Details

sample39.0ms

Algorithm

intervals

Results

21.0ms

256×

body

valid

simplify45.0ms

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

prune14.0ms

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: 27.9b

Counts

2 → 2

localize22.0ms

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)
0.4b	(/ (- 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)))
27.1b	(/ (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))

rewrite25.0ms

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)
10.0ms	(/ (- 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))

series522.0ms

Counts

4 → 12

Calls

4 calls:

39.0ms	(fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894)
26.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
280.0ms	(/ (- 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))

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

prune804.0ms

Filtered

164 candidates to 126 candidates (76.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	158	6	164
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	159	7	166

Merged error: 0.0b

Counts

166 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

10.3b	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
10.3b	(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))))
23.8b	(/ (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)))

rewrite32.0ms

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:

2.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
2.0ms	(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)))

series766.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
104.0ms	(sqrt (fma (fma (fma (+ x 43.3400022514) x 263.505074721) x 313.399215894) x 47.066876606))
182.0ms	(/ (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))))
377.0ms	(/ (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)))

simplify144.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	660	6379
1	3145	5897
2	5002	5794

prune940.0ms

Filtered

260 candidates to 139 candidates (53.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	260	0	260
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	260	7	267

Merged error: 0.0b

Counts

267 → 7

localize24.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
0.4b	(/ (- x 2.0) (/ (fma (fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3))) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
9.5b	(fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3)))
27.0b	(/ (fma (fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3))) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

rewrite22.0ms

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 4.16438922228 78.6994924154) x 137.519416416)
10.0ms	(/ (- x 2.0) (/ (fma (fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3))) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
1.0ms	(fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3)))
3.0ms	(/ (fma (fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3))) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

series496.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(fma (fma x 4.16438922228 78.6994924154) x 137.519416416)
272.0ms	(/ (- x 2.0) (/ (fma (fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3))) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z)))
34.0ms	(fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3)))
165.0ms	(/ (fma (fma 43.3400022514 (pow x 2) (fma 263.505074721 x (pow x 3))) x 47.066876606) (fma (fma (fma (fma x 4.16438922228 78.6994924154) x 137.519416416) x y) x z))

simplify91.0ms

Algorithm

egg-herbie

Counts

164 → 164

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	664	2998
1	2638	2853
2	5002	2851

prune831.0ms

Filtered

164 candidates to 123 candidates (75.0%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	164	0	164
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	164	7	171

Merged error: 0.0b

Counts

171 → 7

localize25.0ms

Local error

Found 4 expressions with local error:

0.7b	(cbrt (- x 2.0))
0.7b	(cbrt (- x 2.0))
0.7b	(cbrt (- x 2.0))
27.1b	(/ (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))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt` `*-un-lft-identity`
15×	`cbrt-prod` `add-cube-cbrt`
9×	`times-frac`
6×	`add-exp-log` `cbrt-div` `add-cbrt-cube`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `associate-/r` `flip--` `associate-/l` `distribute-lft-out--` `difference-of-squares`
1×	`cbrt-undiv` `frac-2neg` `div-exp` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

3.0ms	(cbrt (- x 2.0))
3.0ms	(cbrt (- x 2.0))
3.0ms	(cbrt (- x 2.0))
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))

series664.0ms

Counts

4 → 12

Calls

4 calls:

285.0ms	(cbrt (- x 2.0))
101.0ms	(cbrt (- x 2.0))
100.0ms	(cbrt (- x 2.0))
178.0ms	(/ (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))

simplify95.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 3 (84.0ms)

Iter	Nodes	Cost
0	316	818
1	843	762
2	3241	744
3	5003	738

prune514.0ms

Filtered

92 candidates to 76 candidates (82.6%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	92	7	99

Merged error: 0.0b

Counts

99 → 7

regimes351.0ms

Accuracy

97.2% (0.7b remaining)

Error of 0.7b against oracle of 0.0b and baseline of 24.7b

bsearch251.0ms

Steps

Iters	Range		Point
8	1.330268399502737e+60	5.500878895938276e+62	1.843774352643922e+60
9	-3.742064887211351e+70	-4.498318681586874e+64	-4.5488328791708104e+64

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	22
1	40	22

end0.0ms

sample686.0ms

Algorithm

intervals

Results

510.0ms

8007×

body

valid