Details

sample3.3s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 24.804688%

Results

48.0ms	94×	body	1280	valid
15.0ms	51×	body	640	valid
5.0ms	25×	body	320	valid
5.0ms	69×	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: 14.4b

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)))
3.0b	(cos (+ a b))

rewrite14.0ms

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))

series38.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
25.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify34.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (26.0ms)

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

prune86.0ms

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: 0.1b

Counts

57 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
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))))

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

series88.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
54.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify46.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

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

prune140.0ms

Filtered

64 candidates to 89 candidates (-39.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	76	13	89
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	85	13	98

Merged error: 0.0b

Counts

98 → 13

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

rewrite32.0ms

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)))
6.0ms	(* (sin a) (sin b))
11.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series108.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
11.0ms	(* (sin a) (sin b))
51.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
29.0ms	(/ (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

prune138.0ms

Filtered

84 candidates to 112 candidates (-33.3%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	112	13	125

Merged error: 0.0b

Counts

125 → 13

localize19.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.3b	(pow (* (sin a) (sin b)) 3)
29.6b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

14×	`add-exp-log` `add-cbrt-cube`
12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1`
8×	`cbrt-prod`
4×	`sin-mult` `add-log-exp`
3×	`cube-div` `pow-unpow` `times-frac` `associate-r` `associate-l` `prod-exp` `associate-/r*` `associate-/r/` `cbrt-unprod`
2×	`cbrt-undiv` `cube-mult` `unpow-prod-down` `cbrt-div` `pow-pow` `unpow3` `cube-prod` `div-exp` `pow-prod-down` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `flip3--` `frac-2neg` `pow1/3` `clear-num` `cos-mult` `-commutative` `frac-sub` `flip--` `rem-cbrt-cube` `div-inv` `associate-/l` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

5.0ms	(* (sin a) (sin b))
10.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
5.0ms	(pow (* (sin a) (sin b)) 3)
4.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series90.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin a) (sin b))
53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
17.0ms	(pow (* (sin a) (sin b)) 3)
10.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify50.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	386	791
1	1812	683
2	5001	673

prune104.0ms

Filtered

66 candidates to 96 candidates (-45.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	96	13	109

Merged error: 0.0b

Counts

109 → 13

regimes269.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	10
1	15	10

end0.0ms

sample5.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 24.804688%

Results

1.4s	2946×	body	1280	valid
550.0ms	1836×	body	640	valid
169.0ms	736×	body	320	valid
142.0ms	2152×	body	80	valid
54.0ms	333×	body	160	valid

Details

sample3.3s

simplify6.0ms

prune3.0ms

localize10.0ms

rewrite14.0ms

series38.0ms

simplify34.0ms

prune86.0ms

localize16.0ms

rewrite24.0ms

series88.0ms

simplify46.0ms

prune140.0ms

localize15.0ms

rewrite32.0ms

series108.0ms

simplify52.0ms

prune138.0ms

localize19.0ms

rewrite26.0ms

series90.0ms

simplify50.0ms

prune104.0ms

regimes269.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample5.7s

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