Details

sample136.0ms

Algorithm

intervals

Results

97.0ms

533×

body

valid

simplify72.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (10.0ms)

Iter	Nodes	Cost
0	67	15
1	225	13
2	823	12
3	3028	12
4	5001	12

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.6b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 18.0) y)
0.2b	(* (* j 27.0) k)
5.1b	(* (* (* x 18.0) y) z)
5.2b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
9×	`associate-r`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `*-commutative`
1×	`fma-udef`

Counts

4 → 73

Calls

4 calls:

7.0ms	(* (* x 18.0) y)
7.0ms	(* (* j 27.0) k)
21.0ms	(* (* (* x 18.0) y) z)
0.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))

series2.9s

Counts

4 → 12

Calls

4 calls:

31.0ms	(* (* x 18.0) y)
17.0ms	(* (* j 27.0) k)
27.0ms	(* (* (* x 18.0) y) z)
2.8s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))

simplify54.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	326	447
1	1657	364
2	5002	364

prune345.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 4.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (* 18.0 y))
0.2b	(* (* j 27.0) k)
5.1b	(* (* x (* 18.0 y)) z)
5.2b	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`fma-udef`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* x (* 18.0 y))
7.0ms	(* (* j 27.0) k)
20.0ms	(* (* x (* 18.0 y)) z)
0.0ms	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))

series2.9s

Counts

4 → 12

Calls

4 calls:

24.0ms	(* x (* 18.0 y))
22.0ms	(* (* j 27.0) k)
48.0ms	(* (* x (* 18.0 y)) z)
2.8s	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))

simplify55.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	324	447
1	1472	364
2	5001	364

prune355.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 4.6b

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(* x (* 18.0 y))
0.2b	(* j (* 27.0 k))
5.1b	(* (* x (* 18.0 y)) z)
5.2b	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

23×	`pow1` `add-exp-log` `add-cbrt-cube`
12×	`pow-prod-down` `prod-exp` `cbrt-unprod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*`
5×	`associate-r`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative`
1×	`fma-udef`

Counts

4 → 73

Calls

4 calls:

6.0ms	(* x (* 18.0 y))
6.0ms	(* j (* 27.0 k))
18.0ms	(* (* x (* 18.0 y)) z)
0.0ms	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))

series3.1s

Counts

4 → 12

Calls

4 calls:

22.0ms	(* x (* 18.0 y))
35.0ms	(* j (* 27.0 k))
29.0ms	(* (* x (* 18.0 y)) z)
3.0s	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	316	446
1	1361	363
2	5002	363

prune363.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt z)
1.5b	(* (* (* x (* 18.0 y)) (* (cbrt z) (cbrt z))) (cbrt z))
3.7b	(* (* x (* 18.0 y)) (* (cbrt z) (cbrt z)))
5.2b	(fma t (- (* (* (* x (* 18.0 y)) (* (cbrt z) (cbrt z))) (cbrt z)) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

54×	`pow1` `add-exp-log`
37×	`pow-prod-down` `prod-exp` `cbrt-unprod`
35×	`add-cbrt-cube`
7×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`cbrt-prod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`associate-l` `*-commutative`
1×	`pow1/3` `fma-udef`

Counts

4 → 91

Calls

4 calls:

1.0ms	(cbrt z)
100.0ms	(* (* (* x (* 18.0 y)) (* (cbrt z) (cbrt z))) (cbrt z))
27.0ms	(* (* x (* 18.0 y)) (* (cbrt z) (cbrt z)))
0.0ms	(fma t (- (* (* (* x (* 18.0 y)) (* (cbrt z) (cbrt z))) (cbrt z)) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))

series3.6s

Counts

4 → 12

Calls

4 calls:

193.0ms	(cbrt z)
59.0ms	(* (* (* x (* 18.0 y)) (* (cbrt z) (cbrt z))) (cbrt z))
372.0ms	(* (* x (* 18.0 y)) (* (cbrt z) (cbrt z)))
2.9s	(fma t (- (* (* (* x (* 18.0 y)) (* (cbrt z) (cbrt z))) (cbrt z)) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))

simplify75.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 2 (65.0ms)

Iter	Nodes	Cost
0	407	967
1	1937	706
2	5002	643

prune418.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.6b

regimes868.0ms

Accuracy

19.9% (2.7b remaining)

Error of 4.9b against oracle of 2.2b and baseline of 5.6b

bsearch421.0ms

Steps

Iters	Range		Point
10	2.013048699062109e+110	6.714891876596302e+121	1.2900037542469239e+120
8	-3.540879330516425e+183	-3.5776167958837047e+180	-2.4272481818337534e+181

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	57	33
1	63	33
2	63	33

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.9s

16103×

body

valid