Details

sample90.0ms

Algorithm

intervals

Results

48.0ms	107×	body	1280	valid
15.0ms	56×	body	640	valid
5.0ms	68×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune12.0ms

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: 17.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin b)
0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
4.0b	(cos (+ a b))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
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

4 → 74

Calls

4 calls:

2.0ms	(sin b)
8.0ms	(* r (/ (sin b) (cos (+ a b))))
5.0ms	(/ (sin b) (cos (+ a b)))
4.0ms	(cos (+ a b))

series48.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(sin b)
27.0ms	(* r (/ (sin b) (cos (+ a b))))
13.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify51.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	5760	826

prune134.0ms

Filtered

67 candidates to 86 candidates (-28.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	75	11	86
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	11	87

Merged error: 0.2b

Counts

87 → 11

localize16.0ms

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

rewrite35.0ms

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:

6.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
12.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series120.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
59.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
32.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))

simplify65.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5415	1682

prune185.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	100	12	112
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	109	14	123

Merged error: 0.0b

Counts

123 → 14

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b)))))
4.4b	(log (pow (exp (sin a)) (sin b)))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
15×	`associate-r`
14×	`log-prod`
12×	`add-exp-log`
11×	`add-cbrt-cube`
7×	`associate--r+`
6×	`pow1` `unpow-prod-down`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`flip3--` `rem-log-exp` `associate-l` `associate-/r` `flip--` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `frac-2neg` `diff-log` `associate-r/` `pow-prod-down` `pow-exp` `clear-num` `log-pow` `-commutative`

Counts

4 → 100

Calls

4 calls:

8.0ms	(- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b)))))
4.0ms	(log (pow (exp (sin a)) (sin b)))

series172.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))
69.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
48.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b)))))
21.0ms	(log (pow (exp (sin a)) (sin b)))

simplify58.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5009	1773

prune160.0ms

Filtered

83 candidates to 112 candidates (-34.9%)

Pruning

15 alts after pruning (14 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	13	13
Picked	0	1	1
Done	0	0	0
Total	111	15	126

Merged error: 0.0b

Counts

126 → 15

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `associate-l` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-r` `div-inv`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `pow-prod-down` `associate-l/` `-commutative`

Counts

4 → 100

Calls

4 calls:

7.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
8.0ms	(* (/ (cos a) (sin b)) (cos b))
5.0ms	(/ (cos a) (sin b))
9.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))

series105.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(- (* (/ (cos a) (sin b)) (cos b)) (sin a))
18.0ms	(* (/ (cos a) (sin b)) (cos b))
11.0ms	(/ (cos a) (sin b))
51.0ms	(/ r (- (* (/ (cos a) (sin b)) (cos b)) (sin a)))

simplify38.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (28.0ms)

Iter	Nodes	Cost
0	5160	1446

prune108.0ms

Filtered

88 candidates to 112 candidates (-27.3%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	12	13
Picked	0	1	1
Done	0	1	1
Total	112	15	127

Merged error: 0.0b

Counts

127 → 15

regimes429.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	18
1	16	18

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	2997×	body	1280	valid
532.0ms	1845×	body	640	valid
154.0ms	720×	body	320	valid
146.0ms	2116×	body	80	valid
53.0ms	327×	body	160	valid

Details

sample90.0ms

simplify2.0ms

prune12.0ms

localize10.0ms

rewrite21.0ms

series48.0ms

simplify51.0ms

prune134.0ms

localize16.0ms

rewrite35.0ms

series120.0ms

simplify65.0ms

prune185.0ms

localize22.0ms

rewrite36.0ms

series172.0ms

simplify58.0ms

prune160.0ms

localize14.0ms

rewrite33.0ms

series105.0ms

simplify38.0ms

prune108.0ms

regimes429.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling