Details

sample18.0ms

Algorithm

intervals

Results

8.0ms

324×

body

valid

simplify160.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 8 (57.0ms)

Iter	Nodes	Cost
0	14	4
1	34	4
2	92	4
3	232	4
4	491	4
5	785	4
6	1115	4
7	1482	4
8	2218	3
9	3349	3
10	4819	3
11	5001	3

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	0	1	1
Fresh	1	0	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 2.6b

Counts

2 → 1

localize7.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma (- y 1.0) z 1.0)
2.4b	(* (fma (- y 1.0) z 1.0) x)

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 30

Calls

2 calls:

1.0ms	(fma (- y 1.0) z 1.0)
4.0ms	(* (fma (- y 1.0) z 1.0) x)

series85.0ms

Counts

2 → 6

Calls

2 calls:

29.0ms	(fma (- y 1.0) z 1.0)
56.0ms	(* (fma (- y 1.0) z 1.0) x)

simplify56.0ms

Algorithm

egg-herbie

Counts

36 → 36

Iterations

Useful iterations: 2 (17.0ms)

Iter	Nodes	Cost
0	108	166
1	323	137
2	1922	133
3	5003	133

prune93.0ms

Filtered

36 candidates to 26 candidates (72.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	29	7	36
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	29	8	37

Merged error: 2.5b

Counts

37 → 8

localize11.0ms

Local error

Found 4 expressions with local error:

2.4b	(* (* (* (cbrt (fma (- y 1.0) z 1.0)) (cbrt (fma (- y 1.0) z 1.0))) (cbrt (fma (- y 1.0) z 1.0))) x)
2.6b	(cbrt (fma (- y 1.0) z 1.0))
2.6b	(cbrt (fma (- y 1.0) z 1.0))
2.6b	(cbrt (fma (- y 1.0) z 1.0))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log`
9×	`cbrt-prod` `add-cbrt-cube`
8×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r`
1×	`associate-l` `*-commutative`

Counts

4 → 62

Calls

4 calls:

13.0ms	(* (* (* (cbrt (fma (- y 1.0) z 1.0)) (cbrt (fma (- y 1.0) z 1.0))) (cbrt (fma (- y 1.0) z 1.0))) x)
1.0ms	(cbrt (fma (- y 1.0) z 1.0))
1.0ms	(cbrt (fma (- y 1.0) z 1.0))
1.0ms	(cbrt (fma (- y 1.0) z 1.0))

series373.0ms

Counts

4 → 12

Calls

4 calls:

56.0ms	(* (* (* (cbrt (fma (- y 1.0) z 1.0)) (cbrt (fma (- y 1.0) z 1.0))) (cbrt (fma (- y 1.0) z 1.0))) x)
105.0ms	(cbrt (fma (- y 1.0) z 1.0))
105.0ms	(cbrt (fma (- y 1.0) z 1.0))
106.0ms	(cbrt (fma (- y 1.0) z 1.0))

simplify117.0ms

Algorithm

egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 3 (108.0ms)

Iter	Nodes	Cost
0	273	779
1	963	634
2	4839	536
3	5001	527

prune236.0ms

Filtered

74 candidates to 60 candidates (81.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	3	3	6
Picked	1	0	1
Done	0	1	1
Total	77	5	82

Merged error: 0.0b

Counts

82 → 5

localize8.0ms

Local error

Found 1 expressions with local error:

1.4b	(fma (* x z) (- y 1.0) (* 1.0 x))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

1.0ms

(fma (* x z) (- y 1.0) (* 1.0 x))

series52.0ms

Counts

1 → 3

Calls

1 calls:

52.0ms

(fma (* x z) (- y 1.0) (* 1.0 x))

simplify123.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 3 (26.0ms)

Iter	Nodes	Cost
0	48	80
1	125	65
2	491	62
3	3197	61
4	5001	61

prune45.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	11	2	13
Fresh	2	1	3
Picked	1	0	1
Done	0	1	1
Total	14	4	18

Merged error: 0.0b

Counts

18 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* (* x z) (- y 1.0)) (* 1.0 x))
2.3b	(* (* x z) (- y 1.0))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

36×	`prod-diff`
29×	`add-sqr-sqrt` `*-un-lft-identity`
27×	`add-cube-cbrt`
22×	`distribute-rgt-in` `associate-+l+` `distribute-lft-in`
7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-r`
4×	`sub-neg` `add-log-exp`
3×	`pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
1×	`+-commutative` `flip3--` `fma-def` `flip3-+` `associate-l` `sum-log` `*-commutative` `flip--` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

2 → 82

Calls

2 calls:

11.0ms	(+ (* (* x z) (- y 1.0)) (* 1.0 x))
9.0ms	(* (* x z) (- y 1.0))

series121.0ms

Counts

2 → 6

Calls

2 calls:

71.0ms	(+ (* (* x z) (- y 1.0)) (* 1.0 x))
50.0ms	(* (* x z) (- y 1.0))

simplify68.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (59.0ms)

Iter	Nodes	Cost
0	411	726
1	1762	496
2	5002	490

prune189.0ms

Filtered

88 candidates to 54 candidates (61.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	85	3	88
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	86	6	92

Merged error: 0.0b

Counts

92 → 6

regimes105.0ms

Accuracy

93.5% (0.1b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 1.6b

bsearch93.0ms

Steps

Iters	Range		Point
9	2.3915553452179933e-28	2.8503253665590827e-23	2.4536014589056785e-26
9	-1.069539501402524e+61	-2.452355857273731e+54	-4.019043657210878e+54

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	8
1	25	8

end0.0ms

sample470.0ms

Algorithm

intervals

Results

258.0ms

10169×

body

valid