Details

sample25.0ms

Algorithm

intervals

Results

8.0ms	256×	body	80	valid
7.0ms	272×	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

prune9.0ms

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)

rewrite20.0ms

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))
10.0ms	(/ (- 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)

series169.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
76.0ms	(/ (- 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)

simplify69.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (14.0ms)

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

prune326.0ms

Filtered

151 candidates to 117 candidates (77.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	149	4	153

Merged error: 0b

Counts

153 → 4

localize11.0ms

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

rewrite19.0ms

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)
7.0ms	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

series185.0ms

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)
73.0ms	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

simplify41.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (31.0ms)

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

prune217.0ms

Filtered

99 candidates to 77 candidates (77.8%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	99	4	103

Merged error: 0b

Counts

103 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

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)
0.0b	(* (/ (+ (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)))))
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))))

rewrite111.0ms

Algorithm

rewrite-expression-head

Rules

227×	`add-sqr-sqrt`
200×	`sqrt-prod`
197×	`*-un-lft-identity`
180×	`times-frac`
93×	`add-cube-cbrt`
61×	`associate-r`
52×	`difference-of-squares`
38×	`add-exp-log` `add-cbrt-cube`
35×	`associate-l`
26×	`distribute-lft-out` `distribute-lft-out--`
14×	`associate-/l*`
13×	`prod-exp` `cbrt-unprod`
12×	`associate-/r*`
11×	`pow1`
10×	`cbrt-undiv` `div-exp`
9×	`unswap-sqr`
5×	`associate-*l/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp`
2×	`frac-times` `frac-2neg` `associate-r/` `clear-num` `-commutative`
1×	`flip3--` `flip3-+` `div-sub` `flip--` `flip-+`

Counts

4 → 295

Calls

4 calls:

22.0ms	(* (* (/ (+ (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)
51.0ms	(* (/ (+ (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)))))
12.0ms	(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
9.0ms	(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

series1.3s

Counts

4 → 12

Calls

4 calls:

420.0ms	(* (* (/ (+ (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)
367.0ms	(* (/ (+ (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)))))
246.0ms	(/ (- (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))
242.0ms	(/ (+ (sqrt x) (sqrt 1.0)) (sqrt (fma (sqrt x) 4.0 (+ x 1.0))))

simplify75.0ms

Algorithm

egg-herbie

Counts

307 → 307

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1032	5867
1	5001	5258

prune713.0ms

Filtered

307 candidates to 175 candidates (57.0%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	307	0	307
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	307	4	311

Merged error: 0b

Counts

311 → 4

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- x 1.0))
0.3b	(cbrt (- x 1.0))
0.3b	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
0.6b	(* (/ (* (cbrt (- x 1.0)) (cbrt (- x 1.0))) (sqrt (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))) (/ (cbrt (- x 1.0)) (sqrt (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

285×	`times-frac`
267×	`add-sqr-sqrt`
170×	`*-un-lft-identity`
147×	`sqrt-prod`
141×	`associate-r`
130×	`cbrt-prod`
120×	`add-cube-cbrt`
32×	`unswap-sqr`
29×	`associate-l`
27×	`add-exp-log`
24×	`distribute-lft-out--`
22×	`difference-of-squares`
18×	`add-cbrt-cube`
16×	`cbrt-div`
13×	`pow1`
11×	`div-inv`
10×	`swap-sqr`
9×	`prod-exp` `cbrt-unprod`
8×	`flip3--` `pow1/3` `flip--`
7×	`cbrt-undiv` `div-exp`
5×	`frac-times`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`associate-r/` `pow-prod-down` `associate-l/`
2×	`sqrt-div` `associate-/r/` `pow-sqr` `*-commutative` `pow-prod-up`
1×	`pow2` `pow-plus`

Counts

4 → 300

Calls

4 calls:

3.0ms	(cbrt (- x 1.0))
3.0ms	(cbrt (- x 1.0))
11.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
76.0ms	(* (/ (* (cbrt (- x 1.0)) (cbrt (- x 1.0))) (sqrt (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))) (/ (cbrt (- x 1.0)) (sqrt (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))))

series538.0ms

Counts

4 → 12

Calls

4 calls:

97.0ms	(cbrt (- x 1.0))
98.0ms	(cbrt (- x 1.0))
127.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
216.0ms	(* (/ (* (cbrt (- x 1.0)) (cbrt (- x 1.0))) (sqrt (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))) (/ (cbrt (- x 1.0)) (sqrt (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))))

simplify87.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1522	6020
1	5002	5674

prune932.0ms

Filtered

312 candidates to 222 candidates (71.2%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	312	0	312
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	312	4	316

Merged error: 0b

Counts

316 → 4

regimes17.0ms

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	11	6
1	11	6

end0.0ms

sample636.0ms

Algorithm

intervals

Results

233.0ms	8000×	body	80	valid
213.0ms	8076×	body	80	nan