Details

sample92.0ms

Algorithm

intervals

Results

47.0ms	93×	body	1280	valid
18.0ms	64×	body	640	valid
5.0ms	25×	body	320	valid
4.0ms	63×	body	80	valid
2.0ms	11×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 15.8b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(/ (sin b) (cos (+ a b)))
0.2b	(* r (/ (sin b) (cos (+ a b))))
5.5b	(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:

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

series44.0ms

Counts

3 → 9

Calls

3 calls:

14.0ms	(/ (sin b) (cos (+ a b)))
24.0ms	(* r (/ (sin b) (cos (+ a b))))
6.0ms	(cos (+ a b))

simplify57.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5537	783

prune102.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

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: 0.1b

Counts

77 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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)))
4.0ms	(* (sin a) (sin b))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
50.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
27.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify74.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	5415	1682

prune157.0ms

Filtered

89 candidates to 112 candidates (-25.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	102	10	112
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	109	11	120

Merged error: 0b

Counts

120 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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×	`associate-/r/` `cos-mult`
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 → 76

Calls

4 calls:

4.0ms	(* (sin b) r)
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
6.0ms	(* (sin a) (sin b))
8.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (sin b) r)
17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
52.0ms	(/ (* (sin b) r) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify50.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5586	983

prune116.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	87	1	88
Fresh	1	9	10
Picked	0	1	1
Done	0	0	0
Total	88	11	99

Merged error: 0b

Counts

99 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
4.0ms	(* (sin b) (sin a))
7.0ms	(/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) r)
7.0ms	(/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) r))

series113.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin b) (sin a)))
9.0ms	(* (sin b) (sin a))
27.0ms	(/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) r)
61.0ms	(/ (sin b) (/ (- (* (cos a) (cos b)) (* (sin b) (sin a))) r))

simplify51.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	5029	3027

prune118.0ms

Filtered

119 candidates to 147 candidates (-23.5%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	146	1	147
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	147	11	158

Merged error: 0b

Counts

158 → 11

regimes240.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	16
1	15	16

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.4s	2974×	body	1280	valid
521.0ms	1825×	body	640	valid
148.0ms	742×	body	320	valid
142.0ms	2114×	body	80	valid
51.0ms	348×	body	160	valid

Details

sample92.0ms

simplify3.0ms

prune7.0ms

localize10.0ms

rewrite16.0ms

series44.0ms

simplify57.0ms

prune102.0ms

localize16.0ms

rewrite30.0ms

series103.0ms

simplify74.0ms

prune157.0ms

localize16.0ms

rewrite25.0ms

series85.0ms

simplify50.0ms

prune116.0ms

localize15.0ms

rewrite28.0ms

series113.0ms

simplify51.0ms

prune118.0ms

regimes240.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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