Details

sample313.0ms

Algorithm

intervals

Results

37.0ms	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

simplify11.0ms

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))

rewrite34.0ms

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×	`associate-l` `associate-/r` `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 → 67

Calls

3 calls:

9.0ms	(* r (/ (sin b) (cos (+ a b))))
3.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

series160.0ms

Counts

3 → 9

Calls

3 calls:

96.0ms	(* r (/ (sin b) (cos (+ a b))))
38.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify40.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	252	536
1	1064	480
2	5001	477

prune205.0ms

Filtered

76 candidates to 57 candidates (75.0%)

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))))

rewrite45.0ms

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 a) (cos b)) (* (sin a) (sin b)))
24.0ms	(* 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))))

series449.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
210.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
44.0ms	(* (sin a) (sin b))
114.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify57.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	405	1307
1	1761	1182
2	5001	1173

prune370.0ms

Filtered

112 candidates to 86 candidates (76.8%)

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)))))

rewrite72.0ms

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×	`associate-*r/` `cos-mult` `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 → 118

Calls

4 calls:

10.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
28.0ms	(* 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)))))

series476.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
217.0ms	(* r (* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))))
48.0ms	(* (sin a) (sin b))
113.0ms	(* (sin b) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify58.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	458	1487
1	2012	1272
2	5001	1240

prune374.0ms

Filtered

130 candidates to 83 candidates (63.8%)

Pruning

11 alts after pruning (10 fresh and 1 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))))
0.1b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

10.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
3.0ms	(* r (sin b))
4.0ms	(* (sin a) (sin b))
24.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series402.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
42.0ms	(* r (sin b))
43.0ms	(* (sin a) (sin b))
220.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify63.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	474	1265
1	2419	1084
2	5001	1056

prune315.0ms

Filtered

126 candidates to 77 candidates (61.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 0.0b

regimes170.0ms

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	20	11
1	20	11

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2869×	body	1280	valid
490.0ms	1882×	body	640	valid
132.0ms	719×	body	320	valid
124.0ms	2183×	body	80	valid
50.0ms	348×	body	160	valid