Details

sample78.0ms

Algorithm

intervals

Results

37.0ms	83×	body	1280	valid
15.0ms	53×	body	640	valid
5.0ms	27×	body	320	valid
5.0ms	82×	body	80	valid
1.0ms	11×	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

Filtered

1 candidates to 0 candidates (100.0%)

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: 14.5b

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)))
2.8b	(cos (+ a b))

rewrite19.0ms

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)))
9.0ms	(cos (+ a b))

series36.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
23.0ms	(/ (* 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

prune89.0ms

Filtered

56 candidates to 40 candidates (28.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	47	9	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	48	9	57

Merged error: 0.2b

Counts

57 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
4×	`prod-exp` `associate-/r/` `cbrt-unprod` `add-log-exp`
3×	`times-frac` `pow-prod-down` `associate-/r` `cos-mult` `-commutative` `sin-mult` `unswap-sqr`
2×	`cbrt-undiv` `div-exp`
1×	`flip3--` `frac-2neg` `clear-num` `frac-sub` `flip--` `div-inv` `associate-/l*` `sub-div`

Counts

4 → 81

Calls

4 calls:

4.0ms	(* (cos a) (cos 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))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify45.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	367	682
1	1616	593
2	5001	592

prune147.0ms

Filtered

93 candidates to 65 candidates (30.1%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	81	12	93
Fresh	7	1	8
Picked	1	0	1
Done	0	0	0
Total	89	13	102

Merged error: 0.0b

Counts

102 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
23×	`associate-r`
19×	`times-frac`
15×	`add-exp-log` `add-cbrt-cube`
10×	`pow1`
9×	`associate-l`
8×	`associate-/r/`
5×	`cos-mult` `sin-mult`
4×	`prod-exp` `cbrt-unprod` `add-log-exp` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `-commutative` `associate-/l*`
2×	`cbrt-undiv` `flip3--` `div-exp` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`frac-2neg` `associate-*r/` `clear-num`

Counts

4 → 105

Calls

4 calls:

4.0ms	(* (cos b) (cos a))
11.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos b) (cos a))
50.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
9.0ms	(* (sin a) (sin b))
28.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify54.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	428	1219
1	1840	1102
2	5002	1098

prune141.0ms

Filtered

117 candidates to 86 candidates (26.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	119	11	130

Merged error: 0.0b

Counts

130 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

156×	`times-frac`
108×	`add-sqr-sqrt`
94×	`*-un-lft-identity`
92×	`add-cube-cbrt`
47×	`associate-r`
38×	`add-exp-log`
22×	`add-cbrt-cube`
16×	`associate-/r*`
15×	`div-exp`
10×	`div-inv`
9×	`pow1`
8×	`prod-exp`
7×	`cbrt-undiv`
6×	`associate-l` `associate-/l*` `unswap-sqr`
4×	`rec-exp` `1-exp` `cbrt-unprod` `associate-/l/` `add-log-exp`
3×	`sin-mult`
2×	`frac-2neg` `pow-prod-down` `clear-num` `associate-/r/` `cos-mult` `*-commutative`
1×	`flip3--` `pow-flip` `div-sub` `associate-*r/` `un-div-inv` `frac-sub` `flip--` `inv-pow` `sub-div`

Counts

4 → 200

Calls

4 calls:

15.0ms	(* r (/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))
7.0ms	(/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b)))

series114.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* r (/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))))
9.0ms	(* (sin a) (sin b))
25.0ms	(/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b))
31.0ms	(/ 1 (/ (- (* (cos b) (cos a)) (* (sin a) (sin b))) (sin b)))

simplify94.0ms

Algorithm

egg-herbie

Counts

212 → 212

Iterations

Useful iterations: 2 (71.0ms)

Iter	Nodes	Cost
0	710	3074
1	3564	2766
2	5001	2630

prune164.0ms

Filtered

212 candidates to 135 candidates (36.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	211	1	212
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	212	11	223

Merged error: 0.0b

Counts

223 → 11

regimes246.0ms

Accuracy

0% (0.5b remaining)

Error of 0.6b against oracle of 0.1b and baseline of 0.6b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	12
1	17	12

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.3s	2889×	body	1280	valid
513.0ms	1859×	body	640	valid
152.0ms	812×	body	320	valid
121.0ms	2096×	body	80	valid
46.0ms	345×	body	160	valid

Details

sample78.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite19.0ms

series36.0ms

simplify31.0ms

prune89.0ms

localize16.0ms

rewrite23.0ms

series75.0ms

simplify45.0ms

prune147.0ms

localize15.0ms

rewrite30.0ms

series95.0ms

simplify54.0ms

prune141.0ms

localize16.0ms

rewrite44.0ms

series114.0ms

simplify94.0ms

prune164.0ms

regimes246.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.5s

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