Details

sample77.0ms

Algorithm

intervals

Results

37.0ms	84×	body	1280	valid
17.0ms	56×	body	640	valid
5.0ms	29×	body	320	valid
4.0ms	76×	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

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.7b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
5.5b	(cos (+ a b))

rewrite41.0ms

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×	`expm1-log1p-u` `times-frac` `associate-r` `associate-l` `associate-/r*` `log1p-expm1-u` `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 → 53

Calls

3 calls:

14.0ms	(* r (sin b))
13.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series144.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* r (sin b))
87.0ms	(/ (* r (sin b)) (cos (+ a b)))
22.0ms	(cos (+ a b))

simplify32.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	207	327
1	884	279
2	5001	279

prune208.0ms

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	(* r (sin b))
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))

rewrite75.0ms

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×	`expm1-log1p-u` `associate-/r/` `cos-mult` `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 → 86

Calls

4 calls:

9.0ms	(* r (sin b))
18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
32.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms	(* (sin a) (sin b))

series355.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* r (sin b))
76.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
200.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
44.0ms	(* (sin a) (sin b))

simplify52.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	369	835
1	1591	735
2	5002	730

prune547.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize21.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `prod-exp` `associate-/r*` `cbrt-unprod`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `unswap-sqr`
1×	`frac-2neg` `clear-num` `fma-udef` `div-inv` `sin-mult` `associate-/l*`

Counts

4 → 74

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
9.0ms	(* r (sin b))
12.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
13.0ms	(* (sin a) (sin b))

series360.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
34.0ms	(* r (sin b))
204.0ms	(/ (* r (sin b)) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))
46.0ms	(* (sin a) (sin b))

simplify38.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	273	680
1	1161	578
2	5001	578

prune448.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite140.0ms

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:

19.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
76.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
30.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
13.0ms	(* (sin a) (sin b))

series426.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
200.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
105.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
44.0ms	(* (sin a) (sin b))

simplify59.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	427	1384
1	1820	1255
2	5002	1254

prune709.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.0b

regimes230.0ms

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	15	10
1	15	10

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2915×	body	1280	valid
500.0ms	1880×	body	640	valid
145.0ms	755×	body	320	valid
124.0ms	2121×	body	80	valid
44.0ms	330×	body	160	valid