Details

sample390.0ms

Algorithm

intervals

Results

43.0ms	98×	body	1280	valid
25.0ms	69×	body	80	valid
13.0ms	54×	body	640	valid
4.0ms	23×	body	320	valid
1.0ms	12×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	20	5
3	21	5
4	21	5

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 16.8b

localize12.0ms

Local error

Found 3 expressions with local error:

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

rewrite41.0ms

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:

17.0ms	(* r (/ (sin b) (cos (+ a b))))
9.0ms	(/ (sin b) (cos (+ a b)))
11.0ms	(cos (+ a b))

series177.0ms

Counts

3 → 9

Calls

3 calls:

103.0ms	(* r (/ (sin b) (cos (+ a b))))
41.0ms	(/ (sin b) (cos (+ a b)))
32.0ms	(cos (+ a b))

simplify39.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (8.0ms)

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

prune216.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.2b

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite128.0ms

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:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
69.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
13.0ms	(* (sin a) (sin b))
25.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series484.0ms

Counts

4 → 12

Calls

4 calls:

86.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
229.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
49.0ms	(* (sin a) (sin b))
121.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify55.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

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

prune416.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize18.0ms

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

rewrite68.0ms

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))
19.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* (sin a) (sin b))
27.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series420.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(* r (sin b))
85.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
63.0ms	(* (sin a) (sin b))
229.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify49.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (41.0ms)

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

prune328.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.0b

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite127.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

11.0ms	(* (sin a) (sin b))
20.0ms	(/ (* r (sin b)) (/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b)))))
53.0ms	(* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
39.0ms	(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b))))

series549.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(* (sin a) (sin b))
232.0ms	(/ (* r (sin b)) (/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b)))))
182.0ms	(* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
88.0ms	(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b))))

simplify108.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (89.0ms)

Iter	Nodes	Cost
0	597	2886
1	3547	2303
2	5002	2012

prune406.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 0.0b

regimes186.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	10
1	20	10
2	20	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2921×	body	1280	valid
438.0ms	1807×	body	640	valid
133.0ms	800×	body	320	valid
123.0ms	2129×	body	80	valid
41.0ms	343×	body	160	valid