Details

analyze3.1s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 24.621582%

sample88.0ms

Algorithm

intervals

Results

46.0ms	100×	body	1280	valid
15.0ms	54×	body	640	valid
6.0ms	28×	body	320	valid
4.0ms	61×	body	80	valid
2.0ms	13×	body	160	valid

simplify7.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	20	5
3	21	5
4	21	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: 17.6b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
3.5b	(cos (+ a b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-l` `associate-/r` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

3 → 67

Calls

3 calls:

7.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
4.0ms	(cos (+ a b))

series43.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
7.0ms	(cos (+ a b))

simplify37.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	252	536
1	1064	480
2	5001	477

prune116.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	66	10	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	10	77

Merged error: 0.2b

Counts

77 → 10

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

series109.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* (sin a) (sin b))
53.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	405	1307
1	1761	1182
2	5002	1173

prune175.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	99	13	112
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	109	13	122

Merged error: 0.0b

Counts

122 → 13

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:

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))))

series86.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (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	5002	663

prune119.0ms

Filtered

62 candidates to 88 candidates (-41.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	90	11	101

Merged error: 0.0b

Counts

101 → 11

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
3.6b	(log (exp (* (sin a) (sin b))))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

4.0ms	(* r (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))))

series79.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
10.0ms	(log (exp (* (sin a) (sin b))))

simplify40.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	301	698
1	1309	580
2	5001	574

prune77.0ms

Filtered

62 candidates to 86 candidates (-38.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	85	12	97

Merged error: 0.0b

Counts

97 → 12

regimes266.0ms

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	17	12
1	17	12

end0.0ms

analyze3.3s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 0.146413%

Guaranteed chance to sample good point: 24.621582%

sample2.5s

Algorithm

intervals

Results

1.4s	2936×	body	1280	valid
517.0ms	1874×	body	640	valid
156.0ms	761×	body	320	valid
148.0ms	2071×	body	80	valid
55.0ms	358×	body	160	valid
0.0ms	1×	body	640	invalid

Details

analyze3.1s

sample88.0ms

simplify7.0ms

prune3.0ms

localize10.0ms

rewrite16.0ms

series43.0ms

simplify37.0ms

prune116.0ms

localize16.0ms

rewrite31.0ms

series109.0ms

simplify54.0ms

prune175.0ms

localize16.0ms

rewrite23.0ms

series86.0ms

simplify46.0ms

prune119.0ms

localize19.0ms

rewrite20.0ms

series79.0ms

simplify40.0ms

prune77.0ms

regimes266.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze3.3s

sample2.5s

Profiling