Details

sample37.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify43.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	62	11
1	154	11
2	503	11
3	1840	11
4	5003	11

prune13.0ms

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: 24.7b

Counts

2 → 2

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
0.1b	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.3b	(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
23.9b	(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

128×	`times-frac`
96×	`add-sqr-sqrt` `*-un-lft-identity`
68×	`add-cube-cbrt`
16×	`associate-/r*`
14×	`distribute-lft-out--` `difference-of-squares`
11×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv` `associate-/l*`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `fma-udef` `associate-/l/`
1×	`flip3--` `div-sub` `associate-/r/` `flip--`

Counts

4 → 152

Calls

4 calls:

1.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
1.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
9.0ms	(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
3.0ms	(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series716.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
26.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
284.0ms	(/ (- x 2.0) (/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
368.0ms	(/ (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify89.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	674	2773
1	2618	2640
2	5001	2638

prune716.0ms

Filtered

164 candidates to 126 candidates (76.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	159	5	164
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	160	6	166

Merged error: 0.0b

Counts

166 → 6

localize23.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
7.0b	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
16.3b	(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
20.8b	(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

276×	`times-frac`
160×	`add-sqr-sqrt`
158×	`add-cube-cbrt` `*-un-lft-identity`
150×	`sqrt-prod`
28×	`associate-/r*`
11×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv` `associate-/l*`
6×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `clear-num`
1×	`associate-/r/`

Counts

4 → 248

Calls

4 calls:

1.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
5.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
10.0ms	(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
4.0ms	(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

series750.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
101.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
178.0ms	(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
369.0ms	(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))

simplify137.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	660	6381
1	3118	5897
2	5001	5794

prune821.0ms

Filtered

260 candidates to 140 candidates (53.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	259	1	260
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	260	6	266

Merged error: 0.0b

Counts

266 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

7.0b	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
15.5b	(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
15.5b	(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
16.3b	(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))) (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

5352×	`times-frac`
4529×	`sqrt-prod`
2437×	`add-sqr-sqrt`
2432×	`add-cube-cbrt` `*-un-lft-identity`
283×	`associate-/r*`
71×	`div-inv`
13×	`add-exp-log` `add-cbrt-cube`
9×	`pow1` `sqrt-pow1`
6×	`cbrt-undiv` `div-exp` `associate-/l*`
5×	`rem-sqrt-square` `pow1/2`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
1×	`frac-2neg` `clear-num` `associate-/r/`

Counts

4 → 2063

Calls

4 calls:

2.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
2.0ms	(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
2.0ms	(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
78.0ms	(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))) (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))))

series572.0ms

Counts

4 → 12

Calls

4 calls:

100.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
147.0ms	(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
146.0ms	(sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
178.0ms	(/ (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))) (sqrt (sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))))

simplify1.1s

Algorithm

egg-herbie

Counts

2075 → 2075

Iterations

Useful iterations: 1 (90.0ms)

Iter	Nodes	Cost
0	4353	98477
1	5002	92209

prune4.1s

Filtered

2075 candidates to 535 candidates (25.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	2075	0	2075
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	2075	6	2081

Merged error: 0.0b

Counts

2081 → 6

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.1b	(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
1.4b	(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
24.0b	(/ (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

rewrite56.0ms

Algorithm

rewrite-expression-head

Rules

661×	`times-frac`
380×	`add-sqr-sqrt` `*-un-lft-identity`
288×	`add-cube-cbrt`
46×	`distribute-lft-out--` `difference-of-squares`
37×	`div-inv`
32×	`add-exp-log`
27×	`associate-/l*`
20×	`add-cbrt-cube`
19×	`div-exp` `associate-/r*`
10×	`cbrt-undiv`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `div-sub` `clear-num` `associate-/l/`
1×	`flip3--` `pow-flip` `associate-/r/` `flip--` `fma-udef` `inv-pow`

Counts

4 → 389

Calls

4 calls:

1.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
3.0ms	(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
6.0ms	(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
15.0ms	(/ (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

series492.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
95.0ms	(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
90.0ms	(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
282.0ms	(/ (/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

simplify134.0ms

Algorithm

egg-herbie

Counts

401 → 401

Iterations

Useful iterations: 1 (34.0ms)

Iter	Nodes	Cost
0	1692	8831
1	5002	8373

prune1.3s

Filtered

401 candidates to 224 candidates (55.9%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	399	2	401
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	401	6	407

Merged error: 0b

Counts

407 → 6

regimes299.0ms

Accuracy

95.4% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 24.5b

bsearch212.0ms

Steps

Iters	Range		Point
5	1236178698.9405453	3048118974.682059	3005568268.0445433
10	-1.3002308350545781e+28	-1604508521047215.5	-1.1550559361478097e+28

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	60	22
1	60	22

end0.0ms

sample667.0ms

Algorithm

intervals

Results

494.0ms

8007×

body

valid