Details

sample79.0ms

Algorithm

intervals

Results

41.0ms	95×	body	1280	valid
14.0ms	55×	body	640	valid
8.0ms	79×	body	80	valid
4.0ms	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))

rewrite19.0ms

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:

5.0ms	(* r (sin b))
5.0ms	(/ (* r (sin b)) (cos (+ a b)))
7.0ms	(cos (+ a b))

series165.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(* r (sin b))
101.0ms	(/ (* 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

prune136.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	47	9	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	9	57

Merged error: 0.2b

Counts

57 → 9

localize16.0ms

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))))

rewrite27.0ms

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:

5.0ms	(* (cos a) (cos b))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
10.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series394.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* (cos a) (cos b))
82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(* (sin a) (sin b))
225.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify48.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (40.0ms)

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

prune284.0ms

Filtered

89 candidates to 64 candidates (71.9%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	77	12	89
Fresh	6	2	8
Picked	1	0	1
Done	0	0	0
Total	84	14	98

Merged error: 0.0b

Counts

98 → 14

localize19.0ms

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))))

rewrite36.0ms

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`
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` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

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)))))
9.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series462.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
47.0ms	(* (sin a) (sin b))
216.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
116.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify56.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	401	1307
1	1733	1182
2	5001	1178

prune342.0ms

Filtered

112 candidates to 84 candidates (75.0%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	112	14	126

Merged error: 0.0b

Counts

126 → 14

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(* r (/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b)))))))
0.2b	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
2.9b	(log (exp (* (sin a) (sin b))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`associate-l`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`log-prod` `prod-exp` `associate-/r` `log-pow` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `div-inv`
1×	`exp-prod` `exp-to-pow` `frac-2neg` `associate-*r/` `rem-log-exp` `clear-num` `sin-mult`

Counts

4 → 96

Calls

4 calls:

5.0ms	(* (sin a) (sin b))
12.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b)))))))
9.0ms	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
2.0ms	(log (exp (* (sin a) (sin b))))

series427.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(* (sin a) (sin b))
221.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b)))))))
116.0ms	(/ (sin b) (- (* (cos b) (cos a)) (log (exp (* (sin a) (sin b))))))
45.0ms	(log (exp (* (sin a) (sin b))))

simplify52.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	360	1301
1	1545	1128
2	5001	1121

prune321.0ms

Filtered

108 candidates to 84 candidates (77.8%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	2	11	13
Picked	1	0	1
Done	0	0	0
Total	108	14	122

Merged error: 0.0b

Counts

122 → 14

regimes204.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	20	11
1	20	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2910×	body	1280	valid
477.0ms	1847×	body	640	valid
141.0ms	769×	body	320	valid
126.0ms	2150×	body	80	valid
42.0ms	326×	body	160	valid