Details

analyze1.0s

Algorithm: search

sample86.0ms

Algorithm

intervals

Results

43.0ms	91×	body	1280	valid
20.0ms	54×	body	640	valid
6.0ms	28×	body	320	valid
5.0ms	73×	body	80	valid
1.0ms	10×	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	20	5
3	21	5
4	21	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: 12.0b

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)))
3.0b	(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))

series43.0ms

Counts

3 → 9

Calls

3 calls:

26.0ms	(* r (/ (sin b) (cos (+ a b))))
11.0ms	(/ (sin b) (cos (+ a b)))
5.0ms	(cos (+ a b))

simplify36.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	252	536
1	1064	480
2	5001	477

prune108.0ms

Filtered

57 candidates to 76 candidates (-33.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	67	9	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	68	9	77

Merged error: 0.2b

Counts

77 → 9

localize15.0ms

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

series102.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
48.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
11.0ms	(* (sin a) (sin b))
27.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify52.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	405	1307
1	1761	1182
2	5001	1173

prune172.0ms

Filtered

86 candidates to 112 candidates (-30.2%)

Pruning

14 alts after pruning (14 fresh and 0 done)

	Pruned	Kept	Total
New	98	14	112
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	107	14	121

Merged error: 0.0b

Counts

121 → 14

localize15.0ms

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	(* (sin a) (sin b))
0.2b	(/ (* r (sin b)) (- (* (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	(* r (sin b))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
4.0ms	(* (sin a) (sin b))
8.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series82.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* r (sin b))
16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
9.0ms	(* (sin a) (sin b))
50.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify46.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (38.0ms)

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

prune123.0ms

Filtered

61 candidates to 88 candidates (-44.3%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	3	10	13
Picked	1	0	1
Done	0	0	0
Total	89	13	102

Merged error: 0.0b

Counts

102 → 13

localize18.0ms

Local error

Found 4 expressions with local error:

0.2b	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
0.2b	(* (sin a) (sin b))
0.2b	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
3.1b	(log (exp (* (sin a) (sin b))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
23×	`add-cube-cbrt` `*-un-lft-identity`
19×	`times-frac`
18×	`associate-r`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1`
6×	`associate-l`
5×	`add-log-exp`
4×	`associate-/r/`
3×	`log-prod` `prod-exp` `associate-/r` `log-pow` `cbrt-unprod` `associate-/l` `unswap-sqr`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `*-commutative` `flip--` `div-inv`
1×	`exp-prod` `exp-to-pow` `frac-2neg` `associate-*r/` `rem-log-exp` `clear-num` `sin-mult`

Counts

4 → 96

Calls

4 calls:

10.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
2.0ms	(log (exp (* (sin a) (sin b))))

series96.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))))
9.0ms	(* (sin a) (sin b))
27.0ms	(/ (sin b) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
11.0ms	(log (exp (* (sin a) (sin b))))

simplify47.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	360	1301
1	1546	1128
2	5001	1121

prune92.0ms

Filtered

84 candidates to 108 candidates (-28.6%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	108	0	108
Fresh	0	12	12
Picked	0	1	1
Done	0	0	0
Total	108	13	121

Merged error: 0.0b

Counts

121 → 13

regimes272.0ms

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	12
1	17	12

end0.0ms

analyze1.0s

Algorithm: search

sample2.5s

Algorithm

intervals

Results

1.4s	2930×	body	1280	valid
529.0ms	1810×	body	640	valid
161.0ms	782×	body	320	valid
142.0ms	2122×	body	80	valid
53.0ms	356×	body	160	valid
0.0ms	1×	body	640	invalid

Details

analyze1.0s

sample86.0ms

simplify6.0ms

prune3.0ms

localize10.0ms

rewrite16.0ms

series43.0ms

simplify36.0ms

prune108.0ms

localize15.0ms

rewrite30.0ms

series102.0ms

simplify52.0ms

prune172.0ms

localize15.0ms

rewrite22.0ms

series82.0ms

simplify46.0ms

prune123.0ms

localize18.0ms

rewrite27.0ms

series96.0ms

simplify47.0ms

prune92.0ms

regimes272.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze1.0s

sample2.5s

Profiling