Details

sample90.0ms

Algorithm

intervals

Results

48.0ms

621×

body

valid

simplify91.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* c a) (* y i))
3.1b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
4.9b	(* b (- (* c z) (* t i)))
5.6b	(* x (- (* y z) (* t a)))

rewrite66.0ms

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:

8.0ms	(- (* c a) (* y i))
0.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
26.0ms	(* b (- (* c z) (* t i)))
29.0ms	(* x (- (* y z) (* t a)))

series717.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* c a) (* y i))
542.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
66.0ms	(* b (- (* c z) (* t i)))
65.0ms	(* x (- (* y z) (* t a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	426	646
1	1675	568
2	5002	568

prune903.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 3.7b

localize26.0ms

Local error

Found 4 expressions with local error:

3.1b	(fma (- (* c a) (* y i)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* t i)))))
4.9b	(* b (- (* c z) (* t i)))
5.6b	(* x (fma y z (- (* a t))))
51.4b	(fma (- a) t (* a t))

rewrite253.0ms

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:

0.0ms	(fma (- (* c a) (* y i)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* t i)))))
26.0ms	(* b (- (* c z) (* t i)))
7.0ms	(* x (fma y z (- (* a t))))
0.0ms	(fma (- a) t (* a t))

series3.2s

Counts

4 → 12

Calls

4 calls:

3.1s	(fma (- (* c a) (* y i)) j (- (+ (* x (fma y z (- (* a t)))) (* x (fma (- a) t (* a t)))) (* b (- (* c z) (* t i)))))
67.0ms	(* b (- (* c z) (* t i)))
66.0ms	(* x (fma y z (- (* a t))))
25.0ms	(fma (- a) t (* a t))

simplify48.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	310	624
1	1230	538
2	5001	538

prune970.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.7b

localize26.0ms

Local error

Found 4 expressions with local error:

4.9b	(* b (- (* c z) (* t i)))
5.6b	(* x (* y z))
6.8b	(* x (- (* a t)))
51.4b	(fma (- a) t (* a t))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

26.0ms	(* b (- (* c z) (* t i)))
18.0ms	(* x (* y z))
12.0ms	(* x (- (* a t)))
0.0ms	(fma (- a) t (* a t))

series143.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* b (- (* c z) (* t i)))
22.0ms	(* x (* y z))
30.0ms	(* x (- (* a t)))
25.0ms	(fma (- a) t (* a t))

simplify60.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	348	416
1	1639	363
2	5001	360

prune1.1s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 2.7b

localize35.0ms

Local error

Found 4 expressions with local error:

12.1b	(cbrt (- (* a t)))
12.1b	(cbrt (- (* a t)))
12.1b	(cbrt (- (* a t)))
51.4b	(fma (- a) t (* a t))

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

18×	`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×	`distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `pow1/3`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

2.0ms	(cbrt (- (* a t)))
2.0ms	(cbrt (- (* a t)))
2.0ms	(cbrt (- (* a t)))
0.0ms	(fma (- a) t (* a t))

series326.0ms

Counts

4 → 12

Calls

4 calls:

104.0ms	(cbrt (- (* a t)))
100.0ms	(cbrt (- (* a t)))
96.0ms	(cbrt (- (* a t)))
25.0ms	(fma (- a) t (* a t))

simplify114.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 4 (108.0ms)

Iter	Nodes	Cost
0	111	368
1	215	340
2	629	316
3	2326	308
4	5001	292

prune1.2s

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 2.7b

regimes2.0s

Accuracy

12.8% (8.1b remaining)

Error of 11.3b against oracle of 3.3b and baseline of 12.5b

bsearch533.0ms

Steps

Iters	Range		Point
10	2.37411555039757e-81	9.829068020291528e-64	2.4343330912176048e-81
9	1.5555585354229587e-109	1.2989838861224217e-102	1.2789329666929744e-102
6	-4.094245006482956e+95	-9.909937794960255e+94	-1.1726227582677427e+95

simplify12.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	83	67
1	93	67
2	94	67
3	94	67

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.5s

19095×

body

valid