Details

sample3.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

48.0ms	99×	body	1280	valid
17.0ms	61×	body	640	valid
6.0ms	30×	body	320	valid
4.0ms	58×	body	80	valid
1.0ms	8×	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: 15.2b

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)))
4.1b	(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))

series41.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
27.0ms	(/ (* r (sin b)) (cos (+ a b)))
7.0ms	(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

prune82.0ms

Filtered

40 candidates to 56 candidates (-40.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Merged error: 0.2b

Counts

57 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(- (* (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))))

rewrite27.0ms

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	(* r (sin b))
7.0ms	(- (* (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))))

series80.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* r (sin b))
15.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
47.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5001	663

prune138.0ms

Filtered

64 candidates to 88 candidates (-37.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	7	0	7
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Merged error: 0.0b

Counts

96 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
0.2b	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
0.2b	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
0.2b	(* (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)))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
12.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))

series101.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
29.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
47.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
9.0ms	(* (sin a) (sin b))

simplify53.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	401	1307
1	1734	1182
2	5001	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	0	11	11
Picked	0	1	1
Done	0	0	0
Total	111	13	124

Merged error: 0.0b

Counts

124 → 13

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
3.1b	(log (exp (* (sin a) (sin b))))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 71

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
2.0ms	(log (exp (* (sin a) (sin b))))

series85.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
11.0ms	(* (sin a) (sin b))
48.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
9.0ms	(log (exp (* (sin a) (sin b))))

simplify42.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	322	847
1	1257	710
2	5002	703

prune73.0ms

Filtered

59 candidates to 83 candidates (-40.7%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	81	2	83
Fresh	1	10	11
Picked	0	1	1
Done	0	1	1
Total	82	14	96

Merged error: 0.0b

Counts

96 → 14

regimes291.0ms

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	10
1	15	10

end0.0ms

sample5.7s

Algorithm

intervals

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 0%

Results

1.4s	3001×	body	1280	valid
542.0ms	1896×	body	640	valid
145.0ms	718×	body	320	valid
143.0ms	2059×	body	80	valid
49.0ms	326×	body	160	valid

Details

sample3.4s

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite14.0ms

series41.0ms

simplify30.0ms

prune82.0ms

localize16.0ms

rewrite27.0ms

series80.0ms

simplify45.0ms

prune138.0ms

localize15.0ms

rewrite32.0ms

series101.0ms

simplify53.0ms

prune138.0ms

localize22.0ms

rewrite22.0ms

series85.0ms

simplify42.0ms

prune73.0ms

regimes291.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.7s

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