Details

sample87.0ms

Algorithm

intervals

Results

39.0ms	87×	body	1280	valid
21.0ms	62×	body	640	valid
7.0ms	38×	body	320	valid
4.0ms	60×	body	80	valid
1.0ms	10×	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

prune3.0ms

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: 14.6b

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)))
3.3b	(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))

series35.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
23.0ms	(/ (* r (sin b)) (cos (+ a b)))
5.0ms	(cos (+ a b))

simplify30.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (26.0ms)

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

prune92.0ms

Filtered

56 candidates to 40 candidates (28.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	46	10	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	47	10	57

Merged error: 0.2b

Counts

57 → 10

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))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite23.0ms

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

series81.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* r (sin b))
16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
49.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

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

prune137.0ms

Filtered

88 candidates to 64 candidates (27.3%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	9	0	9
Picked	1	0	1
Done	0	0	0
Total	87	11	98

Merged error: 0.0b

Counts

98 → 11

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite30.0ms

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)))
4.0ms	(* (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))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
47.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))
29.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))

simplify51.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	401	1307
1	1733	1182
2	5002	1178

prune133.0ms

Filtered

112 candidates to 84 candidates (25.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	112	11	123

Merged error: 0.0b

Counts

123 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (sin a) (sin b))
0.3b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
0.3b	(pow (* (sin a) (sin b)) 3)
28.4b	(cbrt (pow (* (sin a) (sin b)) 3))

rewrite24.0ms

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:

4.0ms	(* (sin a) (sin b))
10.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
4.0ms	(pow (* (sin a) (sin b)) 3)
3.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

series82.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (sin a) (sin b))
47.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (cbrt (pow (* (sin a) (sin b)) 3))))
15.0ms	(pow (* (sin a) (sin b)) 3)
12.0ms	(cbrt (pow (* (sin a) (sin b)) 3))

simplify51.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	386	788
1	1812	681
2	5002	671

prune107.0ms

Filtered

96 candidates to 66 candidates (31.3%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	94	2	96
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	95	12	107

Merged error: 0.0b

Counts

107 → 12

regimes269.0ms

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

1.4s	2996×	body	1280	valid
510.0ms	1818×	body	640	valid
152.0ms	783×	body	320	valid
131.0ms	2091×	body	80	valid
48.0ms	313×	body	160	valid

Details

sample87.0ms

simplify6.0ms

prune3.0ms

localize10.0ms

rewrite14.0ms

series35.0ms

simplify30.0ms

prune92.0ms

localize16.0ms

rewrite23.0ms

series81.0ms

simplify45.0ms

prune137.0ms

localize15.0ms

rewrite30.0ms

series101.0ms

simplify51.0ms

prune133.0ms

localize18.0ms

rewrite24.0ms

series82.0ms

simplify51.0ms

prune107.0ms

regimes269.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

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