Details

sample79.0ms

Algorithm

intervals

Results

38.0ms	90×	body	1280	valid
18.0ms	55×	body	640	valid
5.0ms	31×	body	320	valid
4.0ms	65×	body	80	valid
2.0ms	15×	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

prune2.0ms

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: 15.4b

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)))
2.3b	(cos (+ a b))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 47

Calls

3 calls:

4.0ms	(* r (sin b))
5.0ms	(/ (* r (sin b)) (cos (+ a b)))
7.0ms	(cos (+ a b))

series157.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(* r (sin b))
95.0ms	(/ (* r (sin b)) (cos (+ a b)))
23.0ms	(cos (+ a b))

simplify33.0ms

Algorithm

egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	198	305
1	861	257
2	5001	256

prune134.0ms

Filtered

56 candidates to 40 candidates (71.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	49	7	56
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	7	57

Merged error: 0.2b

Counts

57 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

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

rewrite25.0ms

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×	`cos-mult` `sin-mult`
4×	`associate-/r/`
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 → 77

Calls

4 calls:

4.0ms	(* (cos a) (cos b))
5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
5.0ms	(* (sin a) (sin b))
9.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series369.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(* (cos a) (cos b))
80.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
45.0ms	(* (sin a) (sin b))
206.0ms	(/ (* r (sin b)) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify47.0ms

Algorithm

egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	371	798
1	1534	704
2	5002	694

prune286.0ms

Filtered

89 candidates to 64 candidates (71.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	78	11	89
Fresh	6	0	6
Picked	1	0	1
Done	0	0	0
Total	85	11	96

Merged error: 0.0b

Counts

96 → 11

localize18.0ms

Local error

Found 4 expressions with local error:

0.1b	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
0.2b	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.2b	(* (sin a) (sin b))
0.3b	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 110

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
7.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
5.0ms	(* (sin a) (sin b))
13.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

series425.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
100.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
42.0ms	(* (sin a) (sin b))
207.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify69.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	483	1381
1	2301	1194
2	5001	1166

prune335.0ms

Filtered

122 candidates to 74 candidates (60.7%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	2	8	10
Picked	0	1	1
Done	0	0	0
Total	121	12	133

Merged error: 0.0b

Counts

133 → 12

localize20.0ms

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

rewrite34.0ms

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)))
5.0ms	(* (sin a) (sin b))
12.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
9.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series441.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
42.0ms	(* (sin a) (sin b))
211.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
108.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify53.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	405	1308
1	1761	1183
2	5001	1173

prune325.0ms

Filtered

112 candidates to 84 candidates (75.0%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	109	3	112
Fresh	3	7	10
Picked	0	1	1
Done	0	1	1
Total	112	12	124

Merged error: 0.0b

Counts

124 → 12

regimes165.0ms

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	10
1	15	10

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.2s	2875×	body	1280	valid
508.0ms	1889×	body	640	valid
143.0ms	755×	body	320	valid
120.0ms	2152×	body	80	valid
42.0ms	330×	body	160	valid