Details

sample312.0ms

Algorithm

intervals

Results

36.0ms	89×	body	1280	valid
16.0ms	57×	body	640	valid
5.0ms	84×	body	80	valid
3.0ms	18×	body	320	valid
1.0ms	8×	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: 15.0b

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)))
3.2b	(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))))
5.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

series172.0ms

Counts

3 → 9

Calls

3 calls:

99.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
35.0ms	(cos (+ a b))

simplify40.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

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

prune224.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite35.0ms

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:

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

series464.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
113.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
45.0ms	(* (sin a) (sin b))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (47.0ms)

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

prune449.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

6.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
1.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
4.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))

series483.0ms

Counts

4 → 12

Calls

4 calls:

231.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
87.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
119.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
46.0ms	(* (sin a) (sin b))

simplify49.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	329	1173
1	1413	1043
2	5002	1043

prune392.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

10.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (log1p (expm1 (* (sin a) (sin b))))))))
1.0ms	(fma (cos a) (cos b) (- (log1p (expm1 (* (sin a) (sin b))))))
4.0ms	(/ (sin b) (fma (cos a) (cos b) (- (log1p (expm1 (* (sin a) (sin b)))))))
5.0ms	(* (sin a) (sin b))

series584.0ms

Counts

4 → 12

Calls

4 calls:

266.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (log1p (expm1 (* (sin a) (sin b))))))))
119.0ms	(fma (cos a) (cos b) (- (log1p (expm1 (* (sin a) (sin b))))))
154.0ms	(/ (sin b) (fma (cos a) (cos b) (- (log1p (expm1 (* (sin a) (sin b)))))))
44.0ms	(* (sin a) (sin b))

simplify46.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	328	1353
1	1406	1165
2	5001	1160

prune401.0ms

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.0b

regimes194.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	12
1	16	12

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2870×	body	1280	valid
476.0ms	1886×	body	640	valid
135.0ms	749×	body	320	valid
118.0ms	2149×	body	80	valid
44.0ms	349×	body	160	valid