Details

analyze997.0ms

Algorithm: search

sample81.0ms

Algorithm

intervals

Results

44.0ms	95×	body	1280	valid
16.0ms	58×	body	640	valid
5.0ms	76×	body	80	valid
5.0ms	22×	body	320	valid
1.0ms	5×	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: 16.2b

Counts

2 → 1

localize14.0ms

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))

rewrite13.0ms

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))

series38.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(* r (sin b))
24.0ms	(/ (* r (sin b)) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify30.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (25.0ms)

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

prune90.0ms

Filtered

40 candidates to 56 candidates (-40.0%)

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	(* r (sin b))
0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (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)))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))

series86.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* r (sin b))
16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
53.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))

simplify45.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (37.0ms)

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

prune148.0ms

Filtered

64 candidates to 88 candidates (-37.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	77	11	88
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	86	11	97

Merged error: 0b

Counts

97 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite28.0ms

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

series105.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
26.0ms	(/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b))
9.0ms	(* (sin a) (sin b))
53.0ms	(/ r (/ (- (* (cos a) (cos b)) (* (sin a) (sin b))) (sin b)))

simplify74.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (55.0ms)

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

prune173.0ms

Filtered

119 candidates to 147 candidates (-23.5%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	145	2	147
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	147	11	158

Merged error: 0b

Counts

158 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
28×	`*-un-lft-identity`
18×	`add-cube-cbrt` `times-frac`
13×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*`
6×	`pow1` `add-log-exp`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`associate-/l*`
3×	`cbrt-undiv` `div-exp` `associate-r` `associate-l`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `cos-mult` `flip--` `cbrt-unprod` `div-inv`
1×	`sub-neg` `diff-log` `pow-prod-down` `*-commutative` `associate-/l/` `unswap-sqr`

Counts

4 → 92

Calls

4 calls:

7.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
4.0ms	(* (cos a) (cos b))
5.0ms	(/ (* (cos a) (cos b)) (sin b))
8.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (/ (* (cos a) (cos b)) (sin b)) (sin a))
8.0ms	(* (cos a) (cos b))
19.0ms	(/ (* (cos a) (cos b)) (sin b))
45.0ms	(/ r (- (/ (* (cos a) (cos b)) (sin b)) (sin a)))

simplify43.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	365	1006
1	1394	920
2	5001	915

prune233.0ms

Filtered

76 candidates to 104 candidates (-36.8%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	105	10	115

Merged error: 0b

Counts

115 → 10

regimes239.0ms

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	14	10
1	14	10

end0.0ms

analyze996.0ms

Algorithm: search

sample2.5s

Algorithm

intervals

Results

1.4s	2869×	body	1280	valid
514.0ms	1841×	body	640	valid
154.0ms	755×	body	320	valid
139.0ms	2175×	body	80	valid
53.0ms	360×	body	160	valid

Details

analyze997.0ms

sample81.0ms

simplify6.0ms

prune4.0ms

localize14.0ms

rewrite13.0ms

series38.0ms

simplify30.0ms

prune90.0ms

localize16.0ms

rewrite23.0ms

series86.0ms

simplify45.0ms

prune148.0ms

localize16.0ms

rewrite28.0ms

series105.0ms

simplify74.0ms

prune173.0ms

localize16.0ms

rewrite27.0ms

series91.0ms

simplify43.0ms

prune233.0ms

regimes239.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze996.0ms

sample2.5s

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