Details

sample26.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
7.0ms	216×	body	80	nan

simplify19.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	7
1	41	6
2	69	6
3	95	6
4	125	6
5	140	6
6	142	6
7	142	6

prune57.0ms

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

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (sqrt x) 4.0 (+ x 1.0))
0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
0.0b	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 142

Calls

3 calls:

1.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
5.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
15.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

series160.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
46.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
77.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

simplify72.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	627	1691
1	2379	1609
2	5002	1609

prune316.0ms

Filtered

151 candidates to 117 candidates (77.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	146	5	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	148	5	153

Merged error: 0b

Counts

153 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
0.1b	(/ 1.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
0.2b	(/ x (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

168×	`times-frac`
104×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
12×	`div-inv` `associate-/l*`
8×	`cbrt-undiv` `div-exp`
4×	`pow1` `expm1-log1p-u` `frac-2neg` `clear-num` `log1p-expm1-u` `add-log-exp`
2×	`associate-/r/`

Counts

4 → 202

Calls

4 calls:

3.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
6.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
5.0ms	(/ 1.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
6.0ms	(/ x (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

series250.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
46.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
60.0ms	(/ 1.0 (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
96.0ms	(/ x (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

simplify84.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	668	2123
1	2799	2002
2	5001	2002

prune444.0ms

Filtered

214 candidates to 178 candidates (83.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	214	5	219

Merged error: 0b

Counts

219 → 5

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (sqrt x) (sqrt 1.0))
0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
0.1b	(* (+ (sqrt x) (sqrt 1.0)) (/ (- (sqrt x) (sqrt 1.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)))
0.2b	(/ (- (sqrt x) (sqrt 1.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

rewrite91.0ms

Algorithm

rewrite-expression-head

Rules

433×	`add-sqr-sqrt`
417×	`times-frac`
316×	`*-un-lft-identity`
209×	`sqrt-prod`
200×	`add-cube-cbrt`
122×	`associate-r`
112×	`difference-of-squares`
56×	`distribute-lft-out--`
36×	`prod-diff`
22×	`div-inv`
20×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r*`
12×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
6×	`pow1` `fma-neg` `add-log-exp`
5×	`associate-l`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `flip3--` `frac-2neg` `flip3-+` `associate-*l/` `clear-num` `associate-/r/` `flip--` `flip-+` `associate-/l/` `distribute-lft-out`
1×	`sub-neg` `diff-log` `div-sub` `associate-r/` `pow-prod-down` `-commutative`

Counts

4 → 402

Calls

4 calls:

7.0ms	(- (sqrt x) (sqrt 1.0))
3.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
36.0ms	(* (+ (sqrt x) (sqrt 1.0)) (/ (- (sqrt x) (sqrt 1.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)))
16.0ms	(/ (- (sqrt x) (sqrt 1.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

series665.0ms

Counts

4 → 12

Calls

4 calls:

40.0ms	(- (sqrt x) (sqrt 1.0))
48.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
405.0ms	(* (+ (sqrt x) (sqrt 1.0)) (/ (- (sqrt x) (sqrt 1.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)))
172.0ms	(/ (- (sqrt x) (sqrt 1.0)) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

simplify90.0ms

Algorithm

egg-herbie

Counts

414 → 414

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1346	6344
1	5001	5801

prune626.0ms

Filtered

414 candidates to 208 candidates (50.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	414	0	414
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	414	5	419

Merged error: 0b

Counts

419 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
0.0b	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
0.1b	(pow (/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)) 3)
1.0b	(cbrt (pow (/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)) 3))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

568×	`times-frac`
398×	`add-sqr-sqrt` `*-un-lft-identity`
266×	`add-cube-cbrt`
146×	`cbrt-prod`
140×	`unpow-prod-down` `cube-prod`
66×	`distribute-lft-out--` `difference-of-squares`
32×	`div-inv`
17×	`add-exp-log` `add-cbrt-cube`
16×	`associate-/r*`
8×	`associate-/l*`
7×	`cbrt-undiv` `div-exp`
5×	`pow1` `associate-/r/`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow-exp` `rem-cube-cbrt`
2×	`cube-div` `cube-mult` `frac-2neg` `unpow3` `clear-num` `associate-/l/` `sqr-pow`
1×	`pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `pow1/3` `div-sub` `flip--` `rem-cbrt-cube`

Counts

4 → 454

Calls

4 calls:

3.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
9.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
14.0ms	(pow (/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)) 3)
20.0ms	(cbrt (pow (/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)) 3))

series306.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
78.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
105.0ms	(pow (/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)) 3)
78.0ms	(cbrt (pow (/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)) 3))

simplify106.0ms

Algorithm

egg-herbie

Counts

466 → 466

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1542	6695
1	5001	6504

prune693.0ms

Filtered

466 candidates to 233 candidates (50.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	466	0	466
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	466	5	471

Merged error: 0b

Counts

471 → 5

regimes23.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	11
1	12	11

end0.0ms

sample792.0ms

Algorithm

intervals

Results

313.0ms	8000×	body	80	valid
289.0ms	8123×	body	80	nan