Details

sample100.0ms

Algorithm

intervals

Results

51.0ms	105×	body	1280	valid
17.0ms	58×	body	640	valid
6.0ms	10×	body	160	valid
5.0ms	19×	body	320	valid
4.0ms	64×	body	80	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 15.3b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.2b	(cos (+ a b))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`associate-l` `associate-/r` `associate-/l` `add-log-exp`
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

3 → 67

Calls

3 calls:

6.0ms	(* r (/ (sin b) (cos (+ a b))))
4.0ms	(/ (sin b) (cos (+ a b)))
4.0ms	(cos (+ a b))

series44.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* r (/ (sin b) (cos (+ a b))))
16.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify57.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5537	783

prune120.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	69	7	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	7	77

Merged error: 0.2b

Counts

77 → 7

localize18.0ms

Local error

Found 4 expressions with local error:

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))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (* (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 a) (cos b)) (* (sin a) (sin b)))
10.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
7.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series103.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify73.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5415	1682

prune176.0ms

Filtered

89 candidates to 112 candidates (-25.8%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	103	9	112
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	110	9	119

Merged error: 0.0b

Counts

119 → 9

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite22.0ms

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

series84.0ms

Counts

4 → 12

Calls

4 calls:

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

simplify49.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5586	983

prune131.0ms

Filtered

66 candidates to 88 candidates (-33.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	3	5	8
Picked	0	1	1
Done	0	0	0
Total	88	9	97

Merged error: 0b

Counts

97 → 9

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
28×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`add-exp-log` `associate-r` `add-cbrt-cube`
6×	`pow1` `associate-/r` `associate-/l` `add-log-exp`
3×	`cbrt-undiv` `div-exp` `associate-l` `div-inv`
2×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `associate-/r/` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`sub-neg` `diff-log` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 100

Calls

4 calls:

6.0ms	(- (* (cos a) (/ (cos b) (sin b))) (sin a))
4.0ms	(/ (cos b) (sin b))
8.0ms	(* (cos a) (/ (cos b) (sin b)))
7.0ms	(/ r (- (* (cos a) (/ (cos b) (sin b))) (sin a)))

series86.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(- (* (cos a) (/ (cos b) (sin b))) (sin a))
6.0ms	(/ (cos b) (sin b))
16.0ms	(* (cos a) (/ (cos b) (sin b)))
43.0ms	(/ r (- (* (cos a) (/ (cos b) (sin b))) (sin a)))

simplify56.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5066	1450

prune102.0ms

Filtered

84 candidates to 112 candidates (-33.3%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	112	0	112
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	112	9	121

Merged error: 0b

Counts

121 → 9

regimes273.0ms

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	16
1	15	16

end0.0ms

sample2.7s

Algorithm

intervals

Results

1.4s	2865×	body	1280	valid
573.0ms	1867×	body	640	valid
177.0ms	791×	body	320	valid
149.0ms	2127×	body	80	valid
58.0ms	351×	body	160	valid

Details

sample100.0ms

simplify3.0ms

prune8.0ms

localize12.0ms

rewrite16.0ms

series44.0ms

simplify57.0ms

prune120.0ms

localize18.0ms

rewrite30.0ms

series103.0ms

simplify73.0ms

prune176.0ms

localize17.0ms

rewrite22.0ms

series84.0ms

simplify49.0ms

prune131.0ms

localize16.0ms

rewrite29.0ms

series86.0ms

simplify56.0ms

prune102.0ms

regimes273.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample2.7s

Profiling