Details

sample76.0ms

Algorithm

intervals

Results

39.0ms	96×	body	1280	valid
15.0ms	61×	body	640	valid
5.0ms	67×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	11×	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)))
5.4b	(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×	`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))
17.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series144.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* r (sin b))
88.0ms	(/ (* r (sin b)) (cos (+ a b)))
22.0ms	(cos (+ a b))

simplify33.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (6.0ms)

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

prune153.0ms

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

rewrite72.0ms

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:

19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* r (sin b))
12.0ms	(* (sin a) (sin b))
30.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series338.0ms

Counts

4 → 12

Calls

4 calls:

71.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
36.0ms	(* r (sin b))
40.0ms	(* (sin a) (sin b))
191.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify53.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (42.0ms)

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

prune312.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin 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))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
58×	`add-sqr-sqrt`
56×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `div-inv` `associate-/l*` `add-log-exp`
5×	`sin-mult`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `cos-mult` `log1p-expm1-u` `associate-/l/`
3×	`associate-r` `associate-l`
2×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `fma-neg` `diff-log` `div-sub` `prod-diff` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 145

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
12.0ms	(* (sin a) (sin b))
30.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series420.0ms

Counts

4 → 12

Calls

4 calls:

75.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
200.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
39.0ms	(* (sin a) (sin b))
106.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify73.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	595	2224
1	2539	2085
2	5003	2062

prune542.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))
0.2b	(/ r (/ (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))) (sin b)))
0.2b	(* (sin a) (sin b))
0.2b	(/ (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))) (sin b))

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
59×	`add-sqr-sqrt`
57×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `div-inv` `associate-/l*` `add-log-exp`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`associate-r` `associate-l` `prod-diff`
2×	`flip3--` `frac-2neg` `clear-num` `flip--` `associate-/l/`
1×	`sub-neg` `fma-neg` `diff-log` `div-sub` `pow-prod-down` `prod-exp` `associate-/r/` `*-commutative` `cbrt-unprod` `sin-mult` `expm1-udef` `associate--r-` `unswap-sqr`

Counts

4 → 144

Calls

4 calls:

12.0ms	(- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))
18.0ms	(/ r (/ (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))) (sin b)))
12.0ms	(* (sin a) (sin b))
23.0ms	(/ (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))) (sin b))

series535.0ms

Counts

4 → 12

Calls

4 calls:

106.0ms	(- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b)))))
247.0ms	(/ r (/ (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))) (sin b)))
40.0ms	(* (sin a) (sin b))
142.0ms	(/ (- (* (cos a) (cos b)) (expm1 (log1p (* (sin a) (sin b))))) (sin b))

simplify81.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	602	2634
1	2627	2331
2	5001	2322

prune541.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes163.0ms

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	16	12
1	16	12

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	3021×	body	1280	valid
434.0ms	1781×	body	640	valid
142.0ms	813×	body	320	valid
114.0ms	2054×	body	80	valid
46.0ms	332×	body	160	valid