Details

sample95.0ms

Algorithm

intervals

Results

48.0ms	92×	body	1280	valid
14.0ms	51×	body	640	valid
6.0ms	31×	body	320	valid
4.0ms	65×	body	80	valid
3.0ms	17×	body	160	valid

simplify6.0ms

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

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 15.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite16.0ms

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:

6.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
4.0ms	(cos (+ a b))

series39.0ms

Counts

3 → 9

Calls

3 calls:

22.0ms	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify36.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

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

prune111.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 0.2b

Counts

77 → 8

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
7.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series91.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
48.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(* (sin a) (sin b))
26.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify55.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	428	1219
1	1858	1102
2	5001	1098

prune175.0ms

Filtered

87 candidates to 117 candidates (-34.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	105	12	117
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	113	12	125

Merged error: 0.0b

Counts

125 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite24.0ms

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×	`cos-mult` `sin-mult`
4×	`associate-/r/`
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` `diff-log` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 77

Calls

4 calls:

4.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (cos a) (cos b))
6.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* (cos a) (cos b))
9.0ms	(* (sin a) (sin b))
46.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify43.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	371	798
1	1534	703
2	5002	693

prune127.0ms

Filtered

63 candidates to 89 candidates (-41.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	2	9	11
Picked	1	0	1
Done	0	0	0
Total	90	11	101

Merged error: 0.0b

Counts

101 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
108×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
92×	`add-cube-cbrt`
47×	`associate-r`
38×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
9×	`pow1`
8×	`prod-exp`
7×	`cbrt-undiv`
6×	`associate-l` `associate-/l*` `unswap-sqr`
4×	`rec-exp` `1-exp` `cbrt-unprod` `associate-/l/` `add-log-exp`
3×	`sin-mult`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `cos-mult` `*-commutative`
1×	`flip3--` `pow-flip` `div-sub` `associate-*r/` `un-div-inv` `frac-sub` `flip--` `inv-pow` `sub-div`

Counts

4 → 200

Calls

4 calls:

15.0ms	(* r (/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
7.0ms	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series113.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* r (/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))))
9.0ms	(* (sin a) (sin b))
25.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
30.0ms	(/ 1 (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify96.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	720	3078
1	3585	2770
2	5002	2639

prune158.0ms

Filtered

134 candidates to 212 candidates (-58.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	209	3	212
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	212	11	223

Merged error: 0.0b

Counts

223 → 11

regimes263.0ms

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	17	9
1	17	9

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	2882×	body	1280	valid
521.0ms	1842×	body	640	valid
154.0ms	741×	body	320	valid
147.0ms	2159×	body	80	valid
67.0ms	378×	body	160	valid

Details

sample95.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite16.0ms

series39.0ms

simplify36.0ms

prune111.0ms

localize18.0ms

rewrite29.0ms

series91.0ms

simplify55.0ms

prune175.0ms

localize15.0ms

rewrite24.0ms

series79.0ms

simplify43.0ms

prune127.0ms

localize17.0ms

rewrite43.0ms

series113.0ms

simplify96.0ms

prune158.0ms

regimes263.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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