Details

sample103.0ms

Algorithm

intervals

Results

38.0ms	106×	body	1280	valid
21.0ms	98×	body	640	valid
19.0ms	288×	body	80	valid
8.0ms	48×	body	320	valid
3.0ms	22×	body	160	valid

simplify80.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	15	4
1	30	4
2	66	4
3	137	4
4	262	4
5	492	4
6	1390	4
7	4856	4
8	5001	4

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.3b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(sinh y)
0.0b	(/ (sinh y) y)
0.2b	(* (sin x) (/ (sinh y) y))

rewrite13.0ms

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` `sinh-def` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `unswap-sqr`
1×	`frac-2neg` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `associate-/l/`

Counts

3 → 68

Calls

3 calls:

0.0ms	(sinh y)
2.0ms	(/ (sinh y) y)
8.0ms	(* (sin x) (/ (sinh y) y))

series253.0ms

Counts

3 → 9

Calls

3 calls:

65.0ms	(sinh y)
87.0ms	(/ (sinh y) y)
101.0ms	(* (sin x) (/ (sinh y) y))

simplify44.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	333	428
1	1323	384
2	5001	382

prune177.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1))
0.0b	(* (sin x) (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1)))
0.1b	(* 1/120 (pow y 4))
0.2b	(* 1/6 (pow y 2))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
18×	`associate-r`
16×	`add-exp-log`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`add-cbrt-cube`
9×	`associate-l` `add-log-exp`
8×	`unpow-prod-down` `unswap-sqr`
7×	`prod-exp`
6×	`pow1`
4×	`sqr-pow`
3×	`sum-log` `*-commutative` `cbrt-unprod`
2×	`pow-to-exp` `flip3-+` `associate-*r/` `pow-exp` `flip-+` `unpow2`
1×	`+-commutative` `distribute-rgt-in` `associate-+r+` `distribute-lft-in` `pow-prod-down`

Counts

4 → 87

Calls

4 calls:

10.0ms	(+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1))
36.0ms	(* (sin x) (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1)))
5.0ms	(* 1/120 (pow y 4))
6.0ms	(* 1/6 (pow y 2))

series232.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1))
125.0ms	(* (sin x) (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1)))
37.0ms	(* 1/120 (pow y 4))
30.0ms	(* 1/6 (pow y 2))

simplify56.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	408	619
1	1874	548
2	5002	548

prune231.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (log (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1))))
0.1b	(* 1/120 (pow y 4))
0.2b	(* 1/6 (pow y 2))
2.6b	(log (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1)))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
15×	`add-exp-log` `associate-r`
13×	`add-cube-cbrt` `*-un-lft-identity`
8×	`unpow-prod-down` `add-cbrt-cube`
7×	`unswap-sqr`
6×	`pow1` `log-prod` `associate-l` `prod-exp`
4×	`log-div` `exp-prod` `add-log-exp` `sqr-pow`
3×	`exp-sum`
2×	`pow-to-exp` `flip3-+` `exp-diff` `pow-exp` `log-pow` `*-commutative` `cbrt-unprod` `flip-+` `unpow2`
1×	`rem-log-exp` `rem-exp-log`

Counts

4 → 83

Calls

4 calls:

13.0ms	(exp (log (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1))))
5.0ms	(* 1/120 (pow y 4))
5.0ms	(* 1/6 (pow y 2))
9.0ms	(log (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(exp (log (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1))))
41.0ms	(* 1/120 (pow y 4))
25.0ms	(* 1/6 (pow y 2))
112.0ms	(log (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1)))

simplify48.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	361	614
1	1387	550
2	5001	534

prune276.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(cbrt (pow (log (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1))) 3))
0.1b	(* 1/120 (pow y 4))
0.2b	(* 1/6 (pow y 2))
2.6b	(log (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
15×	`add-exp-log` `associate-r`
14×	`cbrt-prod` `add-cube-cbrt` `*-un-lft-identity`
12×	`unpow-prod-down`
8×	`add-cbrt-cube`
7×	`pow1` `unswap-sqr`
6×	`associate-l` `prod-exp`
5×	`sqr-pow`
4×	`cube-prod` `add-log-exp`
3×	`log-prod` `log-pow`
2×	`pow-to-exp` `log-div` `pow-exp` `*-commutative` `cbrt-unprod` `unpow2`
1×	`cube-mult` `flip3-+` `pow1/3` `unpow3` `rem-log-exp` `rem-cbrt-cube` `flip-+`

Counts

4 → 89

Calls

4 calls:

2.0ms	(cbrt (pow (log (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1))) 3))
5.0ms	(* 1/120 (pow y 4))
5.0ms	(* 1/6 (pow y 2))
10.0ms	(log (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(cbrt (pow (log (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1))) 3))
42.0ms	(* 1/120 (pow y 4))
24.0ms	(* 1/6 (pow y 2))
116.0ms	(log (+ (* 1/6 (pow y 2)) (+ (* 1/120 (pow y 4)) 1)))

simplify54.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	385	715
1	1523	681
2	5001	677

prune323.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

regimes49.0ms

Accuracy

0% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 0.7b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	24
1	29	24

end0.0ms

sample2.8s

Algorithm

intervals

Results

1.1s	3108×	body	1280	valid
575.0ms	8775×	body	80	valid
557.0ms	2472×	body	640	valid
199.0ms	1172×	body	320	valid
70.0ms	580×	body	160	valid