Details

analyze1.0s

Algorithm: search

sample85.0ms

Algorithm

intervals

Results

46.0ms	103×	body	1280	valid
14.0ms	49×	body	640	valid
6.0ms	28×	body	320	valid
4.0ms	68×	body	80	valid
1.0ms	8×	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

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: 13.3b

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)))
3.9b	(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))

series36.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify31.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (26.0ms)

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

prune77.0ms

Filtered

40 candidates to 56 candidates (-40.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	50	6	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	6	57

Merged error: 0.2b

Counts

57 → 6

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))))

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

series83.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(* r (sin b))
9.0ms	(* (sin a) (sin b))
51.0ms	(/ (* 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

prune134.0ms

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	5	0	5
Picked	1	0	1
Done	0	0	0
Total	83	11	94

Merged error: 0.0b

Counts

94 → 11

localize17.0ms

Local error

Found 4 expressions with local error:

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

series105.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos b) (cos a)) (* (sin a) (sin b)))
28.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b))))
12.0ms	(* (sin a) (sin b))
49.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

simplify55.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	401	1307
1	1733	1182
2	5001	1178

prune139.0ms

Filtered

84 candidates to 112 candidates (-33.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	111	12	123

Merged error: 0.0b

Counts

123 → 12

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

34×	`add-exp-log`
32×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
23×	`add-cube-cbrt`
22×	`add-cbrt-cube`
21×	`associate-r`
20×	`times-frac`
14×	`pow1` `prod-exp`
9×	`associate-l`
8×	`associate-/r/` `cbrt-unprod`
6×	`div-exp`
5×	`pow-prod-down` `sin-mult`
4×	`associate-*r/` `cos-mult` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `rec-exp` `1-exp` `associate-/r` `-commutative` `associate-/l*`
2×	`flip3--` `un-div-inv` `frac-sub` `flip--` `div-inv` `sub-div`
1×	`pow-flip` `frac-2neg` `clear-num` `inv-pow`

Counts

4 → 118

Calls

4 calls:

7.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
4.0ms	(* (sin a) (sin b))
11.0ms	(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
12.0ms	(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

series112.0ms

Counts

4 → 12

Calls

4 calls:

24.0ms	(/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))
9.0ms	(* (sin a) (sin b))
49.0ms	(* r (* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b))))))
30.0ms	(* (sin b) (/ 1 (- (* (cos b) (cos a)) (* (sin a) (sin b)))))

simplify62.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	456	1485
1	1984	1270
2	5001	1238

prune94.0ms

Filtered

79 candidates to 130 candidates (-64.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	130	0	130
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	130	12	142

Merged error: 0.0b

Counts

142 → 12

regimes258.0ms

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

analyze1.2s

Algorithm: search

sample2.5s

Algorithm

intervals

Results

1.4s	2890×	body	1280	valid
535.0ms	1844×	body	640	valid
154.0ms	729×	body	320	valid
141.0ms	2206×	body	80	valid
54.0ms	331×	body	160	valid
1.0ms	3×	body	1280	invalid
0.0ms	1×	body	320	invalid
0.0ms	1×	body	80	invalid

Details

analyze1.0s

sample85.0ms

simplify6.0ms

prune3.0ms

localize10.0ms

rewrite13.0ms

series36.0ms

simplify31.0ms

prune77.0ms

localize15.0ms

rewrite23.0ms

series83.0ms

simplify48.0ms

prune134.0ms

localize17.0ms

rewrite30.0ms

series105.0ms

simplify55.0ms

prune139.0ms

localize17.0ms

rewrite37.0ms

series112.0ms

simplify62.0ms

prune94.0ms

regimes258.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.2s

sample2.5s

Profiling