Details

sample29.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
9.0ms	250×	body	80	nan

simplify15.0ms

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

prune6.0ms

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

localize8.0ms

Local error

Found 3 expressions with local error:

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

rewrite19.0ms

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))
9.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
3.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)

series166.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
79.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
51.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)

simplify96.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (14.0ms)

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

prune328.0ms

Filtered

151 candidates to 117 candidates (77.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	147	4	151
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	148	5	153

Merged error: 0b

Counts

153 → 5

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 6.0 (- x 1.0))
0.0b	(+ (+ x 1.0) (* 4.0 (sqrt x)))
0.4b	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`prod-diff`
11×	`distribute-rgt-in` `distribute-lft-in`
10×	`add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
5×	`pow1` `associate-r`
4×	`fma-def` `associate-*r/`
3×	`expm1-log1p-u` `times-frac` `associate-l` `associate-/r*` `sum-log` `log1p-expm1-u`
2×	`cbrt-undiv` `sub-neg` `flip3--` `flip3-+` `div-exp` `prod-exp` `associate-/r/` `flip--` `cbrt-unprod` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+l+` `frac-2neg` `pow-prod-down` `clear-num` `-commutative` `div-inv` `distribute-lft-out` `associate-/l` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

3 → 92

Calls

3 calls:

7.0ms	(* 6.0 (- x 1.0))
6.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
15.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

series164.0ms

Counts

3 → 9

Calls

3 calls:

44.0ms	(* 6.0 (- x 1.0))
37.0ms	(+ (+ x 1.0) (* 4.0 (sqrt x)))
82.0ms	(/ (* 6.0 (- x 1.0)) (+ (+ x 1.0) (* 4.0 (sqrt x))))

simplify67.0ms

Algorithm

egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	466	778
1	2126	572
2	5002	560

prune153.0ms

Filtered

101 candidates to 64 candidates (63.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	102	4	106

Merged error: 0b

Counts

106 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
0.1b	(expm1 (/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)))
1.6b	(log1p (expm1 (/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))))

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*`
5×	`log1p-expm1-u`
4×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`log1p-udef` `expm1-log1p` `flip3--` `div-sub` `log1p-expm1` `associate-/r/` `flip--` `expm1-udef`

Counts

4 → 154

Calls

4 calls:

9.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
3.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
1.0ms	(expm1 (/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)))
1.0ms	(log1p (expm1 (/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))))

series458.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
46.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
134.0ms	(expm1 (/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)))
197.0ms	(log1p (expm1 (/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))))

simplify72.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 1 (15.0ms)

Iter	Nodes	Cost
0	692	1875
1	2563	1765
2	5001	1765

prune387.0ms

Filtered

166 candidates to 128 candidates (77.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	166	0	166
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	166	4	170

Merged error: 0b

Counts

170 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(log (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
0.0b	(/ (- x 1.0) (exp (log (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))))
0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
3.1b	(exp (log (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

161×	`times-frac`
126×	`add-sqr-sqrt` `*-un-lft-identity`
104×	`log-prod`
92×	`add-cube-cbrt`
91×	`exp-sum`
19×	`associate-/r*`
17×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `div-inv`
8×	`add-cbrt-cube` `associate-/l*`
6×	`pow1`
4×	`expm1-log1p-u` `exp-prod` `log1p-expm1-u` `add-log-exp`
3×	`log-div` `div-exp`
2×	`cbrt-undiv` `frac-2neg` `exp-diff` `rem-log-exp` `clear-num` `log-pow` `associate-/l/`
1×	`flip3--` `div-sub` `associate-/r/` `flip--` `rem-exp-log`

Counts

4 → 202

Calls

4 calls:

2.0ms	(log (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
14.0ms	(/ (- x 1.0) (exp (log (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))))
3.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
4.0ms	(exp (log (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)))

series323.0ms

Counts

4 → 12

Calls

4 calls:

116.0ms	(log (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
91.0ms	(/ (- x 1.0) (exp (log (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))))
66.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
50.0ms	(exp (log (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)))

simplify79.0ms

Algorithm

egg-herbie

Counts

214 → 214

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	757	2750
1	2467	2360
2	5001	2314

prune462.0ms

Filtered

214 candidates to 156 candidates (72.9%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	214	0	214
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	214	4	218

Merged error: 0b

Counts

218 → 4

regimes39.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 0.3b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	7
1	15	7

end0.0ms

sample791.0ms

Algorithm

intervals

Results

311.0ms	8000×	body	80	valid
293.0ms	8106×	body	80	nan

Details

sample29.0ms

simplify15.0ms

prune6.0ms

localize8.0ms

rewrite19.0ms

series166.0ms

simplify96.0ms

prune328.0ms

localize8.0ms

rewrite31.0ms

series164.0ms

simplify67.0ms

prune153.0ms

localize12.0ms

rewrite22.0ms

series458.0ms

simplify72.0ms

prune387.0ms

localize12.0ms

rewrite34.0ms

series323.0ms

simplify79.0ms

prune462.0ms

regimes39.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample791.0ms

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