Details

sample326.0ms

Algorithm

intervals

Results

51.0ms	100×	body	1280	valid
19.0ms	67×	body	640	valid
4.0ms	19×	body	320	valid
3.0ms	56×	body	80	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: 15.6b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
3.3b	(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:

7.0ms	(* r (/ (sin b) (cos (+ a b))))
18.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series157.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* r (/ (sin b) (cos (+ a b))))
37.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

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

prune196.0ms

Filtered

76 candidates to 57 candidates (75.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	65	11	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	66	11	77

Merged error: 0.2b

Counts

77 → 11

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

rewrite31.0ms

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 a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series448.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
44.0ms	(* (sin a) (sin b))
212.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
113.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	405	1307
1	1761	1182
2	5001	1173

prune347.0ms

Filtered

112 candidates to 86 candidates (76.8%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	9	1	10
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Merged error: 0.0b

Counts

123 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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×	`sin-mult`
4×	`associate-/r/` `cos-mult`
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 → 76

Calls

4 calls:

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

series376.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
40.0ms	(* r (sin b))
43.0ms	(* (sin a) (sin b))
215.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5002	663

prune245.0ms

Filtered

88 candidates to 62 candidates (70.5%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	87	14	101

Merged error: 0.0b

Counts

101 → 14

localize30.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3))) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))))
0.4b	(pow (* (sin a) (sin b)) 3)
0.4b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.6b	(pow (* (cos a) (cos b)) 3)

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

131×	`cos-mult`
120×	`frac-add`
111×	`sin-mult`
94×	`frac-times` `associate-*r/`
60×	`associate-*l/`
51×	`pow1`
37×	`add-sqr-sqrt`
36×	`associate-l`
28×	`times-frac`
27×	`add-exp-log` `add-cbrt-cube`
26×	`*-un-lft-identity`
20×	`add-cube-cbrt` `pow-prod-down`
14×	`sqr-pow`
12×	`prod-exp` `cbrt-unprod` `difference-of-squares`
8×	`flip3-+` `flip-+`
6×	`cube-div` `pow-unpow`
4×	`pow-pow` `associate-r` `pow-exp` `associate-/r/` `pow-sqr` `pow-prod-up` `add-log-exp` `rem-cube-cbrt`
3×	`difference-cubes` `distribute-lft-out--`
2×	`cube-mult` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod` `*-commutative` `unswap-sqr`
1×	`cbrt-undiv` `pow2` `distribute-rgt-in` `flip3--` `distribute-lft-in` `swap-sqr` `div-exp` `frac-sub` `flip--` `div-inv` `sub-div`

Counts

4 → 209

Calls

4 calls:

39.0ms	(* (/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3))) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))))
5.0ms	(pow (* (sin a) (sin b)) 3)
8.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
4.0ms	(pow (* (cos a) (cos b)) 3)

series581.0ms

Counts

4 → 12

Calls

4 calls:

399.0ms	(* (/ (sin b) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3))) (+ (* (* (cos a) (cos b)) (* (cos a) (cos b))) (+ (* (* (sin a) (sin b)) (* (sin a) (sin b))) (* (* (cos a) (cos b)) (* (sin a) (sin b))))))
62.0ms	(pow (* (sin a) (sin b)) 3)
56.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
64.0ms	(pow (* (cos a) (cos b)) 3)

simplify85.0ms

Algorithm

egg-herbie

Counts

221 → 221

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1923	6303
1	5002	6058

prune782.0ms

Filtered

221 candidates to 134 candidates (60.6%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	221	0	221
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	221	14	235

Merged error: 0.0b

Counts

235 → 14

regimes191.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2912×	body	1280	valid
513.0ms	1882×	body	640	valid
144.0ms	727×	body	320	valid
134.0ms	2130×	body	80	valid
47.0ms	350×	body	160	valid