Details

sample79.0ms

Algorithm

intervals

Results

43.0ms	96×	body	1280	valid
17.0ms	65×	body	640	valid
4.0ms	72×	body	80	valid
3.0ms	19×	body	320	valid
1.0ms	4×	body	160	valid

simplify8.0ms

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

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 16.4b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
3.0b	(cos (+ a b))

rewrite24.0ms

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

series159.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* r (sin b))
97.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify33.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (28.0ms)

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

prune123.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	7	57

Merged error: 0.2b

Counts

57 → 7

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(* r (sin 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))))

rewrite26.0ms

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	(* r (sin b))
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))))

series387.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* r (sin b))
79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
48.0ms	(* (sin a) (sin b))
217.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5001	663

prune263.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	5	1	6
Picked	1	0	1
Done	0	0	0
Total	82	13	95

Merged error: 0.0b

Counts

95 → 13

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

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
10.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
7.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

series464.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* (sin a) (sin b))
113.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
221.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify73.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	570	2145
1	2453	2009
2	5002	1988

prune455.0ms

Filtered

147 candidates to 119 candidates (81.0%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	1	11	12
Picked	0	1	1
Done	0	0	0
Total	146	14	160

Merged error: 0.0b

Counts

160 → 14

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite32.0ms

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 b) (cos a)) (* (sin a) (sin b)))
11.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
8.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series456.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
216.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
110.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
47.0ms	(* (sin a) (sin b))

simplify54.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	401	1308
1	1734	1183
2	5002	1178

prune266.0ms

Filtered

112 candidates to 84 candidates (75.0%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	12	12
Picked	0	1	1
Done	0	1	1
Total	112	14	126

Merged error: 0.0b

Counts

126 → 14

regimes184.0ms

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	14	10
1	14	10

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2917×	body	1280	valid
486.0ms	1829×	body	640	valid
139.0ms	720×	body	320	valid
136.0ms	2189×	body	80	valid
46.0ms	345×	body	160	valid

Details

sample79.0ms

simplify8.0ms

prune3.0ms

localize12.0ms

rewrite24.0ms

series159.0ms

simplify33.0ms

prune123.0ms

localize16.0ms

rewrite26.0ms

series387.0ms

simplify49.0ms

prune263.0ms

localize16.0ms

rewrite32.0ms

series464.0ms

simplify73.0ms

prune455.0ms

localize15.0ms

rewrite32.0ms

series456.0ms

simplify54.0ms

prune266.0ms

regimes184.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.3s

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