Details

sample75.0ms

Algorithm

intervals

Results

41.0ms	95×	body	1280	valid
12.0ms	53×	body	640	valid
4.0ms	26×	body	320	valid
4.0ms	69×	body	80	valid
2.0ms	13×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.8b	(cos (+ a b))

rewrite40.0ms

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:

9.0ms	(* r (sin b))
17.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series165.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* r (sin b))
101.0ms	(/ (* r (sin b)) (cos (+ a b)))
25.0ms	(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

prune136.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite63.0ms

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:

9.0ms	(* r (sin b))
10.0ms	(* (cos a) (cos b))
30.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))

series357.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* r (sin b))
41.0ms	(* (cos a) (cos b))
225.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
49.0ms	(* (sin a) (sin b))

simplify49.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	367	682
1	1616	594
2	5001	593

prune286.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

10.0ms	(* (cos a) (cos b))
17.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
12.0ms	(* (sin a) (sin b))
28.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series442.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos a) (cos b))
233.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
48.0ms	(* (sin a) (sin b))
120.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify82.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	573	2072
1	2474	1931
2	5001	1912

prune503.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

10.0ms	(* (cos a) (cos b))
15.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) (sin b)))
12.0ms	(* (sin b) (sin a))
30.0ms	(/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) (sin b))

series448.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(* (cos a) (cos b))
238.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) (sin b)))
46.0ms	(* (sin b) (sin a))
123.0ms	(/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) (sin b))

simplify78.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	580	2072
1	2650	1937
2	5002	1937

prune469.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0b

regimes119.0ms

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	20	10
1	22	10
2	22	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2912×	body	1280	valid
475.0ms	1858×	body	640	valid
131.0ms	767×	body	320	valid
112.0ms	2114×	body	80	valid
43.0ms	353×	body	160	valid