Details

sample3.4s

Algorithm

intervals

sampling

Space saved by range analysis: 0%

Space saved by search: 0%

Guaranteed chance to sample good point: 24.804688%

Results

46.0ms	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

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

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: 14.4b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.3b	(/ (sin b) (cos (+ a b)))
3.0b	(cos (+ a b))

rewrite23.0ms

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:

8.0ms	(* r (/ (sin b) (cos (+ a b))))
9.0ms	(/ (sin b) (cos (+ a b)))
4.0ms	(cos (+ a b))

series42.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify36.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

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

prune125.0ms

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: 0.1b

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))))

rewrite34.0ms

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)))
5.0ms	(* (sin a) (sin b))
13.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series110.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (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)))))
29.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify53.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (42.0ms)

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

prune169.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	102	10	112
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	112	10	122

Merged error: 0.0b

Counts

122 → 10

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

series87.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
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))))

simplify44.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (36.0ms)

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

prune134.0ms

Filtered

64 candidates to 89 candidates (-39.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	84	5	89
Fresh	3	6	9
Picked	1	0	1
Done	0	0	0
Total	88	11	99

Merged error: 0.0b

Counts

99 → 11

localize21.0ms

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))

rewrite25.0ms

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)
3.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series89.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin a) (sin b))
54.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
16.0ms	(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

prune116.0ms

Filtered

66 candidates to 96 candidates (-45.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	96	11	107

Merged error: 0.0b

Counts

107 → 11

regimes280.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	12
1	18	12

end0.0ms

sample5.8s

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
557.0ms	1836×	body	640	valid
156.0ms	736×	body	320	valid
153.0ms	2152×	body	80	valid
55.0ms	333×	body	160	valid

Details

sample3.4s

simplify7.0ms

prune4.0ms

localize10.0ms

rewrite23.0ms

series42.0ms

simplify36.0ms

prune125.0ms

localize16.0ms

rewrite34.0ms

series110.0ms

simplify53.0ms

prune169.0ms

localize16.0ms

rewrite24.0ms

series87.0ms

simplify44.0ms

prune134.0ms

localize21.0ms

rewrite25.0ms

series89.0ms

simplify52.0ms

prune116.0ms

regimes280.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample5.8s

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