Details

sample81.0ms

Algorithm

intervals

Results

39.0ms	90×	body	1280	valid
16.0ms	61×	body	640	valid
8.0ms	63×	body	80	valid
6.0ms	30×	body	320	valid
2.0ms	12×	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

prune2.0ms

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: 14.8b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.3b	(cos (+ a b))

rewrite17.0ms

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)))
6.0ms	(cos (+ a b))

series160.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* r (sin b))
96.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify49.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (41.0ms)

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

prune125.0ms

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

localize15.0ms

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

rewrite24.0ms

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

series380.0ms

Counts

4 → 12

Calls

4 calls:

82.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
42.0ms	(* r (sin b))
42.0ms	(* (sin a) (sin b))
214.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify48.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	344	770
1	1513	673
2	5002	663

prune269.0ms

Filtered

88 candidates to 64 candidates (72.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	76	12	88
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	83	12	95

Merged error: 0.0b

Counts

95 → 12

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)))

rewrite34.0ms

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

series461.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* (sin a) (sin b))
112.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
220.0ms	(/ 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	5001	1988

prune439.0ms

Filtered

147 candidates to 119 candidates (81.0%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	140	7	147
Fresh	7	4	11
Picked	0	1	1
Done	0	0	0
Total	147	12	159

Merged error: 0.0b

Counts

159 → 12

localize15.0ms

Local error

Found 4 expressions with local error:

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

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

49×	`add-sqr-sqrt`
43×	`*-un-lft-identity`
35×	`times-frac`
26×	`add-cube-cbrt`
22×	`add-exp-log`
21×	`associate-r`
16×	`add-cbrt-cube`
8×	`associate-/r*` `distribute-lft-out--` `difference-of-squares`
7×	`pow1`
6×	`div-exp` `add-log-exp`
5×	`prod-exp`
4×	`cbrt-undiv` `associate-/r/` `associate-/l*`
3×	`flip3--` `associate-l` `flip--` `cbrt-unprod` `div-inv` `unswap-sqr`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `diff-log` `associate-r/` `pow-prod-down` `un-div-inv` `cos-mult` `-commutative` `associate-/l/` `inv-pow`

Counts

4 → 121

Calls

4 calls:

7.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
14.0ms	(* r (/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a))))
5.0ms	(/ (* (cos a) (cos b)) (sin b))
9.0ms	(/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series443.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
186.0ms	(* r (/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a))))
68.0ms	(/ (* (cos a) (cos b)) (sin b))
102.0ms	(/ 1 (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify60.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	448	1433
1	1977	1280
2	5002	1231

prune272.0ms

Filtered

133 candidates to 82 candidates (61.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	133	12	145

Merged error: 0.0b

Counts

145 → 12

regimes160.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	9
1	17	9

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2949×	body	1280	valid
484.0ms	1802×	body	640	valid
146.0ms	770×	body	320	valid
130.0ms	2110×	body	80	valid
51.0ms	370×	body	160	valid