Details

sample96.0ms

Algorithm

intervals

Results

55.0ms	107×	body	1280	valid
15.0ms	56×	body	640	valid
5.0ms	68×	body	80	valid
4.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid

simplify9.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	8	9
1	12	9
2	16	9
3	19	9
4	20	9
done	20	9

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: 17.2b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin b)
0.1b	(* r (sin b))
0.3b	(/ (* r (sin b)) (cos (+ a b)))
4.0b	(cos (+ a b))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-exp-log` `add-cbrt-cube`
10×	`add-sqr-sqrt`
8×	`add-cube-cbrt` `*-un-lft-identity`
6×	`pow1`
4×	`add-log-exp`
3×	`times-frac` `associate-r` `associate-l` `associate-/r*`
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

4 → 54

Calls

4 calls:

2.0ms	(sin b)
5.0ms	(* r (sin b))
6.0ms	(/ (* r (sin b)) (cos (+ a b)))
4.0ms	(cos (+ a b))

series46.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(sin b)
12.0ms	(* r (sin b))
26.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify664.0ms

Counts

66 → 66

Iterations

Useful iterations: 3 (232.0ms)

Iter	Nodes	Cost
0	101	582
1	227	576
2	671	495
3	2549	486
done	5000	486

prune102.0ms

Filtered

48 candidates to 66 candidates (-37.5%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	58	8	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	59	8	67

Merged error: 0.2b

Counts

67 → 8

localize19.0ms

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))
0.3b	(/ (* 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:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* r (sin b))
5.0ms	(* (sin a) (sin b))
10.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series94.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(* r (sin b))
10.0ms	(* (sin a) (sin b))
55.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify1.1s

Counts

88 → 88

Iterations

Useful iterations: 3 (400.0ms)

Iter	Nodes	Cost
0	140	1256
1	355	1229
2	1192	1083
3	4531	1023
done	5000	1023

prune155.0ms

Filtered

64 candidates to 88 candidates (-37.5%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	84	12	96

Merged error: 0.0b

Counts

96 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
27×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
22×	`add-cbrt-cube`
18×	`times-frac`
14×	`pow1` `prod-exp`
8×	`associate-/r/` `cbrt-unprod`
7×	`associate-l`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`cos-mult` `add-log-exp`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`flip3--` `frac-sub` `flip--` `div-inv` `sub-div` `unswap-sqr`
1×	`pow-flip` `frac-2neg` `associate-*r/` `clear-num` `un-div-inv` `inv-pow`

Counts

4 → 114

Calls

4 calls:

4.0ms	(* r (sin b))
8.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))
14.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* r (sin b))
26.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(* (sin a) (sin b))
59.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify645.0ms

Counts

126 → 126

Iterations

Useful iterations: done (638.0ms)

Iter	Nodes	Cost
0	182	2093
1	488	1968
2	1812	1679
done	5000	1668

prune154.0ms

Filtered

81 candidates to 126 candidates (-55.6%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	126	0	126
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	126	12	138

Merged error: 0.0b

Counts

138 → 12

localize20.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (sin a)) (cbrt (sin a)))
0.6b	(cbrt (sin a))
0.6b	(cbrt (sin a))
0.6b	(cbrt (sin a))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 73

Calls

4 calls:

7.0ms	(* (cbrt (sin a)) (cbrt (sin a)))
2.0ms	(cbrt (sin a))
2.0ms	(cbrt (sin a))
2.0ms	(cbrt (sin a))

series89.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(* (cbrt (sin a)) (cbrt (sin a)))
20.0ms	(cbrt (sin a))
23.0ms	(cbrt (sin a))
20.0ms	(cbrt (sin a))

simplify772.0ms

Counts

85 → 85

Iterations

Useful iterations: done (770.0ms)

Iter	Nodes	Cost
0	76	792
1	164	715
2	507	586
3	2000	521
done	5001	515

prune83.0ms

Filtered

56 candidates to 85 candidates (-51.8%)

Pruning

12 alts after pruning (10 fresh and 2 done)

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

Merged error: 0.0b

Counts

97 → 12

regimes273.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	18
1	20	18
done	20	18

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	2997×	body	1280	valid
525.0ms	1845×	body	640	valid
153.0ms	2116×	body	80	valid
147.0ms	720×	body	320	valid
49.0ms	327×	body	160	valid

Details

sample96.0ms

simplify9.0ms

prune4.0ms

localize10.0ms

rewrite18.0ms

series46.0ms

simplify664.0ms

prune102.0ms

localize19.0ms

rewrite27.0ms

series94.0ms

simplify1.1s

prune155.0ms

localize20.0ms

rewrite35.0ms

series103.0ms

simplify645.0ms

prune154.0ms

localize20.0ms

rewrite15.0ms

series89.0ms

simplify772.0ms

prune83.0ms

regimes273.0ms

bsearch0.0ms

simplify2.0ms

end0.0ms

sample2.6s

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