Details

sample89.0ms

Algorithm

intervals

Results

52.0ms	109×	body	1280	valid
15.0ms	55×	body	640	valid
4.0ms	61×	body	80	valid
3.0ms	17×	body	320	valid
2.0ms	14×	body	160	valid

simplify8.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	19	5
3	20	5
4	20	5

prune2.0ms

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

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
1.8b	(cos (+ a b))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

4.0ms	(* r (sin b))
5.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

series163.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(* r (sin b))
99.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify34.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256

prune140.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	46	10	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	10	57

Merged error: 0.2b

Counts

57 → 10

localize16.0ms

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))))

rewrite27.0ms

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:

7.0ms	(* (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))))

series336.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos a) (cos b))
41.0ms	(* r (sin b))
44.0ms	(* (sin a) (sin b))
212.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify49.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (41.0ms)

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

prune285.0ms

Filtered

93 candidates to 65 candidates (69.9%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	80	13	93
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	90	13	103

Merged error: 0.0b

Counts

103 → 13

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos b) (cos a))
0.2b	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
0.2b	(/ (sin b) (- (* (cos b) (cos a)) (* (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 b) (cos a))
12.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series418.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos b) (cos a))
219.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
111.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
47.0ms	(* (sin a) (sin b))

simplify58.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	428	1219
1	1841	1102
2	5002	1098

prune346.0ms

Filtered

117 candidates to 86 candidates (73.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	117	13	130

Merged error: 0.0b

Counts

130 → 13

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
0.2b	(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
0.3b	(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

7.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
11.0ms	(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
5.0ms	(* (sin a) (sin b))
15.0ms	(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

series474.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
215.0ms	(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
48.0ms	(* (sin a) (sin b))
111.0ms	(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

simplify60.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	456	1487
1	1977	1270
2	5002	1238

prune275.0ms

Filtered

130 candidates to 80 candidates (61.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	130	13	143

Merged error: 0.0b

Counts

143 → 13

regimes186.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.4s	2978×	body	1280	valid
503.0ms	1781×	body	640	valid
152.0ms	735×	body	320	valid
139.0ms	2149×	body	80	valid
52.0ms	360×	body	160	valid

Details

sample89.0ms

simplify8.0ms

prune2.0ms

localize12.0ms

rewrite17.0ms

series163.0ms

simplify34.0ms

prune140.0ms

localize16.0ms

rewrite27.0ms

series336.0ms

simplify49.0ms

prune285.0ms

localize16.0ms

rewrite33.0ms

series418.0ms

simplify58.0ms

prune346.0ms

localize17.0ms

rewrite42.0ms

series474.0ms

simplify60.0ms

prune275.0ms

regimes186.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.4s

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