Details

sample78.0ms

Algorithm

intervals

Results

34.0ms

495×

body

valid

simplify68.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 2 (9.0ms)

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: 5.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* j 27.0) k)
0.2b	(* (* x 18.0) y)
3.6b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
3.6b	(* (* (* x 18.0) y) z)

rewrite91.0ms

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:

17.0ms	(* (* j 27.0) k)
17.0ms	(* (* x 18.0) y)
0.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
55.0ms	(* (* (* x 18.0) y) z)

series2.8s

Counts

4 → 12

Calls

4 calls:

16.0ms	(* (* j 27.0) k)
18.0ms	(* (* x 18.0) y)
2.8s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
24.0ms	(* (* (* x 18.0) y) z)

simplify57.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (12.0ms)

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

prune327.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.4b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* j (* 27.0 k))
0.2b	(* (* x 18.0) y)
3.6b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
3.6b	(* (* (* x 18.0) y) z)

rewrite90.0ms

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:

15.0ms	(* j (* 27.0 k))
18.0ms	(* (* x 18.0) y)
0.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
54.0ms	(* (* (* x 18.0) y) z)

series2.8s

Counts

4 → 12

Calls

4 calls:

16.0ms	(* j (* 27.0 k))
18.0ms	(* (* x 18.0) y)
2.7s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
25.0ms	(* (* (* x 18.0) y) z)

simplify66.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (12.0ms)

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

prune325.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.3b

localize24.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt y)
0.7b	(cbrt y)
3.6b	(fma t (- (* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
3.6b	(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt y)
1.0ms	(cbrt y)
0.0ms	(fma t (- (* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
365.0ms	(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)

series3.2s

Counts

4 → 12

Calls

4 calls:

195.0ms	(cbrt y)
180.0ms	(cbrt y)
2.8s	(fma t (- (* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
49.0ms	(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)

simplify63.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	349	677
1	1623	524
2	5002	471

prune384.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (* (* y 18.0) x) z) (* a 4.0))
0.2b	(* (* j 27.0) k)
3.6b	(fma t (- (* (* (* y 18.0) x) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
3.6b	(* (* (* y 18.0) x) z)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-r*` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
2×	`associate-l` `*-commutative`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `prod-diff` `flip--` `fma-udef`

Counts

4 → 69

Calls

4 calls:

56.0ms	(- (* (* (* y 18.0) x) z) (* a 4.0))
19.0ms	(* (* j 27.0) k)
0.0ms	(fma t (- (* (* (* y 18.0) x) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
52.0ms	(* (* (* y 18.0) x) z)

series2.9s

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (* (* (* y 18.0) x) z) (* a 4.0))
16.0ms	(* (* j 27.0) k)
2.7s	(fma t (- (* (* (* y 18.0) x) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
26.0ms	(* (* (* y 18.0) x) z)

simplify53.0ms

Algorithm

egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	379	501
1	1647	427
2	5001	426

prune279.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.3b

regimes819.0ms

Accuracy

34.3% (2.1b remaining)

Error of 4.3b against oracle of 2.2b and baseline of 5.4b

bsearch181.0ms

Steps

Iters	Range		Point
7	1.4243574861877123e-135	1.2019133473957847e-133	7.69076956030389e-134
7	-7.901875687515039e-129	-3.531861669565797e-130	-7.802449997962363e-129

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	21
1	58	21
2	58	21

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.0s

16118×

body

valid