Details

sample81.0ms

Algorithm

intervals

Results

44.0ms

644×

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

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.9b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* c a) (* y i))
4.5b	(* x (- (* y z) (* t a)))
6.0b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
7.2b	(* b (- (* c z) (* t i)))

rewrite29.0ms

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:

3.0ms	(- (* c a) (* y i))
13.0ms	(* x (- (* y z) (* t a)))
0.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
11.0ms	(* b (- (* c z) (* t i)))

series734.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* c a) (* y i))
69.0ms	(* x (- (* y z) (* t a)))
565.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
66.0ms	(* b (- (* c z) (* t i)))

simplify55.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	426	646
1	1670	568
2	5001	568

prune415.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.7b

localize25.0ms

Local error

Found 4 expressions with local error:

6.0b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* (* b (* (cbrt (- (* c z) (* t i))) (cbrt (- (* c z) (* t i))))) (cbrt (- (* c z) (* t i))))))
9.6b	(cbrt (- (* c z) (* t i)))
9.6b	(cbrt (- (* c z) (* t i)))
9.6b	(cbrt (- (* c z) (* t i)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

0.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* (* b (* (cbrt (- (* c z) (* t i))) (cbrt (- (* c z) (* t i))))) (cbrt (- (* c z) (* t i))))))
2.0ms	(cbrt (- (* c z) (* t i)))
2.0ms	(cbrt (- (* c z) (* t i)))
3.0ms	(cbrt (- (* c z) (* t i)))

series914.0ms

Counts

4 → 12

Calls

4 calls:

563.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* (* b (* (cbrt (- (* c z) (* t i))) (cbrt (- (* c z) (* t i))))) (cbrt (- (* c z) (* t i))))))
119.0ms	(cbrt (- (* c z) (* t i)))
115.0ms	(cbrt (- (* c z) (* t i)))
116.0ms	(cbrt (- (* c z) (* t i)))

simplify78.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 3 (62.0ms)

Iter	Nodes	Cost
0	265	780
1	715	704
2	2165	671
3	5002	667

prune449.0ms

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 5.7b

localize29.0ms

Local error

Found 4 expressions with local error:

7.2b	(* b (- (* c z) (* t i)))
8.0b	(cbrt (- (* c a) (* y i)))
8.0b	(cbrt (- (* c a) (* y i)))
8.0b	(cbrt (- (* c a) (* y i)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

10.0ms	(* b (- (* c z) (* t i)))
2.0ms	(cbrt (- (* c a) (* y i)))
2.0ms	(cbrt (- (* c a) (* y i)))
3.0ms	(cbrt (- (* c a) (* y i)))

series421.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(* b (- (* c z) (* t i)))
122.0ms	(cbrt (- (* c a) (* y i)))
110.0ms	(cbrt (- (* c a) (* y i)))
111.0ms	(cbrt (- (* c a) (* y i)))

simplify109.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	336	646
1	1154	598
2	4176	580
3	5001	580

prune506.0ms

Pruning

17 alts after pruning (16 fresh and 1 done)

Merged error: 5.7b

localize31.0ms

Local error

Found 4 expressions with local error:

9.6b	(cbrt (- (* c z) (* t i)))
9.6b	(cbrt (- (* c z) (* t i)))
9.6b	(cbrt (- (* c z) (* t i)))
9.6b	(cbrt (- (* c z) (* t i)))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
8×	`add-sqr-sqrt` `add-cube-cbrt` `cbrt-div` `*-un-lft-identity`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `flip3--` `pow1/3` `add-cbrt-cube` `flip--` `log1p-expm1-u` `add-log-exp`

Counts

4 → 60

Calls

4 calls:

2.0ms	(cbrt (- (* c z) (* t i)))
5.0ms	(cbrt (- (* c z) (* t i)))
2.0ms	(cbrt (- (* c z) (* t i)))
2.0ms	(cbrt (- (* c z) (* t i)))

series454.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(cbrt (- (* c z) (* t i)))
110.0ms	(cbrt (- (* c z) (* t i)))
113.0ms	(cbrt (- (* c z) (* t i)))
116.0ms	(cbrt (- (* c z) (* t i)))

simplify100.0ms

Algorithm

egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 4 (89.0ms)

Iter	Nodes	Cost
0	191	616
1	539	580
2	1627	556
3	3857	552
4	5002	540

prune503.0ms

Pruning

17 alts after pruning (15 fresh and 2 done)

Merged error: 5.7b

regimes898.0ms

Accuracy

2.6% (7.8b remaining)

Error of 12.2b against oracle of 4.4b and baseline of 12.4b

bsearch154.0ms

Steps

Iters	Range		Point
5	6.3883688420125556e-242	1.4617548519227034e-241	9.801974584001369e-242
9	-1.3047534056209266e-159	-1.4222811373456052e-168	-5.2318033429786034e-166

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	51
1	51	51

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s

19228×

body

valid