Details

sample75.0ms

Algorithm

intervals

Results

40.0ms

577×

body

valid

simplify88.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	47	14
1	110	13
2	335	13
3	1059	13
4	3442	13
5	5001	13

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* c z) (* i a))
3.8b	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
4.7b	(* b (- (* c z) (* i a)))
5.2b	(* x (- (* y z) (* t a)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
8×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l` `add-log-exp`
5×	`sub-neg` `prod-diff`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-neg` `diff-log` `fma-udef`

Counts

4 → 82

Calls

4 calls:

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

series779.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* c z) (* i a))
594.0ms	(fma (- (* c t) (* i y)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* i a)))))
72.0ms	(* b (- (* c z) (* i a)))
73.0ms	(* x (- (* y z) (* t a)))

simplify49.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (10.0ms)

Iter	Nodes	Cost
0	373	645
1	1485	568
2	5001	568

prune696.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 3.9b

localize26.0ms

Local error

Found 4 expressions with local error:

3.8b	(fma (- (* c t) (* i y)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* i a)))))
4.7b	(* b (- (* c z) (* i a)))
5.2b	(* x (fma y z (- (* a t))))
48.6b	(fma (- a) t (* a t))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

1.0ms	(fma (- (* c t) (* i y)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* i a)))))
6.0ms	(* b (- (* c z) (* i a)))
4.0ms	(* x (fma y z (- (* a t))))
1.0ms	(fma (- a) t (* a t))

series3.7s

Counts

4 → 12

Calls

4 calls:

3.6s	(fma (- (* c t) (* i y)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* i a)))))
72.0ms	(* b (- (* c z) (* i a)))
78.0ms	(* x (fma y z (- (* a t))))
29.0ms	(fma (- a) t (* a t))

simplify43.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	315	624
1	1247	538
2	5002	538

prune452.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 3.9b

localize26.0ms

Local error

Found 4 expressions with local error:

4.7b	(* (- (* c t) (* i y)) j)
4.7b	(* b (- (* c z) (* i a)))
5.2b	(* x (fma y z (- (* a t))))
48.6b	(fma (- a) t (* a t))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `add-exp-log` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
9×	`associate-r` `associate-l`
4×	`distribute-rgt-in` `expm1-log1p-u` `distribute-lft-in` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
2×	`sub-neg` `flip3--` `associate-r/` `prod-diff` `associate-l/` `flip--`

Counts

4 → 82

Calls

4 calls:

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

series239.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* (- (* c t) (* i y)) j)
69.0ms	(* b (- (* c z) (* i a)))
71.0ms	(* x (fma y z (- (* a t))))
32.0ms	(fma (- a) t (* a t))

simplify49.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	388	526
1	1514	457
2	5002	457

prune526.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 3.3b

localize31.0ms

Local error

Found 4 expressions with local error:

7.5b	(cbrt (fma y z (- (* a t))))
7.5b	(cbrt (fma y z (- (* a t))))
7.5b	(cbrt (fma y z (- (* a t))))
48.6b	(fma (- a) t (* a t))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
1×	`fma-udef`

Counts

4 → 49

Calls

4 calls:

1.0ms	(cbrt (fma y z (- (* a t))))
2.0ms	(cbrt (fma y z (- (* a t))))
1.0ms	(cbrt (fma y z (- (* a t))))
1.0ms	(fma (- a) t (* a t))

series429.0ms

Counts

4 → 12

Calls

4 calls:

133.0ms	(cbrt (fma y z (- (* a t))))
131.0ms	(cbrt (fma y z (- (* a t))))
136.0ms	(cbrt (fma y z (- (* a t))))
28.0ms	(fma (- a) t (* a t))

simplify112.0ms

Algorithm

egg-herbie

Counts

61 → 61

Iterations

Useful iterations: 4 (107.0ms)

Iter	Nodes	Cost
0	141	422
1	329	388
2	1006	370
3	3314	359
4	5001	350

prune431.0ms

Pruning

22 alts after pruning (21 fresh and 1 done)

Merged error: 3.3b

regimes1.4s

Accuracy

-4.9% (8.4b remaining)

Error of 12.7b against oracle of 4.3b and baseline of 12.3b

bsearch188.0ms

Steps

Iters	Range		Point
4	3.252789471393584e-124	5.021907344406643e-124	3.288698165822717e-124
10	-2.5799640052418466e-113	-3.3117496423123305e-126	-3.373588334677838e-126

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	39
1	68	39
2	68	39

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s

18962×

body

valid