Details

sample36.0ms

Algorithm

intervals

Results

19.0ms

256×

body

valid

simplify44.0ms

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: 24.6b

Counts

2 → 2

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)
0.3b	(/ (- 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))

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))

series527.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
29.0ms	(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)))
177.0ms	(/ (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 (60.0ms)

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

prune675.0ms

Filtered

164 candidates to 126 candidates (76.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	160	4	164
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	161	5	166

Merged error: 0.0b

Counts

166 → 5

localize26.0ms

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) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
0.3b	(/ (- x 2.0) (/ 1 (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
23.9b	(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

700×	`times-frac`
399×	`add-sqr-sqrt` `*-un-lft-identity`
309×	`add-cube-cbrt`
60×	`associate-/r*`
45×	`distribute-lft-out--` `difference-of-squares`
36×	`add-exp-log`
31×	`div-inv`
22×	`div-exp`
20×	`add-cbrt-cube`
11×	`associate-/l*`
10×	`cbrt-undiv`
8×	`associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `rec-exp` `1-exp` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num`
2×	`associate-/l/`
1×	`flip3--` `pow-flip` `div-sub` `flip--` `fma-udef` `inv-pow`

Counts

4 → 412

Calls

4 calls:

1.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
6.0ms	(/ 1 (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
16.0ms	(/ (- x 2.0) (/ 1 (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
3.0ms	(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

series746.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
179.0ms	(/ 1 (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)))
290.0ms	(/ (- x 2.0) (/ 1 (/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))))
251.0ms	(/ (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

simplify147.0ms

Algorithm

egg-herbie

Counts

424 → 424

Iterations

Useful iterations: 1 (39.0ms)

Iter	Nodes	Cost
0	1714	9283
1	5001	8626

prune1.4s

Filtered

424 candidates to 247 candidates (58.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	422	2	424
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	424	5	429

Merged error: 0b

Counts

429 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

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) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))))
0.4b	(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
23.8b	(* (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)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
32×	`add-exp-log`
27×	`*-un-lft-identity`
25×	`times-frac`
22×	`add-cube-cbrt`
20×	`add-cbrt-cube`
13×	`associate-r`
11×	`div-exp`
8×	`prod-exp` `associate-/l*`
7×	`pow1`
6×	`cbrt-undiv`
4×	`expm1-log1p-u` `associate-/r*` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `1-exp` `associate-l` `div-inv` `unswap-sqr`
2×	`frac-2neg` `associate-*r/` `clear-num` `associate-/r/` `un-div-inv` `associate-/l/` `distribute-lft-out--` `difference-of-squares`
1×	`flip3--` `pow-flip` `div-sub` `pow-prod-down` `*-commutative` `flip--` `fma-udef` `inv-pow`

Counts

4 → 117

Calls

4 calls:

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) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))))
3.0ms	(/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))
7.0ms	(* (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)))

series597.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
291.0ms	(/ (- 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))))
104.0ms	(/ 1 (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) (/ 1 (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))

simplify72.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	447	1412
1	1813	1191
2	5002	1161

prune418.0ms

Filtered

129 candidates to 80 candidates (62.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	129	0	129
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	129	5	134

Merged error: 0b

Counts

134 → 5

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
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)
25.3b	(/ (* (- x 2.0) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`times-frac` `associate-/r*` `fma-udef`
2×	`cbrt-undiv` `div-exp` `associate-*l/` `associate-/l/`
1×	`flip3--` `frac-2neg` `prod-exp` `clear-num` `flip--` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

4 → 55

Calls

4 calls:

1.0ms	(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
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)
7.0ms	(/ (* (- x 2.0) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

series417.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606)
37.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
26.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
295.0ms	(/ (* (- x 2.0) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)) (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))

simplify41.0ms

Algorithm

egg-herbie

Counts

67 → 67

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	319	579
1	1221	485
2	5001	479

prune268.0ms

Filtered

67 candidates to 54 candidates (80.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	67	0	67
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	67	5	72

Merged error: 0b

Counts

72 → 5

regimes209.0ms

Accuracy

96.8% (0.8b remaining)

Error of 0.9b against oracle of 0.0b and baseline of 25.2b

bsearch242.0ms

Steps

Iters	Range		Point
9	9.198045984357059e+49	1.0694899092935235e+55	4.244262775536536e+54
8	-2.1811136181260466e+28	-4.2779340922130005e+24	-7.202435875699678e+26

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	16
1	43	16

end0.0ms

sample810.0ms

Algorithm

intervals

Results

623.0ms

8005×

body

valid