Details

sample127.0ms

Algorithm

intervals

Results

93.0ms

584×

body

valid

simplify92.0ms

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.2b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* y z) (* t a))
4.4b	(* x (- (* y z) (* t a)))
4.4b	(* b (- (* c z) (* i a)))
5.3b	(* j (- (* c t) (* i y)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

3.0ms	(- (* y z) (* t a))
12.0ms	(* x (- (* y z) (* t a)))
10.0ms	(* b (- (* c z) (* i a)))
10.0ms	(* j (- (* c t) (* i y)))

series235.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* y z) (* t a))
67.0ms	(* x (- (* y z) (* t a)))
66.0ms	(* b (- (* c z) (* i a)))
66.0ms	(* j (- (* c t) (* i y)))

simplify59.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	478	643
1	1976	572
2	5001	572

prune518.0ms

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 8.2b

localize28.0ms

Local error

Found 4 expressions with local error:

4.4b	(* x (fma y z (- (* a t))))
4.4b	(* b (- (* c z) (* i a)))
5.3b	(* j (- (* c t) (* i y)))
50.6b	(fma (- a) t (* a t))

rewrite27.0ms

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`
7×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `prod-diff` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`
2×	`flip3--` `flip--`

Counts

4 → 88

Calls

4 calls:

3.0ms	(* x (fma y z (- (* a t))))
10.0ms	(* b (- (* c z) (* i a)))
10.0ms	(* j (- (* c t) (* i y)))
0.0ms	(fma (- a) t (* a t))

series233.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* x (fma y z (- (* a t))))
67.0ms	(* b (- (* c z) (* i a)))
69.0ms	(* j (- (* c t) (* i y)))
26.0ms	(fma (- a) t (* a t))

simplify50.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	412	562
1	1685	493
2	5001	493

prune548.0ms

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 8.2b

localize31.0ms

Local error

Found 4 expressions with local error:

4.4b	(* b (- (* c z) (* i a)))
5.3b	(* j (fma c t (- (* y i))))
47.0b	(fma (- y) i (* y i))
50.6b	(fma (- a) t (* a t))

rewrite16.0ms

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:

10.0ms	(* b (- (* c z) (* i a)))
3.0ms	(* j (fma c t (- (* y i))))
0.0ms	(fma (- y) i (* y i))
1.0ms	(fma (- a) t (* a t))

series193.0ms

Counts

4 → 12

Calls

4 calls:

65.0ms	(* b (- (* c z) (* i a)))
72.0ms	(* j (fma c t (- (* y i))))
25.0ms	(fma (- y) i (* y i))
31.0ms	(fma (- a) t (* a t))

simplify116.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	282	428
1	1101	373
2	4513	373
3	5001	373

prune550.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.2b

localize43.0ms

Local error

Found 4 expressions with local error:

5.3b	(* j (fma c t (- (* y i))))
47.0b	(fma (- y) i (* y i))
49.4b	(fma (- a) i (* a i))
50.6b	(fma (- a) t (* a t))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 52

Calls

4 calls:

3.0ms	(* j (fma c t (- (* y i))))
0.0ms	(fma (- y) i (* y i))
0.0ms	(fma (- a) i (* a i))
0.0ms	(fma (- a) t (* a t))

series158.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* j (fma c t (- (* y i))))
31.0ms	(fma (- y) i (* y i))
25.0ms	(fma (- a) i (* a i))
26.0ms	(fma (- a) t (* a t))

simplify59.0ms

Algorithm

egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 3 (55.0ms)

Iter	Nodes	Cost
0	148	294
1	513	253
2	2122	253
3	5001	229

prune434.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 8.2b

regimes1.1s

Accuracy

5.8% (4.0b remaining)

Error of 12.5b against oracle of 8.6b and baseline of 12.8b

bsearch246.0ms

Steps

Iters	Range		Point
7	8.078646496341031e-220	2.9067844856203846e-218	2.017536666766921e-218
7	-1.474875275850162e-141	-7.322352171897339e-143	-8.80663594933688e-143

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	87	87
1	91	87
2	91	87

end0.0ms

sample4.0s

Algorithm

intervals

Results

3.1s

19242×

body

valid