Details

sample78.0ms

Algorithm

intervals

Results

44.0ms	97×	body	1280	valid
13.0ms	54×	body	640	valid
4.0ms	24×	body	320	valid
4.0ms	73×	body	80	valid
1.0ms	8×	body	160	valid

simplify8.0ms

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

Filtered

1 candidates to 0 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: 14.4b

Counts

2 → 1

localize12.0ms

Local error

Found 3 expressions with local error:

0.1b	(* r (sin b))
0.2b	(/ (* r (sin b)) (cos (+ a b)))
4.1b	(cos (+ a b))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

40×	`add-sqr-sqrt`
36×	`times-frac`
30×	`add-cube-cbrt` `*-un-lft-identity`
15×	`associate-r` `associate-l`
12×	`associate-/l*`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `*-commutative` `unswap-sqr`
3×	`associate-/r*` `add-log-exp`
2×	`cbrt-undiv` `cos-sum` `div-exp` `prod-exp` `cbrt-unprod`
1×	`+-commutative` `frac-2neg` `pow-prod-down` `clear-num` `div-inv`

Counts

3 → 92

Calls

3 calls:

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

series165.0ms

Counts

3 → 9

Calls

3 calls:

38.0ms	(* r (sin b))
102.0ms	(/ (* r (sin b)) (cos (+ a b)))
24.0ms	(cos (+ a b))

simplify45.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	326	781
1	1400	733
2	5001	732

prune201.0ms

Filtered

101 candidates to 75 candidates (74.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	92	9	101
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	9	102

Merged error: 0.2b

Counts

102 → 9

localize16.0ms

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))))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

253×	`add-sqr-sqrt`
169×	`*-un-lft-identity`
132×	`times-frac`
98×	`associate-l`
70×	`unswap-sqr`
57×	`add-cube-cbrt`
56×	`distribute-lft-out--` `difference-of-squares`
42×	`associate-r`
14×	`*-commutative`
13×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/l*`
11×	`associate-/r*`
8×	`pow1`
6×	`add-log-exp`
5×	`sin-mult`
4×	`associate-/r/` `cos-mult`
3×	`prod-exp` `cbrt-unprod`
2×	`cbrt-undiv` `flip3--` `div-exp` `pow-prod-down` `frac-sub` `flip--` `sub-div`
1×	`sub-neg` `frac-2neg` `diff-log` `clear-num` `div-inv`

Counts

4 → 232

Calls

4 calls:

4.0ms	(* r (sin b))
16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
23.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series385.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(* r (sin b))
83.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* (sin a) (sin b))
217.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify93.0ms

Algorithm

egg-herbie

Counts

244 → 244

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	676	3665
1	2931	3568
2	5002	3568

prune546.0ms

Filtered

244 candidates to 149 candidates (61.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	233	11	244
Fresh	8	0	8
Picked	1	0	1
Done	0	0	0
Total	242	11	253

Merged error: 0.0b

Counts

253 → 11

localize16.0ms

Local error

Found 4 expressions with local error:

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

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

155×	`add-sqr-sqrt`
113×	`*-un-lft-identity`
67×	`times-frac`
44×	`associate-r`
42×	`associate-l`
40×	`add-cube-cbrt`
39×	`unswap-sqr`
36×	`distribute-lft-out--` `difference-of-squares`
22×	`associate-/r*`
17×	`associate-*r/`
13×	`add-exp-log` `add-cbrt-cube`
8×	`pow1` `associate-/r/`
7×	`sin-mult` `associate-/l*`
6×	`cos-mult` `add-log-exp`
3×	`flip3--` `prod-exp` `clear-num` `frac-sub` `flip--` `cbrt-unprod` `sub-div`
2×	`cbrt-undiv` `frac-2neg` `div-exp` `pow-prod-down` `un-div-inv` `*-commutative` `div-inv`
1×	`sub-neg` `diff-log`

Counts

4 → 182

Calls

4 calls:

16.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
18.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
31.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series551.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
47.0ms	(* (sin a) (sin b))
187.0ms	(/ r (- (* (cos a) (cos b)) (* (sin a) (sin b))))
233.0ms	(* (sin b) (/ r (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify72.0ms

Algorithm

egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	526	2133
1	2290	2012
2	5001	2010

prune466.0ms

Filtered

194 candidates to 128 candidates (66.0%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	190	4	194
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	194	11	205

Merged error: 0.0b

Counts

205 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
0.2b	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
0.2b	(* (sin a) (sin b))
3.6b	(log (exp (* (sin a) (sin b))))

rewrite68.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
138×	`*-un-lft-identity`
108×	`times-frac`
64×	`associate-l`
56×	`distribute-lft-out--`
54×	`add-cube-cbrt`
42×	`log-pow`
36×	`associate-r`
35×	`pow1`
28×	`difference-of-squares`
26×	`unswap-sqr`
12×	`add-exp-log` `exp-prod` `-commutative` `associate-/l`
11×	`add-cbrt-cube`
9×	`associate-/r*`
8×	`add-log-exp`
6×	`log-prod`
3×	`associate--r+`
2×	`cbrt-undiv` `flip3--` `diff-log` `div-exp` `rem-log-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod`
1×	`sub-neg` `exp-to-pow` `frac-2neg` `pow-prod-down` `clear-num` `div-inv` `sin-mult`

Counts

4 → 212

Calls

4 calls:

19.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
25.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
5.0ms	(* (sin a) (sin b))
8.0ms	(log (exp (* (sin a) (sin b))))

series403.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b)))))
225.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (log (exp (* (sin a) (sin b))))))
44.0ms	(* (sin a) (sin b))
48.0ms	(log (exp (* (sin a) (sin b))))

simplify84.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	615	3391
1	2563	3170
2	5001	3110

prune496.0ms

Filtered

224 candidates to 130 candidates (58.0%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	221	3	224
Fresh	1	8	9
Picked	0	1	1
Done	0	1	1
Total	222	13	235

Merged error: 0.0b

Counts

235 → 13

regimes196.0ms

Accuracy

0% (0.3b remaining)

Error of 0.3b against oracle of 0.0b 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

sample2.2s

Algorithm

intervals

Results

1.2s	2871×	body	1280	valid
472.0ms	1810×	body	640	valid
142.0ms	791×	body	320	valid
139.0ms	2160×	body	80	valid
51.0ms	368×	body	160	valid