Details

sample131.0ms

Algorithm

intervals

Results

92.0ms

496×

body

valid

simplify76.0ms

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

prune14.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 5.4b

localize22.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 18.0) y)
0.2b	(* (* j 27.0) k)
3.6b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
4.4b	(* (* (* x 18.0) y) z)

rewrite40.0ms

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)
9.0ms	(* (* j 27.0) k)
0.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
22.0ms	(* (* (* x 18.0) y) z)

series3.0s

Counts

4 → 12

Calls

4 calls:

22.0ms	(* (* x 18.0) y)
20.0ms	(* (* j 27.0) k)
2.9s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* (* j 27.0) k))))
29.0ms	(* (* (* x 18.0) y) z)

simplify58.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (12.0ms)

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

prune381.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize21.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* x 18.0) y)
0.2b	(* j (* 27.0 k))
3.6b	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
4.4b	(* (* (* x 18.0) y) z)

rewrite37.0ms

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:

7.0ms	(* (* x 18.0) y)
6.0ms	(* j (* 27.0 k))
0.0ms	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
22.0ms	(* (* (* x 18.0) y) z)

series3.0s

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* x 18.0) y)
17.0ms	(* j (* 27.0 k))
2.9s	(fma t (- (* (* (* x 18.0) y) z) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
33.0ms	(* (* (* 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

prune379.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.9b

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt y)
0.6b	(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)))))
4.4b	(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)

rewrite205.0ms

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)))))
201.0ms	(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)

series3.5s

Counts

4 → 12

Calls

4 calls:

198.0ms	(cbrt y)
198.0ms	(cbrt y)
3.0s	(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)))))
56.0ms	(* (* (* (* x 18.0) (* (cbrt y) (cbrt y))) (cbrt y)) z)

simplify64.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (56.0ms)

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

prune648.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.9b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k))))
0.2b	(* j (* 27.0 k))
3.6b	(fma t (- (* (* z y) (* x 18.0)) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
4.2b	(* (* z y) (* x 18.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

3.0ms	(- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k))))
6.0ms	(* j (* 27.0 k))
0.0ms	(fma t (- (* (* z y) (* x 18.0)) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
13.0ms	(* (* z y) (* x 18.0))

series3.1s

Counts

4 → 12

Calls

4 calls:

97.0ms	(- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k))))
20.0ms	(* j (* 27.0 k))
2.9s	(fma t (- (* (* z y) (* x 18.0)) (* a 4.0)) (- (* b c) (fma x (* 4.0 i) (* j (* 27.0 k)))))
30.0ms	(* (* z y) (* x 18.0))

simplify60.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	395	627
1	1547	488
2	5002	488

prune321.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 2.9b

regimes1.0s

Accuracy

31.8% (2.4b remaining)

Error of 4.7b against oracle of 2.3b and baseline of 5.8b

bsearch266.0ms

Steps

Iters	Range		Point
7	1.2616975511295526e-207	1.316055524870703e-205	6.216162519181201e-206
7	-8.74334302503735e-109	-3.098806504709037e-110	-2.359730340784048e-109

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	38
1	61	38
2	61	38

end0.0ms

sample3.8s

Algorithm

intervals

Results

2.9s

16091×

body

valid