Details

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

sample84.0ms

Algorithm

intervals

Results

39.0ms	85×	body	1280	valid
21.0ms	60×	body	640	valid
5.0ms	73×	body	80	valid
4.0ms	21×	body	320	valid
3.0ms	17×	body	160	valid

simplify3.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	9
1	20	9

prune9.0ms

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: 13.7b

Counts

2 → 1

localize10.0ms

Local error

Found 3 expressions with local error:

0.2b	(* r (/ (sin b) (cos (+ a b))))
0.2b	(/ (sin b) (cos (+ a b)))
2.5b	(cos (+ a b))

rewrite17.0ms

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:

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

series42.0ms

Counts

3 → 9

Calls

3 calls:

24.0ms	(* r (/ (sin b) (cos (+ a b))))
12.0ms	(/ (sin b) (cos (+ a b)))
6.0ms	(cos (+ a b))

simplify55.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5145	783

prune114.0ms

Filtered

60 candidates to 76 candidates (-26.7%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	68	8	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	69	8	77

Merged error: 0.2b

Counts

77 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos 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))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 105

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series98.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
52.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(* (sin a) (sin b))
28.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify54.0ms

Algorithm

egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5207	1580

prune186.0ms

Filtered

91 candidates to 117 candidates (-28.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	107	10	117
Fresh	5	2	7
Picked	1	0	1
Done	0	0	0
Total	113	12	125

Merged error: 0.0b

Counts

125 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

4.0ms	(* (sin b) r)
7.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
12.0ms	(* (* (sin b) r) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))

series96.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (sin b) r)
24.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
56.0ms	(* (* (sin b) r) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(* (sin a) (sin b))

simplify54.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5378	1557

prune168.0ms

Filtered

78 candidates to 126 candidates (-61.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	1	10	11
Picked	1	0	1
Done	0	0	0
Total	125	13	138

Merged error: 0.0b

Counts

138 → 13

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (cos a) (cos b))
0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b)))))
2.6b	(log (pow (exp (sin a)) (sin b)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

31×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
14×	`add-exp-log`
13×	`add-cbrt-cube`
8×	`pow1`
7×	`log-prod`
6×	`associate-l`
4×	`associate-/r/` `add-log-exp`
3×	`unpow-prod-down` `rem-log-exp` `prod-exp` `associate-/r` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `div-inv`
1×	`pow-to-exp` `frac-2neg` `associate-*r/` `pow-exp` `clear-num` `log-pow` `cos-mult` `sqr-pow`

Counts

4 → 100

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
11.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b)))))
3.0ms	(log (pow (exp (sin a)) (sin b)))

series134.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (cos a) (cos b))
61.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b))))))
43.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (pow (exp (sin a)) (sin b)))))
22.0ms	(log (pow (exp (sin a)) (sin b)))

simplify59.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5018	1597

prune108.0ms

Filtered

82 candidates to 112 candidates (-36.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	108	4	112
Fresh	4	8	12
Picked	1	0	1
Done	0	0	0
Total	113	12	125

Merged error: 0.0b

Counts

125 → 12

regimes407.0ms

Accuracy

0% (0.3b 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	17	18
1	17	18

end0.0ms

analyze1.1s

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
6.2%	93.6%	0.1%	7
9.4%	90.5%	0.1%	8
14%	85.8%	0.1%	9
19.5%	80.4%	0.1%	10
20.7%	79.2%	0.1%	11
22%	77.8%	0.1%	12
23.5%	76.4%	0.1%	13
23.8%	76%	0.1%	14

sample2.7s

Algorithm

intervals

Results

1.6s	2923×	body	1280	valid
522.0ms	1845×	body	640	valid
161.0ms	2162×	body	80	valid
151.0ms	734×	body	320	valid
51.0ms	336×	body	160	valid
0.0ms	1×	body	640	invalid

Details

analyze1.1s

sample84.0ms

simplify3.0ms

prune9.0ms

localize10.0ms

rewrite17.0ms

series42.0ms

simplify55.0ms

prune114.0ms

localize17.0ms

rewrite31.0ms

series98.0ms

simplify54.0ms

prune186.0ms

localize19.0ms

rewrite31.0ms

series96.0ms

simplify54.0ms

prune168.0ms

localize20.0ms

rewrite30.0ms

series134.0ms

simplify59.0ms

prune108.0ms

regimes407.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.1s

sample2.7s

Profiling