Details

sample123.0ms

Algorithm

intervals

Results

88.0ms

589×

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: 14.9b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* c t) (* i y))
5.4b	(* j (- (* c t) (* i y)))
6.0b	(* b (- (* c z) (* i a)))
7.4b	(* x (- (* y z) (* t a)))

rewrite35.0ms

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

series239.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (* c t) (* i y))
63.0ms	(* j (- (* c t) (* i y)))
67.0ms	(* b (- (* c z) (* i a)))
68.0ms	(* x (- (* y z) (* t a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 1 (13.0ms)

Iter	Nodes	Cost
0	478	643
1	1975	572
2	5002	572

prune532.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.1b

localize31.0ms

Local error

Found 4 expressions with local error:

5.4b	(* j (fma c t (- (* y i))))
6.0b	(* b (- (* c z) (* i a)))
7.4b	(* x (- (* y z) (* t a)))
50.4b	(fma (- y) i (* y i))

rewrite25.0ms

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

series229.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* j (fma c t (- (* y i))))
69.0ms	(* b (- (* c z) (* i a)))
69.0ms	(* x (- (* y z) (* t a)))
24.0ms	(fma (- y) i (* y i))

simplify52.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 1 (11.0ms)

Iter	Nodes	Cost
0	411	562
1	1680	493
2	5002	493

prune555.0ms

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 11.1b

localize31.0ms

Local error

Found 4 expressions with local error:

6.0b	(* b (- (* c z) (* i a)))
6.0b	(* b (- (* c z) (* i a)))
7.4b	(* x (- (* y z) (* t a)))
50.4b	(fma (- y) i (* y i))

rewrite35.0ms

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`
6×	`sub-neg` `associate-*r/` `prod-diff`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow-prod-down` `prod-exp` `*-commutative` `flip--` `cbrt-unprod` `unswap-sqr`
1×	`fma-udef`

Counts

4 → 94

Calls

4 calls:

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

series224.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(* b (- (* c z) (* i a)))
63.0ms	(* b (- (* c z) (* i a)))
70.0ms	(* x (- (* y z) (* t a)))
24.0ms	(fma (- y) i (* y i))

simplify41.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 1 (8.0ms)

Iter	Nodes	Cost
0	325	602
1	1305	532
2	5001	532

prune670.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.1b

localize38.0ms

Local error

Found 4 expressions with local error:

6.9b	(cbrt (- (* c z) (* i a)))
6.9b	(cbrt (- (* c z) (* i a)))
7.4b	(* x (- (* y z) (* t a)))
50.4b	(fma (- y) i (* y i))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 68

Calls

4 calls:

2.0ms	(cbrt (- (* c z) (* i a)))
2.0ms	(cbrt (- (* c z) (* i a)))
12.0ms	(* x (- (* y z) (* t a)))
0.0ms	(fma (- y) i (* y i))

series329.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt (- (* c z) (* i a)))
117.0ms	(cbrt (- (* c z) (* i a)))
70.0ms	(* x (- (* y z) (* t a)))
23.0ms	(fma (- y) i (* y i))

simplify109.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	357	542
1	1205	496
2	4350	484
3	5001	484

prune609.0ms

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 11.1b

regimes1.3s

Accuracy

5.9% (4.1b remaining)

Error of 12.5b against oracle of 8.4b and baseline of 12.8b

bsearch185.0ms

Steps

Iters	Range		Point
8	2.975059531632948e-207	1.2284337081449927e-203	8.066554338695772e-207
5	-6.243414601497811e-231	-2.1846869901506548e-231	-3.4404428017653185e-231

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	70	51
1	72	51
2	72	51

end0.0ms

sample3.7s

Algorithm

intervals

Results

2.8s

18903×

body

valid