64_132`
4×	`associate-l_binary64_12` `prod-exp_binary64_120` `cbrt-unprod_binary64_104` `pow-prod-down_binary64_142`
3×	`unswap-sqr_binary64_39`
2×	`add-log-exp_binary64_110` `*-commutative_binary64_2`

Counts

2 → 50

Calls

4 calls:

10.0ms	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))
6.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
0.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
0.0ms	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

series74.0ms (2.6%)

Counts

2 → 6

Calls

2 calls:

43.0ms	(*.f64 x (sqrt.f64 (sqrt.f64 2)))
31.0ms	(.f64 (.f64 x (sqrt.f64 (sqrt.f64 2))) (sqrt.f64 (sqrt.f64 2)))

Compiler

Compiled 78 to 78 computations (0% saved)

simplify76.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	5269	559

prune53.0ms (1.9%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	54	2	56
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	55	8	63

Error

0.1b

Counts

63 → 8

Compiler

Compiled 693 to 599 computations (13.6% saved)

localize8.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.3b	(.f64 (.f64 x (pow.f64 (sqrt.f64 (sqrt.f64 2)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 2))))
0.1b	(*.f64 x (pow.f64 (sqrt.f64 (sqrt.f64 2)) 3/2))
0.1b	(*.f64 x (pow.f64 (sqrt.f64 (sqrt.f64 2)) 3/2))
0.3b	(.f64 (.f64 x (pow.f64 (sqrt.f64 (sqrt.f64 2)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 2))))

rewrite24.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`sqrt-prod_binary64_87`
25×	`associate-r_binary64_11`
20×	`add-sqr-sqrt_binary64_93`
17×	`add-exp-log_binary64_109`
12×	`unpow-prod-down_binary64_150`
11×	`*-un-lft-identity_binary64_71` `add-cube-cbrt_binary64_106`
10×	`prod-exp_binary64_120`
9×	`add-cbrt-cube_binary64_107`
5×	`unswap-sqr_binary64_39`
4×	`associate-l_binary64_12` `cbrt-unprod_binary64_104` `pow1_binary64_132`
2×	`pow-exp_binary64_139` `pow-to-exp_binary64_140` `add-log-exp_binary64_110` `sqr-pow_binary64_43` `*-commutative_binary64_2`
1×	`pow-prod-down_binary64_142`

Counts

2 → 61

Calls

4 calls:

11.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 (sqrt.f64 2)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 2))))
8.0ms	(*.f64 x (pow.f64 (sqrt.f64 (sqrt.f64 2)) 3/2))
0.0ms	(*.f64 x (pow.f64 (sqrt.f64 (sqrt.f64 2)) 3/2))
0.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 (sqrt.f64 2)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 2))))

series168.0ms (6%)

Counts

2 → 6

Calls

2 calls:

132.0ms	(*.f64 x (pow.f64 (sqrt.f64 (sqrt.f64 2)) 3/2))
35.0ms	(.f64 (.f64 x (pow.f64 (sqrt.f64 (sqrt.f64 2)) 3/2)) (sqrt.f64 (sqrt.f64 (sqrt.f64 2))))

Compiler

Compiled 102 to 102 computations (0% saved)

simplify75.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4887	1083
1	4887	1083

prune78.0ms (2.8%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	67	8	75

Error

0.1b

Counts

75 → 8

Compiler

Compiled 1100 to 1003 computations (8.8% saved)

simplify6.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	104	320
1	104	320

regimes205.0ms (7.3%)

Accuracy

Total 0.2b remaining (68.7%)

Threshold costs 0.2b (68.7%)

Compiler

Compiled 907 to 736 computations (18.9% saved)

bsearch19.0ms (0.7%)

Steps

Iters	Range		Point
10	-1.2041969862679864e-297	6.2677593593086e-307	-1.52521227020015e-310

Compiler

Compiled 1 to 1 computations (0% saved)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	42	34
1	42	34

end0.0ms (0%)

sample1.6s (57.8%)

Algorithm

1×

intervals

Results

188.0ms

8000×

body

128

valid

Compiler

Compiled 651 to 545 computations (16.3% saved)

Pareto

-0.09939187152915481

Details

analyze4.0ms (0.1%)

sample11.0ms (0.4%)

simplify103.0ms (3.7%)

prune4.0ms (0.1%)

localize4.0ms (0.1%)

rewrite6.0ms (0.2%)

series28.0ms (1%)

simplify70.0ms (2.5%)

prune23.0ms (0.8%)

localize3.0ms (0.1%)

rewrite6.0ms (0.2%)

series33.0ms (1.2%)

simplify43.0ms (1.6%)

prune25.0ms (0.9%)

localize5.0ms (0.2%)

rewrite22.0ms (0.8%)

series74.0ms (2.6%)

simplify76.0ms (2.7%)

prune53.0ms (1.9%)

localize8.0ms (0.3%)

rewrite24.0ms (0.9%)

series168.0ms (6%)

simplify75.0ms (2.7%)

prune78.0ms (2.8%)

simplify6.0ms (0.2%)

regimes205.0ms (7.3%)

bsearch19.0ms (0.7%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.6s (57.8%)

Profiling