Details

sample320.0ms

Algorithm

intervals

Results

38.0ms	90×	body	1280	valid
18.0ms	61×	body	640	valid
4.0ms	75×	body	80	valid
3.0ms	16×	body	320	valid
2.0ms	14×	body	160	valid

simplify11.0ms

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: 13.4b

localize13.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.8b	(cos (+ a b))

rewrite22.0ms

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:

7.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

series171.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* r (/ (sin b) (cos (+ a b))))
39.0ms	(/ (sin b) (cos (+ a b)))
36.0ms	(cos (+ a b))

simplify40.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

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

prune226.0ms

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

rewrite36.0ms

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)))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series457.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
218.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
44.0ms	(* (sin a) (sin b))
112.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify57.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	432	1384
1	1847	1255
2	5001	1249

prune450.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
14.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))

series578.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))
262.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b)))))))
48.0ms	(* (sin a) (sin b))
152.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (* (sin a) (sin b))))))

simplify61.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	434	1601
1	1871	1338
2	5002	1334

prune488.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

localize23.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 107

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (log1p (expm1 (expm1 (log1p (* (sin a) (sin b)))))))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (expm1 (log1p (* (sin a) (sin b)))))))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (expm1 (log1p (* (sin a) (sin b))))))))

series695.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(- (* (cos a) (cos b)) (log1p (expm1 (expm1 (log1p (* (sin a) (sin b)))))))
308.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (expm1 (log1p (* (sin a) (sin b)))))))))
50.0ms	(* (sin a) (sin b))
182.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log1p (expm1 (expm1 (log1p (* (sin a) (sin b))))))))

simplify62.0ms

Algorithm

egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	436	1825
1	1875	1459
2	5002	1455

prune478.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

regimes183.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	20	10
2	20	10

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2887×	body	1280	valid
473.0ms	1848×	body	640	valid
144.0ms	786×	body	320	valid
129.0ms	2130×	body	80	valid
46.0ms	351×	body	160	valid