Details

sample105.0ms

Algorithm

intervals

Results

57.0ms	95×	body	1280	valid
21.0ms	61×	body	640	valid
8.0ms	26×	body	320	valid
5.0ms	63×	body	80	valid
2.0ms	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

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.9b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.6b	(cos (+ a b))

rewrite16.0ms

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×	`times-frac` `associate-r` `associate-l` `associate-/r*` `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 → 47

Calls

3 calls:

3.0ms	(* r (sin b))
4.0ms	(/ (* r (sin b)) (cos (+ a b)))
7.0ms	(cos (+ a b))

series48.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
28.0ms	(/ (* r (sin b)) (cos (+ a b)))
13.0ms	(cos (+ a b))

simplify37.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256

prune350.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

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))))

rewrite23.0ms

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))))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (39.0ms)

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

prune765.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite46.0ms

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 b) (cos a)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
24.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series114.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
11.0ms	(* (sin a) (sin b))
55.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
32.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify53.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	401	1307
1	1733	1182
2	5001	1178

prune1.0s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (sin b) (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
0.3b	(* (/ (sin b) (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos b) (cos a)) (* (sin a) (sin b))))
0.3b	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
0.4b	(* (* (cos b) (cos a)) (* (cos b) (cos a)))

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

84×	`pow1`
42×	`cos-mult` `sin-mult`
35×	`add-exp-log` `pow-prod-down` `add-cbrt-cube`
34×	`associate-l`
32×	`associate-/r/`
27×	`add-sqr-sqrt`
25×	`times-frac` `associate-*r/`
23×	`associate-*l/`
22×	`add-cube-cbrt` `*-un-lft-identity`
21×	`frac-times`
18×	`prod-exp` `frac-sub` `cbrt-unprod`
10×	`sub-div`
8×	`pow-sqr` `pow-prod-up`
7×	`difference-of-squares`
5×	`associate-r`
4×	`pow-plus` `associate-/r*` `add-log-exp`
3×	`-commutative` `associate-/l`
2×	`cbrt-undiv` `pow2` `flip3--` `flip3-+` `swap-sqr` `div-exp` `frac-add` `flip--` `flip-+` `div-inv` `unswap-sqr`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `clear-num`

Counts

4 → 180

Calls

4 calls:

33.0ms	(/ (sin b) (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
118.0ms	(* (/ (sin b) (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos b) (cos a)) (* (sin a) (sin b))))
14.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
13.0ms	(* (* (cos b) (cos a)) (* (cos b) (cos a)))

series170.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(/ (sin b) (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin a) (sin b)) (* (sin a) (sin b)))))
81.0ms	(* (/ (sin b) (- (* (* (cos b) (cos a)) (* (cos b) (cos a))) (* (* (sin a) (sin b)) (* (sin a) (sin b))))) (+ (* (cos b) (cos a)) (* (sin a) (sin b))))
17.0ms	(* (* (sin a) (sin b)) (* (sin a) (sin b)))
14.0ms	(* (* (cos b) (cos a)) (* (cos b) (cos a)))

simplify142.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	940	3187
1	4864	2746
2	5001	2746

prune2.1s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

regimes444.0ms

Accuracy

0% (0.4b 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	26	25
1	26	25

end0.0ms

sample2.9s

Algorithm

intervals

Results

1.6s	2963×	body	1280	valid
644.0ms	1807×	body	640	valid
207.0ms	814×	body	320	valid
175.0ms	2080×	body	80	valid
61.0ms	337×	body	160	valid