Details

sample76.0ms

Algorithm

intervals

Results

29.0ms	98×	body	1280	valid
15.0ms	74×	body	640	valid
11.0ms	268×	body	80	valid
6.0ms	43×	body	320	valid
2.0ms	21×	body	160	valid

simplify58.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	15	4
1	28	4
2	56	4
3	102	4
4	153	4
5	334	4
6	924	4
7	1912	4
8	5001	4

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: 0.2b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (cosh x) (/ (sin y) y))
0.0b	(cosh x)
0.1b	(/ (sin y) y)

rewrite14.0ms

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` `cosh-def` `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×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 75

Calls

3 calls:

7.0ms	(* (cosh x) (/ (sin y) y))
1.0ms	(cosh x)
4.0ms	(/ (sin y) y)

series156.0ms

Counts

3 → 9

Calls

3 calls:

78.0ms	(* (cosh x) (/ (sin y) y))
51.0ms	(cosh x)
26.0ms	(/ (sin y) y)

simplify43.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	303	450
1	1150	402
2	5002	380

prune204.0ms

Filtered

84 candidates to 65 candidates (77.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	75	9	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	9	85

Merged error: 0.0b

Counts

85 → 9

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(* (/ (sin y) y) (cosh x))
0.0b	(cosh x)
0.1b	(/ (sin y) y)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
13×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
5×	`pow1`
3×	`expm1-log1p-u` `cosh-def` `associate-r` `associate-/r` `log1p-expm1-u` `associate-/l` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

3 → 75

Calls

3 calls:

7.0ms	(* (/ (sin y) y) (cosh x))
1.0ms	(cosh x)
4.0ms	(/ (sin y) y)

series370.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(* (/ (sin y) y) (cosh x))
257.0ms	(cosh x)
27.0ms	(/ (sin y) y)

simplify117.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	313	444
1	1125	395
2	4646	375
3	5001	375

prune200.0ms

Filtered

84 candidates to 66 candidates (78.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	81	3	84
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	84	9	93

Merged error: 0.0b

Counts

93 → 9

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(cosh x)
0.0b	(* (* (/ (sin y) y) (* (cbrt (cosh x)) (cbrt (cosh x)))) (cbrt (cosh x)))
0.0b	(* (cbrt (cosh x)) (cbrt (cosh x)))
0.1b	(/ (sin y) y)

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

30×	`add-sqr-sqrt`
29×	`cosh-def`
28×	`cbrt-div`
26×	`add-exp-log`
22×	`add-cube-cbrt` `*-un-lft-identity`
20×	`pow1`
19×	`cbrt-prod`
18×	`frac-times`
15×	`add-cbrt-cube`
14×	`associate-*l/`
12×	`associate-r/` `associate-r*` `prod-exp` `cbrt-unprod`
9×	`times-frac`
8×	`pow-prod-down`
7×	`associate-l`
6×	`pow1/3` `swap-sqr`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`cbrt-undiv` `div-exp` `associate-/r` `associate-/l`
2×	`pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `div-inv`

Counts

4 → 129

Calls

4 calls:

1.0ms	(cosh x)
14.0ms	(* (* (/ (sin y) y) (* (cbrt (cosh x)) (cbrt (cosh x)))) (cbrt (cosh x)))
6.0ms	(* (cbrt (cosh x)) (cbrt (cosh x)))
4.0ms	(/ (sin y) y)

series399.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(cosh x)
86.0ms	(* (* (/ (sin y) y) (* (cbrt (cosh x)) (cbrt (cosh x)))) (cbrt (cosh x)))
232.0ms	(* (cbrt (cosh x)) (cbrt (cosh x)))
31.0ms	(/ (sin y) y)

simplify76.0ms

Algorithm

egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 2 (64.0ms)

Iter	Nodes	Cost
0	540	1222
1	2297	1035
2	5001	939

prune355.0ms

Filtered

141 candidates to 94 candidates (66.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	6	2	8
Picked	0	1	1
Done	0	0	0
Total	143	7	150

Merged error: 0.0b

Counts

150 → 7

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (exp (* -1 x)) (exp x))
0.0b	(* (sin y) (+ (exp (* -1 x)) (exp x)))
0.2b	(/ 1/2 (/ y (* (sin y) (+ (exp (* -1 x)) (exp x)))))
0.2b	(/ y (* (sin y) (+ (exp (* -1 x)) (exp x))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

42×	`times-frac`
31×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
27×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
12×	`associate-*r/`
11×	`associate-/r/`
10×	`associate-/r*`
7×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
6×	`pow1` `div-inv` `associate-/l*` `add-log-exp`
4×	`expm1-log1p-u` `associate-r` `log1p-expm1-u`
3×	`fma-def` `associate-l` `prod-exp` `cbrt-unprod`
2×	`frac-2neg` `clear-num` `distribute-lft-out`
1×	`+-commutative` `distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `sum-log` `*-commutative` `unswap-sqr`

Counts

4 → 125

Calls

4 calls:

5.0ms	(+ (exp (* -1 x)) (exp x))
8.0ms	(* (sin y) (+ (exp (* -1 x)) (exp x)))
10.0ms	(/ 1/2 (/ y (* (sin y) (+ (exp (* -1 x)) (exp x)))))
9.0ms	(/ y (* (sin y) (+ (exp (* -1 x)) (exp x))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

21.0ms	(+ (exp (* -1 x)) (exp x))
55.0ms	(* (sin y) (+ (exp (* -1 x)) (exp x)))
75.0ms	(/ 1/2 (/ y (* (sin y) (+ (exp (* -1 x)) (exp x)))))
98.0ms	(/ y (* (sin y) (+ (exp (* -1 x)) (exp x))))

simplify75.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (60.0ms)

Iter	Nodes	Cost
0	526	1419
1	2539	1259
2	5001	1251

prune382.0ms

Filtered

137 candidates to 106 candidates (77.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	135	2	137
Fresh	2	3	5
Picked	0	1	1
Done	1	0	1
Total	138	6	144

Merged error: 0b

Counts

144 → 6

regimes151.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	8
1	16	8

end0.0ms

sample2.2s

Algorithm

intervals

Results

916.0ms	3059×	body	1280	valid
439.0ms	2379×	body	640	valid
357.0ms	8516×	body	80	valid
159.0ms	1193×	body	320	valid
55.0ms	632×	body	160	valid