Details

sample78.0ms

Algorithm

intervals

Results

42.0ms	92×	body	1280	valid
15.0ms	60×	body	640	valid
5.0ms	25×	body	320	valid
4.0ms	69×	body	80	valid
1.0ms	10×	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: 19.0b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
5.5b	(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))

series159.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* r (sin b))
96.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify34.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (29.0ms)

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

prune131.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	7	57

Merged error: 0.2b

Counts

57 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(- (* (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×	`associate-/r/`
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` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 77

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))))

series374.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos a) (cos b))
79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(* (sin a) (sin b))
211.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	371	798
1	1534	704
2	5002	694

prune259.0ms

Filtered

89 candidates to 64 candidates (71.9%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	79	10	89
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Merged error: 0.0b

Counts

96 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
9.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
8.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series455.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms	(* (sin a) (sin b))
110.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
219.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify77.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	570	2145
1	2453	2009
2	5001	1988

prune453.0ms

Filtered

147 candidates to 119 candidates (81.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	141	6	147
Fresh	6	5	11
Picked	0	1	1
Done	0	0	0
Total	147	12	159

Merged error: 0.0b

Counts

159 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
2.7b	(log (exp (* (sin a) (sin b))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
11×	`add-exp-log` `add-cbrt-cube`
10×	`add-cube-cbrt` `*-un-lft-identity`
7×	`pow1`
6×	`log-prod` `add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*` `log-pow` `associate--r+`
2×	`cbrt-undiv` `flip3--` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod`
1×	`sub-neg` `exp-prod` `exp-to-pow` `frac-2neg` `diff-log` `rem-log-exp` `pow-prod-down` `clear-num` `-commutative` `div-inv` `sin-mult` `associate-/l` `unswap-sqr`

Counts

4 → 71

Calls

4 calls:

6.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
2.0ms	(log (exp (* (sin a) (sin b))))

series388.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
49.0ms	(* (sin a) (sin b))
210.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
47.0ms	(log (exp (* (sin a) (sin b))))

simplify39.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	322	847
1	1257	710
2	5002	703

prune214.0ms

Filtered

83 candidates to 59 candidates (71.1%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	82	1	83
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	82	13	95

Merged error: 0.0b

Counts

95 → 13

regimes181.0ms

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	14	10
1	14	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2881×	body	1280	valid
480.0ms	1860×	body	640	valid
143.0ms	752×	body	320	valid
118.0ms	2163×	body	80	valid
44.0ms	346×	body	160	valid