Details

sample306.0ms

Algorithm

intervals

Results

36.0ms	78×	body	1280	valid
17.0ms	67×	body	640	valid
5.0ms	27×	body	320	valid
4.0ms	75×	body	80	valid
1.0ms	9×	body	160	valid

simplify12.0ms

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

prune4.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.8b

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)))
3.5b	(cos (+ a b))

rewrite35.0ms

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:

8.0ms	(* r (/ (sin b) (cos (+ a b))))
3.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

series158.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(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

prune215.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

10 alts after pruning (10 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))
0.2b	(/ (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`
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:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
26.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series435.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
207.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
42.0ms	(* (sin a) (sin b))
108.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify56.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (45.0ms)

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

prune399.0ms

Filtered

122 candidates to 96 candidates (78.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
16×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1`
6×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `*-commutative` `div-inv`
1×	`frac-2neg` `associate-*r/` `clear-num` `fma-udef` `sin-mult`

Counts

4 → 94

Calls

4 calls:

0.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
9.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
4.0ms	(* (sin a) (sin b))
3.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

series443.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(fma (cos a) (cos b) (- (* (sin a) (sin b))))
210.0ms	(* r (/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b))))))
42.0ms	(* (sin a) (sin b))
109.0ms	(/ (sin b) (fma (cos a) (cos b) (- (* (sin a) (sin b)))))

simplify46.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	329	1173
1	1413	1043
2	5002	1043

prune358.0ms

Filtered

106 candidates to 82 candidates (77.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
0.3b	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
22×	`add-cbrt-cube`
21×	`associate-r`
20×	`times-frac`
14×	`pow1` `prod-exp`
9×	`associate-l`
8×	`associate-/r/` `cbrt-unprod`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`expm1-log1p-u` `associate-*r/` `cos-mult` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`flip3--` `un-div-inv` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 126

Calls

4 calls:

10.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
25.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
4.0ms	(* (sin a) (sin b))
26.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
204.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
44.0ms	(* (sin a) (sin b))
108.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

138 → 138

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	476	1553
1	2058	1336
2	5002	1307

prune351.0ms

Filtered

138 candidates to 91 candidates (65.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.0b

regimes146.0ms

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	21	25
1	21	25

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.2s	2869×	body	1280	valid
484.0ms	1882×	body	640	valid
131.0ms	719×	body	320	valid
119.0ms	2183×	body	80	valid
44.0ms	348×	body	160	valid