Details

sample24.0ms

Algorithm

intervals

Results

9.0ms	256×	body	80	valid
6.0ms	227×	body	80	nan

simplify16.0ms

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)

rewrite18.0ms

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))
8.0ms	(/ (- 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)

series161.0ms

Counts

3 → 9

Calls

3 calls:

34.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
78.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))
49.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)

simplify65.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (13.0ms)

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

prune345.0ms

Filtered

151 candidates to 117 candidates (77.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	147	4	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	149	4	153

Merged error: 0b

Counts

153 → 4

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)
0.1b	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
19×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-/l*`
3×	`expm1-log1p-u` `associate-r` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`flip3--` `frac-2neg` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--` `fma-udef`

Counts

3 → 90

Calls

3 calls:

1.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
8.0ms	(* (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)
6.0ms	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

series183.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
78.0ms	(* (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)
71.0ms	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

simplify39.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	357	827
1	1182	752
2	5001	738

prune213.0ms

Filtered

99 candidates to 77 candidates (77.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	2	1	3
Picked	0	1	1
Done	0	0	0
Total	100	3	103

Merged error: 0b

Counts

103 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

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

rewrite55.0ms

Algorithm

rewrite-expression-head

Rules

148×	`*-un-lft-identity`
134×	`sqrt-prod`
125×	`add-sqr-sqrt`
114×	`times-frac`
68×	`add-cube-cbrt`
34×	`associate-l`
29×	`add-exp-log` `add-cbrt-cube`
28×	`difference-of-squares`
26×	`distribute-lft-out`
14×	`associate-/l*` `distribute-lft-out--`
12×	`associate-/r*`
10×	`pow1` `prod-exp` `cbrt-unprod`
7×	`cbrt-undiv` `div-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`pow-prod-down` `associate-*l/` `div-inv`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `flip3-+` `pow1/2` `div-sub` `associate-r/` `associate-r` `-commutative` `flip--` `flip-+`

Counts

4 → 220

Calls

4 calls:

1.0ms	(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
8.0ms	(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
25.0ms	(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (* (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0))
11.0ms	(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

series965.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(sqrt (fma (sqrt x) 4.0 (+ x 1.0)))
233.0ms	(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
419.0ms	(* (/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) (* (/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0)))) 6.0))
241.0ms	(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

simplify103.0ms

Algorithm

egg-herbie

Counts

232 → 232

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	868	3996
1	3543	3578
2	5001	3522

prune486.0ms

Filtered

232 candidates to 124 candidates (53.4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	232	0	232
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	232	3	235

Merged error: 0b

Counts

235 → 3

localize16.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (fma (sqrt x) 4.0 (+ x 1.0))) (cbrt (fma (sqrt x) 4.0 (+ x 1.0))))
1.0b	(cbrt 6.0)
1.0b	(cbrt 6.0)
1.0b	(cbrt 6.0)

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt (fma (sqrt x) 4.0 (+ x 1.0))) (cbrt (fma (sqrt x) 4.0 (+ x 1.0))))
1.0ms	(cbrt 6.0)
1.0ms	(cbrt 6.0)
1.0ms	(cbrt 6.0)

series147.0ms

Counts

4 → 6

Calls

4 calls:

147.0ms	(* (cbrt (fma (sqrt x) 4.0 (+ x 1.0))) (cbrt (fma (sqrt x) 4.0 (+ x 1.0))))
0.0ms	(cbrt 6.0)
0.0ms	(cbrt 6.0)
0.0ms	(cbrt 6.0)

simplify110.0ms

Algorithm

egg-herbie

Counts

87 → 87

Iterations

Useful iterations: 3 (103.0ms)

Iter	Nodes	Cost
0	208	653
1	729	601
2	3641	532
3	5001	524

prune234.0ms

Filtered

87 candidates to 64 candidates (73.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	87	0	87
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	87	3	90

Merged error: 0b

Counts

90 → 3

regimes14.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	12	6
1	12	6

end0.0ms

sample591.0ms

Algorithm

intervals

Results

226.0ms	8000×	body	80	valid
195.0ms	8087×	body	80	nan