Details

sample93.0ms

Algorithm

intervals

Results

45.0ms	98×	body	1280	valid
19.0ms	71×	body	640	valid
8.0ms	20×	body	320	valid
4.0ms	57×	body	80	valid
1.0ms	10×	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

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: 16.5b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
2.4b	(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))
23.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify30.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (26.0ms)

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

prune104.0ms

Filtered

40 candidates to 56 candidates (-40.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	45	11	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	46	11	57

Merged error: 0.2b

Counts

57 → 11

localize25.0ms

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

rewrite22.0ms

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	(- (* (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))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
49.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify44.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (36.0ms)

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

prune150.0ms

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	10	0	10
Picked	1	0	1
Done	0	0	0
Total	84	15	99

Merged error: 0.0b

Counts

99 → 15

localize15.0ms

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

rewrite30.0ms

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 a) (sin b)))
6.0ms	(* (sin a) (sin b))
7.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
8.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

series99.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
50.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
25.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify70.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	570	2145
1	2453	2009
2	5002	1988

prune185.0ms

Filtered

119 candidates to 147 candidates (-23.5%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	3	11	14
Picked	1	0	1
Done	0	0	0
Total	148	14	162

Merged error: 0.0b

Counts

162 → 14

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`associate-l`
19×	`times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult`
6×	`associate-r` `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-*l/` `clear-num`

Counts

4 → 100

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
11.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))

series117.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
43.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
50.0ms	(* (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (sin b))

simplify48.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	404	1239
1	1533	1118
2	5001	1103

prune93.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	2	11	13
Picked	0	1	1
Done	0	0	0
Total	113	13	126

Merged error: 0.0b

Counts

126 → 13

regimes279.0ms

Accuracy

0% (0.3b 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	15	10
1	15	10

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	2931×	body	1280	valid
516.0ms	1877×	body	640	valid
155.0ms	774×	body	320	valid
123.0ms	2068×	body	80	valid
51.0ms	351×	body	160	valid

Details

sample93.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite13.0ms

series36.0ms

simplify30.0ms

prune104.0ms

localize25.0ms

rewrite22.0ms

series80.0ms

simplify44.0ms

prune150.0ms

localize15.0ms

rewrite30.0ms

series99.0ms

simplify70.0ms

prune185.0ms

localize16.0ms

rewrite31.0ms

series117.0ms

simplify48.0ms

prune93.0ms

regimes279.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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