Details

analyze162.0ms

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%	68.7%	6.3%	5
25%	65.6%	9.5%	6
37.5%	39%	23.5%	7
37.5%	36.7%	25.9%	8
43.7%	20.7%	35.6%	9
43.7%	19.3%	37%	10
46.8%	10.6%	42.5%	11
46.8%	9.9%	43.3%	12
48.4%	5.4%	46.2%	13
48.4%	5%	46.6%	14

sample33.0ms

Algorithm

intervals

Results

23.0ms	256×	body	80	valid
1.0ms	11×	body	80	nan

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (15.0ms)

Iter	Nodes	Cost
0	334	14
1	334	14

prune8.0ms

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: 1.0b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* 2.0 PI) (acos (/ g (neg h))))
0.0b	(/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0)
1.0b	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
5×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
3×	`pow1` `acos-asin` `associate-+r-` `associate-/r` `associate-/l`
2×	`flip3-+` `div-sub` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `cos-diff` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv`

Counts

3 → 50

Calls

3 calls:

4.0ms	(+ (* 2.0 PI) (acos (/ g (neg h))))
6.0ms	(/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0)
5.0ms	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))

series24.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ (* 2.0 PI) (acos (/ g (neg h))))
6.0ms	(/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0)
15.0ms	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))

simplify55.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5034	901

prune102.0ms

Filtered

45 candidates to 59 candidates (-31.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	57	2	59
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	57	3	60

Merged error: 0.9b

Counts

60 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (asin (/ g (neg h))) 3.0)
0.2b	(/ (asin (/ g (neg h))) 3.0)
1.0b	(sin (/ (* PI (+ 2.0 1/2)) 3.0))
1.0b	(cos (/ (* PI (+ 2.0 1/2)) 3.0))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`associate-/r` `associate-/l`
4×	`pow1` `add-log-exp`
2×	`cbrt-undiv` `asin-acos` `frac-2neg` `div-sub` `div-exp` `clear-num` `div-inv`

Counts

4 → 70

Calls

4 calls:

3.0ms	(/ (asin (/ g (neg h))) 3.0)
3.0ms	(/ (asin (/ g (neg h))) 3.0)
2.0ms	(sin (/ (* PI (+ 2.0 1/2)) 3.0))
2.0ms	(cos (/ (* PI (+ 2.0 1/2)) 3.0))

series7.0ms

Counts

4 → 8

Calls

4 calls:

3.0ms	(/ (asin (/ g (neg h))) 3.0)
3.0ms	(/ (asin (/ g (neg h))) 3.0)
0.0ms	(sin (/ (* PI (+ 2.0 1/2)) 3.0))
0.0ms	(cos (/ (* PI (+ 2.0 1/2)) 3.0))

simplify105.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	5071	908

prune194.0ms

Filtered

63 candidates to 78 candidates (-23.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	78	0	78
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	78	3	81

Merged error: 0.9b

Counts

81 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

1.0b	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))
1.0b	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))
1.0b	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))
1.0b	(* (cbrt (cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))) (cbrt (cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
3×	`acos-asin` `cos-diff` `associate-+r-` `div-sub`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 64

Calls

4 calls:

5.0ms	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))
5.0ms	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))
5.0ms	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))
5.0ms	(* (cbrt (cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))) (cbrt (cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))))

series84.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))
14.0ms	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))
18.0ms	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))
37.0ms	(* (cbrt (cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))) (cbrt (cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))))

simplify54.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4855	1305
1	4855	1305

prune188.0ms

Filtered

52 candidates to 76 candidates (-46.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	75	1	76
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	76	3	79

Merged error: 0b

Counts

79 → 3

localize21.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (cbrt (pow (cos (* (+ (* 2.0 PI) (acos (/ g (neg h)))) 0.3333333333333333)) 2)) (cbrt (cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))))
1.0b	(cos (* (+ (* 2.0 PI) (acos (/ g (neg h)))) 0.3333333333333333))
1.0b	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))
1.0b	(cbrt (pow (cos (* (+ (* 2.0 PI) (acos (/ g (neg h)))) 0.3333333333333333)) 2))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

32×	`cbrt-prod`
27×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `-un-lft-identity` `associate-l*`
10×	`unswap-sqr`
8×	`unpow-prod-down`
6×	`pow1` `add-exp-log` `associate-r`
4×	`add-cbrt-cube` `unpow2` `add-log-exp` `sqr-pow`
3×	`pow1/3`
2×	`pow-prod-down`
1×	`acos-asin` `cos-diff` `associate-+r-` `div-sub` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 70

Calls

4 calls:

8.0ms	(* (cbrt (pow (cos (* (+ (* 2.0 PI) (acos (/ g (neg h)))) 0.3333333333333333)) 2)) (cbrt (cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))))
3.0ms	(cos (* (+ (* 2.0 PI) (acos (/ g (neg h)))) 0.3333333333333333))
5.0ms	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))
3.0ms	(cbrt (pow (cos (* (+ (* 2.0 PI) (acos (/ g (neg h)))) 0.3333333333333333)) 2))

series83.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(* (cbrt (pow (cos (* (+ (* 2.0 PI) (acos (/ g (neg h)))) 0.3333333333333333)) 2)) (cbrt (cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))))
14.0ms	(cos (* (+ (* 2.0 PI) (acos (/ g (neg h)))) 0.3333333333333333))
18.0ms	(cos (/ (+ (* 2.0 PI) (acos (/ g (neg h)))) 3.0))
36.0ms	(cbrt (pow (cos (* (+ (* 2.0 PI) (acos (/ g (neg h)))) 0.3333333333333333)) 2))

simplify65.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4860	2143
1	4860	2143

prune207.0ms

Filtered

59 candidates to 82 candidates (-39.0%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	82	0	82
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	82	3	85

Merged error: 0b

Counts

85 → 3

regimes80.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	84	31
1	84	31

end0.0ms

sample814.0ms

Algorithm

intervals

Results

618.0ms	8000×	body	80	valid
35.0ms	561×	body	80	nan

Details

analyze162.0ms

sample33.0ms

simplify17.0ms

prune8.0ms

localize11.0ms

rewrite17.0ms

series24.0ms

simplify55.0ms

prune102.0ms

localize23.0ms

rewrite12.0ms

series7.0ms

simplify105.0ms

prune194.0ms

localize17.0ms

rewrite22.0ms

series84.0ms

simplify54.0ms

prune188.0ms

localize21.0ms

rewrite21.0ms

series83.0ms

simplify65.0ms

prune207.0ms

regimes80.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample814.0ms

Profiling