Details

sample93.0ms

Algorithm

intervals

Results

42.0ms	92×	body	1280	valid
19.0ms	51×	body	640	valid
6.0ms	31×	body	320	valid
4.0ms	65×	body	80	valid
2.0ms	17×	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: 15.6b

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))

rewrite14.0ms

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)))
4.0ms	(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))

simplify33.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (25.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256

prune88.0ms

Filtered

40 candidates to 56 candidates (-40.0%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	48	8	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	49	8	57

Merged error: 0.2b

Counts

57 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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

series85.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
8.0ms	(* (cos a) (cos b))
9.0ms	(* (sin a) (sin b))
52.0ms	(/ (* 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

prune144.0ms

Filtered

64 candidates to 89 candidates (-39.1%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	78	11	89
Fresh	6	1	7
Picked	1	0	1
Done	0	0	0
Total	85	12	97

Merged error: 0.0b

Counts

97 → 12

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

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))
10.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
7.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

series95.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (cos b) (cos a))
49.0ms	(* 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))))

simplify52.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 2 (42.0ms)

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

prune143.0ms

Filtered

86 candidates to 117 candidates (-36.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	114	3	117
Fresh	4	7	11
Picked	0	1	1
Done	0	0	0
Total	118	11	129

Merged error: 0.0b

Counts

129 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 140

Calls

4 calls:

6.0ms	(* (cos a) (cos b))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
7.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series95.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
11.0ms	(* (sin a) (sin b))
26.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
50.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify71.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	573	2071
1	2474	1929
2	5001	1910

prune134.0ms

Filtered

121 candidates to 152 candidates (-25.6%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	150	2	152
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	152	11	163

Merged error: 0.0b

Counts

163 → 11

regimes263.0ms

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

sample2.6s

Algorithm

intervals

Results

1.3s	2882×	body	1280	valid
521.0ms	1842×	body	640	valid
292.0ms	741×	body	320	valid
135.0ms	2159×	body	80	valid
58.0ms	378×	body	160	valid

Details

sample93.0ms

simplify6.0ms

prune4.0ms

localize10.0ms

rewrite14.0ms

series37.0ms

simplify33.0ms

prune88.0ms

localize16.0ms

rewrite22.0ms

series85.0ms

simplify44.0ms

prune144.0ms

localize16.0ms

rewrite31.0ms

series95.0ms

simplify52.0ms

prune143.0ms

localize16.0ms

rewrite30.0ms

series95.0ms

simplify71.0ms

prune134.0ms

regimes263.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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