Details

sample338.0ms

Algorithm

intervals

Results

46.0ms	92×	body	1280	valid
18.0ms	60×	body	640	valid
5.0ms	25×	body	320	valid
5.0ms	69×	body	80	valid
2.0ms	10×	body	160	valid

simplify12.0ms

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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 19.1b

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
5.5b	(cos (+ a b))

rewrite31.0ms

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×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `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 → 73

Calls

3 calls:

9.0ms	(* r (/ (sin b) (cos (+ a b))))
3.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

series158.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify41.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	263	560
1	1093	504
2	5002	504

prune218.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

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

rewrite49.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
27.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series443.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms	(* (sin a) (sin b))
209.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
110.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify56.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	432	1384
1	1847	1255
2	5002	1249

prune410.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

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×	`cos-mult` `sin-mult`
4×	`expm1-log1p-u` `associate-/r/` `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 → 87

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
7.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series376.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (cos a) (cos b))
81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(* (sin a) (sin b))
210.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify49.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	397	865
1	1625	767
2	5001	757

prune327.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

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

rewrite32.0ms

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:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
10.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
8.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series463.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
43.0ms	(* (sin a) (sin b))
112.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
227.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify81.0ms

Algorithm

egg-herbie

Counts

157 → 157

Iterations

Useful iterations: 2 (60.0ms)

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

prune529.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes160.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	9
1	18	9
2	18	9

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.4s	2881×	body	1280	valid
565.0ms	1860×	body	640	valid
170.0ms	752×	body	320	valid
162.0ms	2163×	body	80	valid
56.0ms	346×	body	160	valid