Details

analyze67.0ms

Algorithm

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
25%	74.9%	0.1%	5
25%	50%	25.1%	6
25%	31.2%	43.8%	7
31.2%	25%	43.8%	8
39%	17.2%	43.8%	9
42.9%	13.3%	43.8%	10
47.2%	9%	43.8%	11
49.4%	6.8%	43.8%	12
51.6%	4.6%	43.8%	13
52.7%	3.5%	43.8%	14

sample12.0ms

Algorithm

intervals

Results

6.0ms

256×

body

128

valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	38	13
1	38	13

prune4.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.1b

Counts

2 → 2

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y y))
0.0b	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
0.1b	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-log-exp_binary64`
10×	`sum-log_binary64`
3×	`flip3-+_binary64` `*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `add-sqr-sqrt_binary64` `+-commutative_binary64` `flip-+_binary64`
2×	`associate-+l+_binary64`

Counts

3 → 38

Calls

3 calls:

7.0ms	(+.f64 (.f64 x x) (.f64 y y))
7.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
10.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

series134.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(+.f64 (.f64 x x) (.f64 y y))
47.0ms	(+.f64 (+.f64 (.f64 x x) (.f64 y y)) (*.f64 y y))
50.0ms	(+.f64 (+.f64 (+.f64 (.f64 x x) (.f64 y y)) (.f64 y y)) (.f64 y y))

simplify84.0ms

Algorithm

egg-herbie

Counts

47 → 47

Iterations

Useful iterations: 0 (71.0ms)

Iter	Nodes	Cost
0	4844	758
1	4844	758

prune35.0ms

Filtered

33 candidates to 47 candidates (-42.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	44	3	47
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	44	5	49

Merged error: 0.0b

Counts

49 → 5

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (.f64 x x) (.f64 y (*.f64 y 3)))
0.2b	(.f64 y (.f64 y 3))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `-un-lft-identity_binary64` `cbrt-unprod_binary64` `add-cube-cbrt_binary64` `associate-l*_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
1×	`flip3-+_binary64` `associate-r_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 29

Calls

2 calls:

5.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 3)))
5.0ms	(.f64 y (.f64 y 3))

series82.0ms

Counts

2 → 6

Calls

2 calls:

46.0ms	(+.f64 (.f64 x x) (.f64 y (*.f64 y 3)))
36.0ms	(.f64 y (.f64 y 3))

simplify50.0ms

Algorithm

egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4976	410
1	4976	410

prune22.0ms

Filtered

21 candidates to 35 candidates (-66.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	34	1	35
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	34	6	40

Merged error: 0.0b

Counts

40 → 6

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) (.f64 y y))
0.2b	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
6.6b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
6.6b	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
24×	`sqrt-prod_binary64`
21×	`pow1_binary64`
16×	`sqrt-div_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1/2_binary64` `sqrt-pow1_binary64`
9×	`flip3-+_binary64` `flip-+_binary64`
8×	`swap-sqr_binary64`
6×	`add-log-exp_binary64` `associate-r_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-l_binary64`
5×	`pow-prod-up_binary64`
4×	`unswap-sqr_binary64` `frac-times_binary64`
3×	`pow-prod-down_binary64` `pow-sqr_binary64`
2×	`associate-r/_binary64` `rem-sqrt-square_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `rem-square-sqrt_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `prod-exp_binary64` `+-commutative_binary64` `pow2_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 98

Calls

4 calls:

14.0ms	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) (.f64 y y))
14.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
5.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
4.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

series233.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(+.f64 (.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) (.f64 y y))
51.0ms	(.f64 (sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y)))) (sqrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
66.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
58.0ms	(sqrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

simplify79.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4955	2047
1	4955	2047

prune65.0ms

Filtered

67 candidates to 110 candidates (-64.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	109	1	110
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	111	5	116

Merged error: 0.0b

Counts

116 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.4b	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) 4) (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
0.9b	(pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) 4)
7.2b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
7.2b	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
24×	`unpow-prod-down_binary64`
22×	`cbrt-prod_binary64`
16×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
13×	`associate-l_binary64`
10×	`add-exp-log_binary64` `unswap-sqr_binary64`
6×	`cbrt-div_binary64` `pow1_binary64` `associate-r_binary64`
5×	`add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `sqr-pow_binary64`
3×	`flip3-+_binary64` `pow-unpow_binary64` `pow1/3_binary64` `prod-exp_binary64` `flip-+_binary64`
2×	`pow-to-exp_binary64` `associate-*r/_binary64` `sqrt-pow1_binary64` `pow-exp_binary64`
1×	`pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow2_binary64` `*-commutative_binary64`

Counts

4 → 96

Calls

4 calls:

16.0ms	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) 4) (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
8.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) 4)
4.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
4.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

series596.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(.f64 (pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) 4) (cbrt.f64 (+.f64 (.f64 x x) (*.f64 y (+.f64 y y)))))
222.0ms	(pow.f64 (sqrt.f64 (cbrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))) 4)
157.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))
163.0ms	(cbrt.f64 (+.f64 (.f64 x x) (.f64 y (+.f64 y y))))

simplify94.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (65.0ms)

Iter	Nodes	Cost
0	4952	2660
1	4952	2660

prune93.0ms

Filtered

83 candidates to 108 candidates (-30.1%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	107	1	108
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	107	6	113

Merged error: 0.0b

Counts

113 → 6

regimes74.0ms

Accuracy

0% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	11	22
1	11	22

end0.0ms

sample356.0ms

Algorithm

intervals

Results

226.0ms	8000×	body	128	valid
0.0ms	5×	body	128	invalid

Details

analyze67.0ms

sample12.0ms

simplify9.0ms

prune4.0ms

localize7.0ms

rewrite28.0ms

series134.0ms

simplify84.0ms

prune35.0ms

localize6.0ms

rewrite12.0ms

series82.0ms

simplify50.0ms

prune22.0ms

localize10.0ms

rewrite52.0ms

series233.0ms

simplify79.0ms

prune65.0ms

localize13.0ms

rewrite49.0ms

series596.0ms

simplify94.0ms

prune93.0ms

regimes74.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample356.0ms

Profiling