Details

sample295.0ms

Algorithm

intervals

Results

241.0ms	95×	body	1280	valid
22.0ms	61×	body	640	valid
9.0ms	26×	body	320	valid
5.0ms	63×	body	80	valid
2.0ms	11×	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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

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)))
4.6b	(cos (+ a b))

rewrite23.0ms

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×	`associate-l` `associate-/r` `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 → 67

Calls

3 calls:

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

series62.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(* r (/ (sin b) (cos (+ a b))))
14.0ms	(/ (sin b) (cos (+ a b)))
13.0ms	(cos (+ a b))

simplify38.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	252	536
1	1064	480
2	5001	477

prune513.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

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`
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` `diff-log` `associate-*r/` `clear-num`

Counts

4 → 100

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
25.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series116.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
58.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
32.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	405	1307
1	1761	1182
2	5001	1173

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(- (* (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))))

rewrite24.0ms

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×	`associate-/r/` `cos-mult`
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` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 76

Calls

4 calls:

3.0ms	(* r (sin b))
5.0ms	(- (* (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))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* r (sin b))
17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
57.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5001	663

prune785.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (* 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-exp-log`
20×	`add-cbrt-cube`
12×	`add-sqr-sqrt`
9×	`prod-exp`
8×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`div-exp` `associate-r` `associate-l` `cbrt-unprod` `add-log-exp`
5×	`sin-mult`
4×	`cbrt-undiv` `associate-*r/` `associate-/r/` `cos-mult`
2×	`flip3--` `1-exp` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`sub-neg` `frac-2neg` `times-frac` `diff-log` `clear-num` `associate-/r` `div-inv` `associate-/l`

Counts

4 → 78

Calls

4 calls:

3.0ms	(* r (sin b))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
12.0ms	(/ (* r (sin b)) (* 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series89.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* r (sin b))
17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
57.0ms	(/ (* r (sin b)) (* 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify57.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	422	814
1	2021	673
2	5001	673

prune644.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.0b

regimes523.0ms

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	20	11
1	22	11
2	22	11

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.6s	2963×	body	1280	valid
652.0ms	1807×	body	640	valid
214.0ms	814×	body	320	valid
171.0ms	2080×	body	80	valid
66.0ms	337×	body	160	valid