Details

sample34.0ms

Algorithm

intervals

Results

17.0ms

386×

body

valid

simplify25.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 5 (19.0ms)

Iter	Nodes	Cost
0	26	7
1	68	4
2	140	4
3	200	4
4	214	4
5	217	3
6	217	3

prune10.0ms

Filtered

1 candidates to 1 candidates (100.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 0.0b

Counts

2 → 2

localize9.0ms

Local error

Found 1 expressions with local error:

2.4b	(fma (fma a b y) z (fma a t 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 (fma a b y) z (fma a t x))

series95.0ms

Counts

1 → 3

Calls

1 calls:

94.0ms

(fma (fma a b y) z (fma a t x))

simplify75.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 2 (9.0ms)

Iter	Nodes	Cost
0	44	58
1	93	51
2	307	49
3	2032	49
4	5002	49

prune55.0ms

Filtered

13 candidates to 12 candidates (92.3%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	10	3	13
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	10	5	15

Merged error: 0.0b

Counts

15 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(* (cbrt (fma (fma a b y) z (fma a t x))) (cbrt (fma (fma a b y) z (fma a t x))))
2.4b	(fma (fma a b y) z (fma a t x))
2.4b	(fma (fma a b y) z (fma a t x))
2.4b	(fma (fma a b y) z (fma a t x))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
8×	`add-cbrt-cube`
6×	`add-exp-log` `pow1/3` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative`

Counts

4 → 75

Calls

4 calls:

6.0ms	(* (cbrt (fma (fma a b y) z (fma a t x))) (cbrt (fma (fma a b y) z (fma a t x))))
1.0ms	(fma (fma a b y) z (fma a t x))
1.0ms	(fma (fma a b y) z (fma a t x))
1.0ms	(fma (fma a b y) z (fma a t x))

series714.0ms

Counts

4 → 12

Calls

4 calls:

430.0ms	(* (cbrt (fma (fma a b y) z (fma a t x))) (cbrt (fma (fma a b y) z (fma a t x))))
95.0ms	(fma (fma a b y) z (fma a t x))
95.0ms	(fma (fma a b y) z (fma a t x))
94.0ms	(fma (fma a b y) z (fma a t x))

simplify111.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (98.0ms)

Iter	Nodes	Cost
0	205	707
1	728	625
2	3539	531
3	5002	524

prune298.0ms

Filtered

87 candidates to 66 candidates (75.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	87	5	92

Merged error: 0.0b

Counts

92 → 5

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))
0.0b	(+ (+ x (* y z)) (* t a))
7.4b	(* (* a z) b)

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

117×	`*-un-lft-identity`
73×	`distribute-lft-out`
62×	`associate-l`
17×	`add-log-exp`
16×	`add-sqr-sqrt`
14×	`fma-def`
9×	`add-cube-cbrt` `sum-log`
8×	`pow1` `add-exp-log` `associate-+l+` `add-cbrt-cube`
6×	`associate-r`
5×	`+-commutative`
4×	`unswap-sqr`
3×	`expm1-log1p-u` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`flip3-+` `*-commutative` `flip-+`

Counts

3 → 109

Calls

3 calls:

30.0ms	(+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))
14.0ms	(+ (+ x (* y z)) (* t a))
10.0ms	(* (* a z) b)

series164.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(+ (+ (+ x (* y z)) (* t a)) (* (* a z) b))
50.0ms	(+ (+ x (* y z)) (* t a))
27.0ms	(* (* a z) b)

simplify64.0ms

Algorithm

egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	347	555
1	1619	468
2	5001	436

prune271.0ms

Filtered

118 candidates to 69 candidates (58.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	114	4	118
Fresh	2	0	2
Picked	1	0	1
Done	0	2	2
Total	117	6	123

Merged error: 0.0b

Counts

123 → 6

localize10.0ms

Local error

Found 2 expressions with local error:

0.0b	(fma z y (* a t))
3.4b	(fma a (* z b) (fma z y (* a t)))

rewrite2.0ms

Algorithm

rewrite-expression-head

Rules

2×	`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

2 → 20

Calls

2 calls:

1.0ms	(fma z y (* a t))
1.0ms	(fma a (* z b) (fma z y (* a t)))

series106.0ms

Counts

2 → 6

Calls

2 calls:

42.0ms	(fma z y (* a t))
64.0ms	(fma a (* z b) (fma z y (* a t)))

simplify155.0ms

Algorithm

egg-herbie

Counts

26 → 26

Iterations

Useful iterations: 4 (151.0ms)

Iter	Nodes	Cost
0	48	111
1	139	97
2	645	97
3	4091	97
4	5001	95

prune92.0ms

Filtered

26 candidates to 24 candidates (92.3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	26	0	26
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	26	6	32

Merged error: 0.0b

Counts

32 → 6

regimes236.0ms

Accuracy

87.1% (0.3b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 2.4b

bsearch118.0ms

Steps

Iters	Range		Point
10	1.3745571897142734e-118	9.131830933029053e-100	2.882103223667287e-106
9	-6.431558208262041e+28	-5.336323348079087e+20	-7.706728458325138e+20

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	8
1	26	8

end0.0ms

sample845.0ms

Algorithm

intervals

Results

451.0ms

11765×

body

valid