Details

sample85.0ms

Algorithm

intervals

Results

45.0ms	86×	body	1280	valid
13.0ms	50×	body	640	valid
5.0ms	25×	body	320	valid
4.0ms	77×	body	80	valid
3.0ms	18×	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	19	5
3	20	5
4	20	5

prune3.0ms

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: 14.2b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.1b	(cos (+ a b))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-exp-log` `add-cbrt-cube`
9×	`add-sqr-sqrt`
7×	`add-cube-cbrt` `*-un-lft-identity`
5×	`pow1`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod`
1×	`cos-sum` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `associate-/l` `unswap-sqr`

Counts

3 → 47

Calls

3 calls:

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

series36.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
24.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify29.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256

prune88.0ms

Filtered

40 candidates to 56 candidates (-40.0%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	47	9	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	9	57

Merged error: 0.2b

Counts

57 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite23.0ms

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:

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

series83.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
51.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify43.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5002	663

prune146.0ms

Filtered

64 candidates to 88 candidates (-37.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	73	15	88
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	82	15	97

Merged error: 0.0b

Counts

97 → 15

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite33.0ms

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 b) (cos a)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
13.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
50.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
28.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify52.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	401	1307
1	1733	1182
2	5002	1178

prune147.0ms

Filtered

84 candidates to 112 candidates (-33.3%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	4	10	14
Picked	0	1	1
Done	0	0	0
Total	113	14	127

Merged error: 0.0b

Counts

127 → 14

localize27.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* r (sin b)) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)))
0.3b	(pow (* (sin a) (sin b)) 3)
0.3b	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
0.4b	(pow (* (cos a) (cos b)) 3)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

49×	`pow1`
27×	`add-exp-log` `add-cbrt-cube`
19×	`pow-prod-down`
16×	`add-sqr-sqrt`
12×	`*-un-lft-identity`
11×	`prod-exp` `cbrt-unprod`
10×	`sqr-pow`
9×	`times-frac` `associate-/r*`
8×	`add-cube-cbrt` `difference-of-squares`
7×	`cos-mult`
6×	`cube-div` `pow-unpow`
4×	`pow-pow` `pow-exp` `associate-/r/` `pow-sqr` `pow-prod-up` `add-log-exp` `rem-cube-cbrt`
3×	`sin-mult`
2×	`difference-cubes` `cbrt-undiv` `cube-mult` `pow-to-exp` `unpow-prod-down` `pow-plus` `unpow3` `cube-prod` `div-exp` `distribute-lft-out--`
1×	`pow2` `frac-times` `flip3--` `frac-2neg` `associate-r/` `swap-sqr` `associate-r` `associate-l` `associate-l/` `clear-num` `-commutative` `frac-sub` `flip--` `div-inv` `associate-/l` `sub-div`

Counts

4 → 120

Calls

4 calls:

13.0ms	(/ (* r (sin b)) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)))
4.0ms	(pow (* (sin a) (sin b)) 3)
8.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
4.0ms	(pow (* (cos a) (cos b)) 3)

series135.0ms

Counts

4 → 12

Calls

4 calls:

90.0ms	(/ (* r (sin b)) (- (pow (* (cos a) (cos b)) 3) (pow (* (sin a) (sin b)) 3)))
16.0ms	(pow (* (sin a) (sin b)) 3)
14.0ms	(* (* (cos a) (cos b)) (* (cos a) (cos b)))
15.0ms	(pow (* (cos a) (cos b)) 3)

simplify84.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (72.0ms)

Iter	Nodes	Cost
0	571	1094
1	2865	978
2	5001	977

prune155.0ms

Filtered

78 candidates to 132 candidates (-69.2%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	131	1	132
Fresh	1	11	12
Picked	0	1	1
Done	0	1	1
Total	132	14	146

Merged error: 0.0b

Counts

146 → 14

regimes295.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	2915×	body	1280	valid
505.0ms	1810×	body	640	valid
142.0ms	737×	body	320	valid
129.0ms	2176×	body	80	valid
50.0ms	362×	body	160	valid

Details

sample85.0ms

simplify6.0ms

prune3.0ms

localize10.0ms

rewrite13.0ms

series36.0ms

simplify29.0ms

prune88.0ms

localize15.0ms

rewrite23.0ms

series83.0ms

simplify43.0ms

prune146.0ms

localize15.0ms

rewrite33.0ms

series103.0ms

simplify52.0ms

prune147.0ms

localize27.0ms

rewrite34.0ms

series135.0ms

simplify84.0ms

prune155.0ms

regimes295.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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