Details

sample76.0ms

Algorithm

intervals

Results

41.0ms	98×	body	1280	valid
13.0ms	54×	body	640	valid
4.0ms	23×	body	320	valid
4.0ms	69×	body	80	valid
1.0ms	12×	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: 16.8b

localize11.0ms

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))

rewrite41.0ms

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×	`expm1-log1p-u` `times-frac` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `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 → 53

Calls

3 calls:

9.0ms	(* r (sin b))
18.0ms	(/ (* r (sin b)) (cos (+ a b)))
11.0ms	(cos (+ a b))

series166.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* r (sin b))
102.0ms	(/ (* r (sin b)) (cos (+ a b)))
26.0ms	(cos (+ a b))

simplify32.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	207	327
1	884	279
2	5001	279

prune155.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin 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))))

rewrite71.0ms

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×	`expm1-log1p-u` `associate-/r/` `cos-mult` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 86

Calls

4 calls:

10.0ms	(* r (sin b))
17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
29.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series405.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* r (sin b))
88.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
46.0ms	(* (sin a) (sin b))
229.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify48.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	369	835
1	1591	735
2	5002	730

prune359.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

9.0ms	(* r (sin b))
0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
11.0ms	(* (sin a) (sin b))
11.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series414.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* r (sin b))
90.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
52.0ms	(* (sin a) (sin b))
234.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify36.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (7.0ms)

Iter	Nodes	Cost
0	273	680
1	1161	578
2	5002	578

prune303.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log` `add-cbrt-cube`
18×	`add-sqr-sqrt`
16×	`times-frac`
14×	`add-cube-cbrt` `*-un-lft-identity`
12×	`cbrt-undiv` `div-exp`
10×	`associate-/r*`
8×	`pow1` `associate-*r/` `prod-exp` `cbrt-unprod`
6×	`associate-r` `associate-l`
5×	`sin-mult`
4×	`expm1-log1p-u` `cos-mult` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `flip3--` `frac-2neg` `prod-diff` `pow-prod-down` `clear-num` `-commutative` `frac-sub` `flip--` `associate-/l` `sub-div` `unswap-sqr`
1×	`associate-/r/`

Counts

4 → 118

Calls

4 calls:

12.0ms	(* (sin a) (sin b))
20.0ms	(/ (* r (sin b)) (/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b)))))
54.0ms	(* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
39.0ms	(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b))))

series540.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* (sin a) (sin b))
234.0ms	(/ (* r (sin b)) (/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b)))))
173.0ms	(* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
88.0ms	(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b))))

simplify104.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (87.0ms)

Iter	Nodes	Cost
0	597	2885
1	3547	2302
2	5002	2011

prune409.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

regimes175.0ms

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	23	11
1	25	11
2	25	11

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2921×	body	1280	valid
446.0ms	1807×	body	640	valid
133.0ms	800×	body	320	valid
120.0ms	2129×	body	80	valid
41.0ms	343×	body	160	valid