Details

sample75.0ms

Algorithm

intervals

Results

40.0ms	95×	body	1280	valid
12.0ms	53×	body	640	valid
4.0ms	26×	body	320	valid
4.0ms	69×	body	80	valid
2.0ms	13×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.8b	(cos (+ a b))

rewrite42.0ms

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:

9.0ms	(* r (sin b))
19.0ms	(/ (* r (sin b)) (cos (+ a b)))
12.0ms	(cos (+ a b))

series145.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(* r (sin b))
88.0ms	(/ (* r (sin b)) (cos (+ a b)))
22.0ms	(cos (+ a b))

simplify33.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 1 (6.0ms)

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

prune151.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `prod-exp` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv` `associate-/l*` `sub-div`

Counts

4 → 89

Calls

4 calls:

9.0ms	(* r (sin b))
11.0ms	(* (cos a) (cos b))
32.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
13.0ms	(* (sin a) (sin b))

series312.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* r (sin b))
36.0ms	(* (cos a) (cos b))
196.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
44.0ms	(* (sin a) (sin b))

simplify48.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	382	724
1	1662	634
2	5001	633

prune310.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

84×	`times-frac`
62×	`add-sqr-sqrt`
58×	`add-cube-cbrt` `*-un-lft-identity`
16×	`associate-/r*`
15×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-r` `associate-l` `div-inv` `associate-/l*`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`cos-mult` `sin-mult`
2×	`frac-2neg` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`flip3--` `div-sub` `associate-/r/` `frac-sub` `flip--` `sub-div`

Counts

4 → 148

Calls

4 calls:

12.0ms	(* (cos a) (cos b))
15.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
13.0ms	(* (sin a) (sin b))
30.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series388.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (cos a) (cos b))
206.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
41.0ms	(* (sin a) (sin b))
105.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify74.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	589	2127
1	2538	1985
2	5002	1965

prune543.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

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

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
12×	`add-exp-log` `times-frac`
10×	`add-cbrt-cube`
6×	`associate-/l*`
4×	`div-exp` `associate-/r*`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `prod-exp` `clear-num` `div-inv`
1×	`1-exp` `cbrt-unprod` `fma-udef`

Counts

3 → 63

Calls

3 calls:

0.0ms	(fma (/ (cos a) (sin b)) (cos b) (- (sin a)))
8.0ms	(/ r (* 1 (fma (/ (cos a) (sin b)) (cos b) (- (sin a)))))
10.0ms	(/ (cos a) (sin b))

series300.0ms

Counts

3 → 9

Calls

3 calls:

83.0ms	(fma (/ (cos a) (sin b)) (cos b) (- (sin a)))
179.0ms	(/ r (* 1 (fma (/ (cos a) (sin b)) (cos b) (- (sin a)))))
38.0ms	(/ (cos a) (sin b))

simplify130.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 3 (124.0ms)

Iter	Nodes	Cost
0	270	625
1	964	541
2	4405	539
3	5001	537

prune224.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0b

regimes134.0ms

Accuracy

0% (0.3b 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	15	10
1	15	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2912×	body	1280	valid
462.0ms	1858×	body	640	valid
132.0ms	767×	body	320	valid
110.0ms	2114×	body	80	valid
48.0ms	353×	body	160	valid