Details

sample36.0ms

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

prune12.0ms

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: 23.7b

Counts

2 → 2

localize19.0ms

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)
0.5b	(/ (- 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)))
23.0b	(/ (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))

rewrite23.0ms

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))

series495.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
24.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
267.0ms	(/ (- 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)))
167.0ms	(/ (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 (56.0ms)

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

prune741.0ms

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

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.2b	(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
2.1b	(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
22.9b	(/ (/ (- 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)))

rewrite55.0ms

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))
19.0ms	(/ (/ (- 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:

24.0ms	(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))
88.0ms	(/ (- x 2.0) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
284.0ms	(/ (/ (- 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)))

simplify140.0ms

Algorithm

egg-herbie

Counts

401 → 401

Iterations

Useful iterations: 1 (36.0ms)

Iter	Nodes	Cost
0	1692	8831
1	5002	8373

prune1.4s

Filtered

401 candidates to 224 candidates (55.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	400	1	401
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	401	6	407

Merged error: 0.0b

Counts

407 → 6

localize24.0ms

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)
0.5b	(/ (- 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)))
23.0b	(/ (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))

rewrite20.0ms

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))

series525.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
31.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
281.0ms	(/ (- 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)))
176.0ms	(/ (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))

simplify97.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (58.0ms)

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

prune688.0ms

Filtered

164 candidates to 122 candidates (74.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	164	6	170

Merged error: 0.0b

Counts

170 → 6

localize24.0ms

Local error

Found 4 expressions with local error:

19.6b	(cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894))
19.6b	(cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894))
19.6b	(cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894))
23.0b	(/ (fma (* (* (cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)) (cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894))) (cbrt (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))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

15×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`cbrt-prod` `times-frac`
6×	`add-exp-log` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-/r` `associate-/l`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 68

Calls

4 calls:

1.0ms	(cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894))
1.0ms	(cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894))
5.0ms	(cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894))
3.0ms	(/ (fma (* (* (cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)) (cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894))) (cbrt (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))

series588.0ms

Counts

4 → 12

Calls

4 calls:

134.0ms	(cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894))
139.0ms	(cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894))
135.0ms	(cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894))
180.0ms	(/ (fma (* (* (cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)) (cbrt (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894))) (cbrt (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))

simplify137.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 3 (114.0ms)

Iter	Nodes	Cost
0	238	1319
1	679	1201
2	3490	1127
3	5002	1081

prune450.0ms

Filtered

80 candidates to 68 candidates (85.0%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	80	6	86

Merged error: 0.0b

Counts

86 → 6

regimes439.0ms

Accuracy

95.7% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 25.0b

bsearch223.0ms

Steps

Iters	Range		Point
7	555429331548894.9	20657595575902116.0	20293546711004988.0
9	-6.51773788957297e+22	-3.7127638754609146e+17	-4.394796063145287e+22

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	42	16
1	42	16

end0.0ms

sample655.0ms

Algorithm

intervals

Results

483.0ms

8009×

body

valid