Details

sample4.0s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 23.254395%

Results

47.0ms	102×	body	1280	valid
18.0ms	61×	body	640	valid
4.0ms	62×	body	80	valid
4.0ms	19×	body	320	valid
2.0ms	12×	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: 14.9b

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)))
3.8b	(cos (+ a b))

rewrite18.0ms

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)))
8.0ms	(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

prune92.0ms

Filtered

40 candidates to 56 candidates (-40.0%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	46	10	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	10	57

Merged error: 0.1b

Counts

57 → 10

localize16.0ms

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))))

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))))

simplify47.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (39.0ms)

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

prune136.0ms

Filtered

64 candidates to 88 candidates (-37.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	10	88
Fresh	7	2	9
Picked	1	0	1
Done	0	0	0
Total	86	12	98

Merged error: 0.0b

Counts

98 → 12

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (cos a)) (* (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))))
0.2b	(* (sin a) (sin b))

rewrite31.0ms

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)))
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))))
5.0ms	(* (sin a) (sin b))

series103.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
51.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
27.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))

simplify57.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	401	1307
1	1734	1182
2	5002	1178

prune137.0ms

Filtered

84 candidates to 112 candidates (-33.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	112	12	124

Merged error: 0.0b

Counts

124 → 12

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))

rewrite29.0ms

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)))
4.0ms	(* (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))

series101.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
51.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))
26.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))

simplify74.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (54.0ms)

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

prune128.0ms

Filtered

119 candidates to 147 candidates (-23.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	144	3	147
Fresh	3	7	10
Picked	0	1	1
Done	1	0	1
Total	148	11	159

Merged error: 0b

Counts

159 → 11

regimes246.0ms

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

sample6.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 23.254395%

Results

1.4s	2920×	body	1280	valid
523.0ms	1799×	body	640	valid
158.0ms	777×	body	320	valid
151.0ms	2156×	body	80	valid
51.0ms	348×	body	160	valid
1.0ms	3×	body	1280	invalid
0.0ms	1×	body	160	invalid

Details

sample4.0s

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite18.0ms

series37.0ms

simplify31.0ms

prune92.0ms

localize16.0ms

rewrite23.0ms

series83.0ms

simplify47.0ms

prune136.0ms

localize18.0ms

rewrite31.0ms

series103.0ms

simplify57.0ms

prune137.0ms

localize15.0ms

rewrite29.0ms

series101.0ms

simplify74.0ms

prune128.0ms

regimes246.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample6.4s

Profiling