Details

sample324.0ms

Algorithm

intervals

Results

43.0ms	98×	body	1280	valid
14.0ms	55×	body	640	valid
7.0ms	26×	body	320	valid
4.0ms	64×	body	80	valid
2.0ms	13×	body	160	valid

simplify14.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	12	5
1	16	5
2	20	5
3	21	5
4	21	5

prune4.0ms

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: 15.6b

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)))
5.0b	(cos (+ a b))

rewrite37.0ms

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×	`expm1-log1p-u` `associate-l` `associate-/r` `log1p-expm1-u` `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 → 73

Calls

3 calls:

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

series156.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(* r (/ (sin b) (cos (+ a b))))
37.0ms	(/ (sin b) (cos (+ a b)))
25.0ms	(cos (+ a b))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	263	560
1	1093	504
2	5002	504

prune228.0ms

Filtered

82 candidates to 63 candidates (76.8%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 0.2b

Counts

83 → 11

localize16.0ms

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))
0.3b	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

rewrite37.0ms

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`
4×	`expm1-log1p-u` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num`

Counts

4 → 110

Calls

4 calls:

5.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
15.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
5.0ms	(* (sin a) (sin b))
8.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

series438.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
210.0ms	(* r (/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b)))))
43.0ms	(* (sin a) (sin b))
108.0ms	(/ (sin b) (- (* (cos a) (cos b)) (* (sin a) (sin b))))

simplify60.0ms

Algorithm

egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	432	1384
1	1847	1255
2	5001	1249

prune419.0ms

Filtered

122 candidates to 96 candidates (78.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	110	12	122
Fresh	10	0	10
Picked	1	0	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:

0.2b	(* (sin a) (sin b))
0.3b	(/ (sin b) (/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b)))))
0.3b	(* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
0.4b	(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b))))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

36×	`times-frac`
30×	`add-sqr-sqrt`
26×	`add-cube-cbrt` `*-un-lft-identity`
22×	`add-exp-log` `add-cbrt-cube`
10×	`associate-/r*`
8×	`pow1` `associate-*r/`
7×	`cbrt-undiv` `div-exp`
6×	`associate-r` `associate-l` `div-inv`
5×	`sin-mult`
4×	`expm1-log1p-u` `prod-exp` `cos-mult` `cbrt-unprod` `log1p-expm1-u` `associate-/l/` `associate-/l*` `add-log-exp`
3×	`distribute-rgt-in` `distribute-lft-in`
2×	`sub-neg` `flip3--` `frac-2neg` `prod-diff` `pow-prod-down` `clear-num` `*-commutative` `frac-sub` `flip--` `sub-div` `unswap-sqr`
1×	`associate-/r/`

Counts

4 → 128

Calls

4 calls:

5.0ms	(* (sin a) (sin b))
11.0ms	(/ (sin b) (/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b)))))
9.0ms	(* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
10.0ms	(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b))))

series400.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(* (sin a) (sin b))
112.0ms	(/ (sin b) (/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b)))))
163.0ms	(* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b))))
82.0ms	(/ (* (fma (cos a) (cos b) (* (sin a) (sin b))) (- (* (cos a) (cos b)) (* (sin a) (sin b)))) (fma (cos a) (cos b) (* (sin a) (sin b))))

simplify108.0ms

Algorithm

egg-herbie

Counts

140 → 140

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	568	3176
1	3126	2735
2	5001	2599

prune526.0ms

Filtered

140 candidates to 106 candidates (75.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	138	2	140
Fresh	1	10	11
Picked	0	1	1
Done	0	0	0
Total	139	13	152

Merged error: 0.0b

Counts

152 → 13

localize19.0ms

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)))))

rewrite34.0ms

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×	`expm1-log1p-u` `associate-l` `pow-prod-down` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-*r/` `prod-diff` `clear-num` `un-div-inv` `inv-pow` `unswap-sqr`

Counts

4 → 120

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)))))

series422.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(- (* (cos a) (cos b)) (* (sin a) (sin b)))
94.0ms	(/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b))))
44.0ms	(* (sin a) (sin b))
205.0ms	(* (* r (sin b)) (/ 1 (- (* (cos a) (cos b)) (* (sin a) (sin b)))))

simplify67.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	510	1458
1	2384	1267
2	5001	1239

prune349.0ms

Filtered

132 candidates to 86 candidates (65.2%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	130	2	132
Fresh	2	9	11
Picked	0	1	1
Done	0	1	1
Total	132	13	145

Merged error: 0.0b

Counts

145 → 13

regimes189.0ms

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	19	24
1	19	24

end0.0ms

sample2.3s

Algorithm

intervals

Results

1.3s	2919×	body	1280	valid
487.0ms	1866×	body	640	valid
138.0ms	765×	body	320	valid
127.0ms	2109×	body	80	valid
45.0ms	344×	body	160	valid