Details

sample329.0ms

Algorithm

intervals

Results

53.0ms	109×	body	1280	valid
16.0ms	55×	body	640	valid
4.0ms	61×	body	80	valid
4.0ms	17×	body	320	valid
2.0ms	14×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	20	5
3	21	5
4	21	5

prune4.0ms

Filtered

1 candidates to 0 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: 13.3b

Counts

2 → 1

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
1.8b	(cos (+ a b))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-l` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 67

Calls

3 calls:

21.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series163.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(* r (/ (sin b) (cos (+ a b))))
39.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify42.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	252	536
1	1064	480
2	5001	477

prune203.0ms

Filtered

76 candidates to 57 candidates (75.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	9	77

Merged error: 0.2b

Counts

77 → 9

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 105

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
12.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series417.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos a) (cos b))
216.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
115.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
46.0ms	(* (sin a) (sin b))

simplify59.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	428	1219
1	1858	1102
2	5001	1098

prune380.0ms

Filtered

117 candidates to 87 candidates (74.4%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	105	12	117
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	112	14	126

Merged error: 0.0b

Counts

126 → 14

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.2b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv` `associate-/l*` `sub-div`

Counts

4 → 81

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
4.0ms	(* r (sin b))
5.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series343.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos a) (cos b))
37.0ms	(* r (sin b))
46.0ms	(* (sin a) (sin b))
216.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify50.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	367	682
1	1616	593
2	5001	592

prune281.0ms

Filtered

93 candidates to 65 candidates (69.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	90	3	93
Fresh	4	9	13
Picked	1	0	1
Done	0	0	0
Total	95	12	107

Merged error: 0.0b

Counts

107 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.3b	(pow (* (sin a) (sin b)) 3)
29.9b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`cbrt-prod`
4×	`sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `times-frac` `associate-r` `associate-l` `prod-exp` `associate-/r*` `associate-/r/` `cbrt-unprod`
2×	`cbrt-undiv` `cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `div-exp` `pow-prod-down` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `clear-num` `cos-mult` `-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

5.0ms	(* (sin a) (sin b))
11.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
5.0ms	(pow (* (sin a) (sin b)) 3)
3.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series377.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin a) (sin b))
219.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
64.0ms	(pow (* (sin a) (sin b)) 3)
49.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify54.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	386	788
1	1812	681
2	5002	671

prune262.0ms

Filtered

96 candidates to 67 candidates (69.8%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	96	12	108

Merged error: 0.0b

Counts

108 → 12

regimes178.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	12
1	18	12

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.4s	2978×	body	1280	valid
508.0ms	1781×	body	640	valid
146.0ms	735×	body	320	valid
136.0ms	2149×	body	80	valid
50.0ms	360×	body	160	valid

Details

sample329.0ms

simplify13.0ms

prune4.0ms

localize13.0ms

rewrite35.0ms

series163.0ms

simplify42.0ms

prune203.0ms

localize20.0ms

rewrite33.0ms

series417.0ms

simplify59.0ms

prune380.0ms

localize19.0ms

rewrite24.0ms

series343.0ms

simplify50.0ms

prune281.0ms

localize20.0ms

rewrite26.0ms

series377.0ms

simplify54.0ms

prune262.0ms

regimes178.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.4s

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