Details

sample90.0ms

Algorithm

intervals

Results

49.0ms	107×	body	1280	valid
15.0ms	56×	body	640	valid
5.0ms	68×	body	80	valid
5.0ms	21×	body	320	valid
1.0ms	6×	body	160	valid

simplify2.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune16.0ms

Filtered

1 candidates to 1 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: 17.1b

Counts

2 → 2

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(sin b)
0.2b	(* r (/ (sin b) (cos (+ b a))))
0.2b	(/ (sin b) (cos (+ b a)))
4.0b	(cos (+ b a))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
20×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
13×	`associate-r`
11×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
4×	`add-log-exp`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`cos-sum` `frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 74

Calls

4 calls:

2.0ms	(sin b)
8.0ms	(* r (/ (sin b) (cos (+ b a))))
5.0ms	(/ (sin b) (cos (+ b a)))
5.0ms	(cos (+ b a))

series48.0ms

Counts

4 → 12

Calls

4 calls:

2.0ms	(sin b)
26.0ms	(* r (/ (sin b) (cos (+ b a))))
13.0ms	(/ (sin b) (cos (+ b a)))
6.0ms	(cos (+ b a))

simplify50.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5732	826

prune131.0ms

Filtered

67 candidates to 86 candidates (-28.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	76	10	86
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	77	11	88

Merged error: 0.2b

Counts

88 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite36.0ms

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:

6.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
13.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
9.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
5.0ms	(* (sin b) (sin a))

series120.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
59.0ms	(* r (/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a)))))
32.0ms	(/ (sin b) (- (* (cos b) (cos a)) (* (sin b) (sin a))))
10.0ms	(* (sin b) (sin a))

simplify46.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	5283	1662

prune192.0ms

Filtered

87 candidates to 112 candidates (-28.7%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	101	11	112
Fresh	8	2	10
Picked	1	0	1
Done	0	0	0
Total	110	13	123

Merged error: 0.0b

Counts

123 → 13

localize15.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
0.1b	(* (sin b) r)
0.2b	(* (sin b) (sin a))
0.3b	(/ (* (sin b) r) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

rewrite27.0ms

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

series99.0ms

Counts

4 → 12

Calls

4 calls:

18.0ms	(- (* (cos b) (cos a)) (* (sin b) (sin a)))
8.0ms	(* (sin b) r)
13.0ms	(* (sin b) (sin a))
60.0ms	(/ (* (sin b) r) (- (* (cos b) (cos a)) (* (sin b) (sin a))))

simplify33.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (26.0ms)

Iter	Nodes	Cost
0	5022	1023

prune128.0ms

Filtered

64 candidates to 88 candidates (-37.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	86	2	88
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	91	10	101

Merged error: 0.0b

Counts

101 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (sin b) r) (/ (- (* (cos b) (* (cos b) (* (cos a) (cos a)))) (* (sin b) (* (sin b) (* (sin a) (sin a))))) (+ (* (cos b) (cos a)) (* (sin b) (sin a)))))
0.3b	(* (sin a) (sin a))
0.3b	(* (cos b) (* (cos b) (* (cos a) (cos a))))
0.4b	(/ (- (* (cos b) (* (cos b) (* (cos a) (cos a)))) (* (sin b) (* (sin b) (* (sin a) (sin a))))) (+ (* (cos b) (cos a)) (* (sin b) (sin a))))

rewrite61.0ms

Algorithm

rewrite-expression-head

Rules

43×	`times-frac`
33×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
29×	`add-exp-log` `add-cbrt-cube`
20×	`pow1`
19×	`associate-/r*`
10×	`associate-*r/` `associate-/r/`
9×	`prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp` `pow-prod-down`
6×	`associate-l` `cos-mult` `sin-mult`
4×	`distribute-rgt-in` `sqr-cos` `distribute-lft-in` `associate-r` `div-inv` `associate-/l/` `associate-/l*` `add-log-exp`
3×	`flip3-+` `swap-sqr` `frac-add` `flip-+`
2×	`frac-2neg` `clear-num` `*-commutative`
1×	`pow2` `flip3--` `pow-plus` `div-sub` `pow-sqr` `pow-prod-up` `frac-sub` `flip--` `sqr-sin` `sub-div` `unswap-sqr`

Counts

4 → 140

Calls

4 calls:

16.0ms	(/ (* (sin b) r) (/ (- (* (cos b) (* (cos b) (* (cos a) (cos a)))) (* (sin b) (* (sin b) (* (sin a) (sin a))))) (+ (* (cos b) (cos a)) (* (sin b) (sin a)))))
6.0ms	(* (sin a) (sin a))
13.0ms	(* (cos b) (* (cos b) (* (cos a) (cos a))))
21.0ms	(/ (- (* (cos b) (* (cos b) (* (cos a) (cos a)))) (* (sin b) (* (sin b) (* (sin a) (sin a))))) (+ (* (cos b) (cos a)) (* (sin b) (sin a))))

series220.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(/ (* (sin b) r) (/ (- (* (cos b) (* (cos b) (* (cos a) (cos a)))) (* (sin b) (* (sin b) (* (sin a) (sin a))))) (+ (* (cos b) (cos a)) (* (sin b) (sin a)))))
4.0ms	(* (sin a) (sin a))
17.0ms	(* (cos b) (* (cos b) (* (cos a) (cos a))))
64.0ms	(/ (- (* (cos b) (* (cos b) (* (cos a) (cos a)))) (* (sin b) (* (sin b) (* (sin a) (sin a))))) (+ (* (cos b) (cos a)) (* (sin b) (sin a))))

simplify47.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5064	3935

prune277.0ms

Filtered

111 candidates to 152 candidates (-36.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	151	1	152
Fresh	1	8	9
Picked	0	1	1
Done	0	0	0
Total	152	10	162

Merged error: 0b

Counts

162 → 10

regimes257.0ms

Accuracy

0% (0.4b 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	28	40
1	28	40

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.3s	2997×	body	1280	valid
529.0ms	1845×	body	640	valid
151.0ms	720×	body	320	valid
147.0ms	2116×	body	80	valid
53.0ms	327×	body	160	valid

Details

sample90.0ms

simplify2.0ms

prune16.0ms

localize10.0ms

rewrite21.0ms

series48.0ms

simplify50.0ms

prune131.0ms

localize18.0ms

rewrite36.0ms

series120.0ms

simplify46.0ms

prune192.0ms

localize15.0ms

rewrite27.0ms

series99.0ms

simplify33.0ms

prune128.0ms

localize25.0ms

rewrite61.0ms

series220.0ms

simplify47.0ms

prune277.0ms

regimes257.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.6s

Profiling