Details

sample990.0ms

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0%

Results

40.0ms	80×	body	1280	valid
17.0ms	60×	body	640	valid
5.0ms	27×	body	320	valid
5.0ms	75×	body	80	valid
2.0ms	14×	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: 13.8b

Counts

2 → 1

localize15.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.4b	(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))

series37.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify31.0ms

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

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	7	57

Merged error: 0.2b

Counts

57 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
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 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:

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

series87.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* r (sin b))
17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

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

prune140.0ms

Filtered

64 candidates to 88 candidates (-37.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	4	2	6
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Merged error: 0.0b

Counts

95 → 13

localize163.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.2b	(* (sin a) (sin b))
0.3b	(pow (* (sin a) (sin b)) 3)
28.0b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite24.0ms

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:

10.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
5.0ms	(* (sin a) (sin b))
4.0ms	(pow (* (sin a) (sin b)) 3)
3.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series93.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
9.0ms	(* (sin a) (sin b))
17.0ms	(pow (* (sin a) (sin b)) 3)
10.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify52.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	386	788
1	1812	681
2	5002	671

prune163.0ms

Filtered

67 candidates to 96 candidates (-43.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	4	96
Fresh	5	7	12
Picked	1	0	1
Done	0	0	0
Total	98	11	109

Merged error: 0b

Counts

109 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (pow (sin a) 3) (pow (sin b) 3)))))
0.3b	(pow (sin b) 3)
0.4b	(pow (sin a) 3)
28.0b	(cbrt (* (pow (sin a) 3) (pow (sin b) 3)))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1` `unpow-prod-down` `pow-unpow` `cube-prod`
4×	`add-log-exp`
3×	`times-frac` `associate-/r*`
2×	`cbrt-undiv` `cube-mult` `pow-to-exp` `pow-pow` `unpow3` `div-exp` `pow-exp` `associate-/r/` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-prod` `flip3--` `frac-2neg` `pow1/3` `pow-prod-down` `prod-exp` `clear-num` `flip--` `rem-cbrt-cube` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 79

Calls

4 calls:

9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (pow (sin a) 3) (pow (sin b) 3)))))
3.0ms	(pow (sin b) 3)
3.0ms	(pow (sin a) 3)
5.0ms	(cbrt (* (pow (sin a) 3) (pow (sin b) 3)))

series75.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (* (pow (sin a) 3) (pow (sin b) 3)))))
6.0ms	(pow (sin b) 3)
5.0ms	(pow (sin a) 3)
10.0ms	(cbrt (* (pow (sin a) 3) (pow (sin b) 3)))

simplify59.0ms

Algorithm

egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	372	707
1	1919	614
2	5001	606

prune121.0ms

Filtered

56 candidates to 91 candidates (-62.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	91	0	91
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	91	11	102

Merged error: 0b

Counts

102 → 11

regimes256.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	13
1	19	13

end0.0ms

sample3.5s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 0%

Results

1.4s	2909×	body	1280	valid
529.0ms	1810×	body	640	valid
167.0ms	782×	body	320	valid
146.0ms	2145×	body	80	valid
53.0ms	354×	body	160	valid

Details

sample990.0ms

simplify6.0ms

prune4.0ms

localize15.0ms

rewrite14.0ms

series37.0ms

simplify31.0ms

prune82.0ms

localize16.0ms

rewrite23.0ms

series87.0ms

simplify46.0ms

prune140.0ms

localize163.0ms

rewrite24.0ms

series93.0ms

simplify52.0ms

prune163.0ms

localize20.0ms

rewrite21.0ms

series75.0ms

simplify59.0ms

prune121.0ms

regimes256.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample3.5s

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