Details

sample79.0ms

Algorithm

intervals

Results

44.0ms	95×	body	1280	valid
13.0ms	55×	body	640	valid
5.0ms	79×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	8×	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: 16.7b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.8b	(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×	`expm1-log1p-u` `times-frac` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `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 → 53

Calls

3 calls:

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

series162.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(* r (sin b))
97.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify35.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	207	327
1	884	279
2	5001	279

prune156.0ms

Filtered

62 candidates to 46 candidates (74.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	52	10	62
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	53	10	63

Merged error: 0.2b

Counts

63 → 10

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`associate-r` `associate-l` `add-log-exp`
5×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 87

Calls

4 calls:

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

series386.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos a) (cos b))
81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
49.0ms	(* (sin a) (sin b))
217.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify50.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	397	865
1	1625	767
2	5001	757

prune320.0ms

Filtered

99 candidates to 74 candidates (74.7%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	86	13	99
Fresh	8	1	9
Picked	1	0	1
Done	0	0	0
Total	95	14	109

Merged error: 0.0b

Counts

109 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(expm1 (log1p (* (cos a) (cos b))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (expm1 (log1p (* (cos a) (cos b)))) (* (sin a) (sin b))))
0.3b	(log1p (* (cos a) (cos b)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
5×	`expm1-log1p-u`
4×	`log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `div-exp` `prod-exp` `associate-/r/` `cbrt-unprod`
1×	`log1p-udef` `expm1-log1p` `flip3--` `frac-2neg` `log1p-expm1` `pow-prod-down` `clear-num` `-commutative` `flip--` `div-inv` `sin-mult` `associate-/l` `expm1-udef` `unswap-sqr`

Counts

4 → 68

Calls

4 calls:

1.0ms	(expm1 (log1p (* (cos a) (cos b))))
8.0ms	(* (sin a) (sin b))
6.0ms	(/ (* r (sin b)) (- (expm1 (log1p (* (cos a) (cos b)))) (* (sin a) (sin b))))
1.0ms	(log1p (* (cos a) (cos b)))

series437.0ms

Counts

4 → 12

Calls

4 calls:

66.0ms	(expm1 (log1p (* (cos a) (cos b))))
47.0ms	(* (sin a) (sin b))
256.0ms	(/ (* r (sin b)) (- (expm1 (log1p (* (cos a) (cos b)))) (* (sin a) (sin b))))
67.0ms	(log1p (* (cos a) (cos b)))

simplify40.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	319	726
1	1281	611
2	5002	600

prune260.0ms

Filtered

80 candidates to 57 candidates (71.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	78	2	80
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	80	14	94

Merged error: 0.0b

Counts

94 → 14

localize16.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
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))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-r`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-l` `cos-mult` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `prod-exp` `associate-/r` `frac-sub` `flip--` `cbrt-unprod` `associate-/l` `sub-div` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`sub-neg` `frac-2neg` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

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

series462.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
48.0ms	(* (sin a) (sin b))
219.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
113.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify58.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	427	1385
1	1819	1256
2	5001	1254

prune324.0ms

Filtered

122 candidates to 94 candidates (77.0%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	2	10	12
Picked	1	0	1
Done	0	1	1
Total	123	13	136

Merged error: 0.0b

Counts

136 → 13

regimes183.0ms

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	17	12
1	17	12

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2910×	body	1280	valid
457.0ms	1847×	body	640	valid
133.0ms	769×	body	320	valid
120.0ms	2150×	body	80	valid
40.0ms	326×	body	160	valid