Details

sample77.0ms

Algorithm

intervals

Results

43.0ms	106×	body	1280	valid
12.0ms	51×	body	640	valid
4.0ms	67×	body	80	valid
3.0ms	17×	body	320	valid
2.0ms	15×	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: 15.3b

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.5b	(cos (+ a b))

rewrite43.0ms

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:

10.0ms	(* r (sin b))
19.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series149.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* r (sin b))
91.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify33.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (28.0ms)

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

prune150.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.3b	(* (sin a) (sin b))

rewrite68.0ms

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:

11.0ms	(* (cos a) (cos b))
10.0ms	(* r (sin b))
32.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms	(* (sin a) (sin b))

series316.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(* (cos a) (cos b))
34.0ms	(* r (sin b))
197.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
44.0ms	(* (sin a) (sin b))

simplify47.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (41.0ms)

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

prune311.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos b) (cos a))
0.2b	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
0.2b	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
0.3b	(* (sin a) (sin b))

rewrite136.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 105

Calls

4 calls:

11.0ms	(* (cos b) (cos a))
30.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
78.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
13.0ms	(* (sin a) (sin b))

series386.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (cos b) (cos a))
107.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
201.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
42.0ms	(* (sin a) (sin b))

simplify55.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	428	1219
1	1841	1103
2	5001	1098

prune395.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
0.3b	(* (sin a) (sin b))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

rewrite139.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
22×	`add-cbrt-cube`
18×	`times-frac`
14×	`pow1` `prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`associate-l`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`cos-mult` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`flip3--` `frac-sub` `flip--` `div-inv` `sub-div` `unswap-sqr`
1×	`pow-flip` `frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 114

Calls

4 calls:

10.0ms	(* r (sin b))
36.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
13.0ms	(* (sin a) (sin b))
77.0ms	(* (* r (sin b)) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

series366.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* r (sin b))
89.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
41.0ms	(* (sin a) (sin b))
199.0ms	(* (* r (sin b)) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	472	1265
1	2389	1084
2	5001	1056

prune313.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0b

regimes152.0ms

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	20	11
1	20	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2898×	body	1280	valid
447.0ms	1837×	body	640	valid
127.0ms	738×	body	320	valid
123.0ms	2180×	body	80	valid
43.0ms	349×	body	160	valid