Details

analyze4.0ms

Algorithm

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

sample10.0ms

Algorithm

intervals

Results

5.0ms

256×

body

128

valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	13	9
1	13	9

prune3.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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

Merged error: 27.4b

Counts

2 → 1

localize4.0ms

Local error

Found 1 expressions with local error:

26.6b

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

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

4×	`pow1_binary64`
2×	`associate-*r/_binary64` `sqrt-pow1_binary64` `sqrt-div_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `*-un-lft-identity_binary64` `add-log-exp_binary64` `pow1/2_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `sqrt-prod_binary64` `flip-+_binary64`

Counts

1 → 13

Calls

1 calls:

5.0ms

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

series46.0ms

Counts

1 → 3

Calls

1 calls:

46.0ms

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

simplify72.0ms

Algorithm

egg-herbie

Counts

16 → 16

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5010	140

prune18.0ms

Filtered

13 candidates to 16 candidates (-23.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	11	5	16
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	11	6	17

Merged error: 0.2b

Counts

17 → 6

localize6.0ms

Local error

Found 4 expressions with local error:

0.1b	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
26.6b	(sqrt.f64 (*.f64 x (+.f64 x x)))
26.6b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

84×	`sqrt-pow1_binary64`
71×	`pow1_binary64`
33×	`sqrt-prod_binary64`
32×	`sqrt-div_binary64`
26×	`add-sqr-sqrt_binary64`
25×	`pow-prod-down_binary64`
22×	`pow1/2_binary64`
20×	`associate-*r/_binary64`
14×	`pow-prod-up_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`flip3-+_binary64` `swap-sqr_binary64` `flip-+_binary64`
8×	`pow-sqr_binary64`
7×	`associate-r_binary64` `associate-l_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 124

Calls

4 calls:

6.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
20.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series192.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))
50.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
44.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
45.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify79.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	5098	1446

prune59.0ms

Filtered

70 candidates to 136 candidates (-94.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	132	4	136
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	134	8	142

Merged error: 0.2b

Counts

142 → 8

localize13.0ms

Local error

Found 4 expressions with local error:

0.9b	(pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 4)
26.6b	(sqrt.f64 (*.f64 x (+.f64 x x)))
26.6b	(sqrt.f64 (*.f64 x (+.f64 x x)))
26.6b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1_binary64`
11×	`sqrt-prod_binary64`
10×	`unpow-prod-down_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-pow1_binary64` `add-sqr-sqrt_binary64`
6×	`associate-*r/_binary64` `sqrt-div_binary64`
5×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `pow-pow_binary64` `add-cbrt-cube_binary64` `cbrt-prod_binary64`
3×	`pow-prod-down_binary64` `flip3-+_binary64` `pow-unpow_binary64` `flip-+_binary64`
1×	`pow-to-exp_binary64` `sqrt-pow2_binary64` `pow1/3_binary64` `sqr-pow_binary64` `pow-exp_binary64`

Counts

4 → 67

Calls

4 calls:

6.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 4)
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series456.0ms

Counts

4 → 12

Calls

4 calls:

328.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (sqrt.f64 (*.f64 x (+.f64 x x))))) 4)
48.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
39.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
40.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify86.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4727	893
1	4727	893

prune70.0ms

Filtered

60 candidates to 79 candidates (-31.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	79	0	79
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	79	8	87

Merged error: 0.2b

Counts

87 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))))
5.6b	(exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
26.6b	(sqrt.f64 (*.f64 x (+.f64 x x)))
26.6b	(sqrt.f64 (*.f64 x (+.f64 x x)))

rewrite58.0ms

Algorithm

rewrite-expression-head

Rules

30×	`sqrt-div_binary64`
23×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
20×	`associate-*r/_binary64`
18×	`pow1_binary64`
11×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`associate-r_binary64` `log-prod_binary64` `exp-sum_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`sqrt-pow1_binary64` `exp-diff_binary64` `log-div_binary64`
7×	`associate-l_binary64` `exp-prod_binary64`
6×	`pow-prod-down_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64`
5×	`pow1/2_binary64`
4×	`add-log-exp_binary64` `log-pow_binary64` `frac-times_binary64`
2×	`associate-*l/_binary64`
1×	`cbrt-unprod_binary64` `rem-exp-log_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 92

Calls

4 calls:

29.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))))
8.0ms	(exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
5.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
6.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

series498.0ms

Counts

4 → 12

Calls

4 calls:

212.0ms	(.f64 (sqrt.f64 (sqrt.f64 (.f64 x (+.f64 x x)))) (sqrt.f64 (exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))))
192.0ms	(exp.f64 (log.f64 (sqrt.f64 (*.f64 x (+.f64 x x)))))
46.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))
47.0ms	(sqrt.f64 (*.f64 x (+.f64 x x)))

simplify75.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5704	1343

prune76.0ms

Filtered

78 candidates to 104 candidates (-33.3%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	102	2	104
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	102	10	112

Merged error: 0.1b

Counts

112 → 10

regimes21.0ms

Accuracy

0% (0.5b remaining)

Error of 0.7b against oracle of 0.1b and baseline of 0.7b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	22
1	9	22

end0.0ms

sample261.0ms

Algorithm

intervals

Results

169.0ms

8000×

body

128

valid

Details

analyze4.0ms

sample10.0ms

simplify8.0ms

prune3.0ms

localize4.0ms

rewrite6.0ms

series46.0ms

simplify72.0ms

prune18.0ms

localize6.0ms

rewrite54.0ms

series192.0ms

simplify79.0ms

prune59.0ms

localize13.0ms

rewrite30.0ms

series456.0ms

simplify86.0ms

prune70.0ms

localize11.0ms

rewrite58.0ms

series498.0ms

simplify75.0ms

prune76.0ms

regimes21.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample261.0ms

Profiling