Details

sample82.0ms

Algorithm

intervals

Results

41.0ms

525×

body

valid

simplify75.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (11.0ms)

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

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.6b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* j 27.0) k)
0.4b	(* (* x 18.0) y)
4.3b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
4.5b	(* (* (* x 18.0) y) z)

rewrite21.0ms

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:

5.0ms	(* (* j 27.0) k)
5.0ms	(* (* x 18.0) y)
1.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
7.0ms	(* (* (* x 18.0) y) z)

series3.0s

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* j 27.0) k)
24.0ms	(* (* x 18.0) y)
2.9s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
30.0ms	(* (* (* x 18.0) y) z)

simplify64.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	326	447
1	1657	364
2	5001	364

prune404.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* j 27.0) k)
0.2b	(* x (* 18.0 y))
4.3b	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
4.5b	(* (* x (* 18.0 y)) z)

rewrite23.0ms

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	(* (* j 27.0) k)
6.0ms	(* x (* 18.0 y))
1.0ms	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
8.0ms	(* (* x (* 18.0 y)) z)

series3.0s

Counts

4 → 12

Calls

4 calls:

20.0ms	(* (* j 27.0) k)
24.0ms	(* x (* 18.0 y))
3.0s	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
35.0ms	(* (* x (* 18.0 y)) z)

simplify66.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	324	447
1	1471	364
2	5001	364

prune349.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.2b	(* j (* 27.0 k))
0.4b	(* (* x 18.0) y)
4.3b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
4.5b	(* (* (* x 18.0) y) z)

rewrite21.0ms

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	(* j (* 27.0 k))
6.0ms	(* (* x 18.0) y)
1.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
7.0ms	(* (* (* x 18.0) y) z)

series3.0s

Counts

4 → 12

Calls

4 calls:

19.0ms	(* j (* 27.0 k))
23.0ms	(* (* x 18.0) y)
2.9s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
35.0ms	(* (* (* x 18.0) y) z)

simplify57.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	318	446
1	1546	363
2	5002	363

prune587.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.5b	(cbrt k)
0.5b	(cbrt k)
4.3b	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* (* j 27.0) (* (cbrt k) (cbrt k))) (cbrt k)))))
4.5b	(* (* x (* 18.0 y)) z)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 59

Calls

4 calls:

1.0ms	(cbrt k)
1.0ms	(cbrt k)
1.0ms	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* (* j 27.0) (* (cbrt k) (cbrt k))) (cbrt k)))))
8.0ms	(* (* x (* 18.0 y)) z)

series3.3s

Counts

4 → 12

Calls

4 calls:

182.0ms	(cbrt k)
185.0ms	(cbrt k)
2.9s	(fma t (- (* (* x (* 18.0 y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* (* j 27.0) (* (cbrt k) (cbrt k))) (cbrt k)))))
29.0ms	(* (* x (* 18.0 y)) z)

simplify43.0ms

Algorithm

egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	254	438
1	1042	369
2	5001	363

prune358.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.0b

regimes1.1s

Accuracy

30.8% (2.5b remaining)

Error of 4.7b against oracle of 2.2b and baseline of 5.8b

bsearch277.0ms

Steps

Iters	Range		Point
9	1.0954468849478197e-98	2.9587187397732723e-93	2.4037056843120258e-98
9	-1.5670530706074278e-123	-3.4172981461518462e-130	-2.5613291814136577e-127

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

sample2.1s

Algorithm

intervals

Results

1.2s

16069×

body

valid