Details

sample29.0ms

Algorithm

intervals

Results

10.0ms	256×	body	80	valid
9.0ms	263×	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

localize10.0ms

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))

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))
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))

series163.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
44.0ms	(/ (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))

simplify106.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (22.0ms)

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

prune327.0ms

Filtered

151 candidates to 117 candidates (77.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	148	3	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	150	3	153

Merged error: 0b

Counts

153 → 3

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	(/ (- 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)))

series191.0ms

Counts

3 → 9

Calls

3 calls:

42.0ms	(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)))

simplify47.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (37.0ms)

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

prune194.0ms

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	1	1	2
Picked	0	1	1
Done	0	0	0
Total	99	3	102

Merged error: 0b

Counts

102 → 3

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite51.0ms

Algorithm

rewrite-expression-head

Rules

132×	`add-sqr-sqrt`
117×	`*-un-lft-identity`
107×	`times-frac`
94×	`cbrt-prod`
73×	`add-cube-cbrt`
59×	`unpow-prod-down` `cube-prod`
47×	`associate-l`
22×	`distribute-lft-out--` `difference-of-squares`
11×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`pow1` `div-inv` `unswap-sqr`
5×	`associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp` `sqr-pow`
3×	`cube-div` `cube-mult` `pow-unpow` `unpow3` `associate-r` `associate-/r*`
2×	`cbrt-undiv` `cbrt-div` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `pow-prod-down` `associate-l/` `prod-exp` `clear-num` `-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 227

Calls

4 calls:

15.0ms	(* (cbrt (pow (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 3)) 6.0)
6.0ms	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))
8.0ms	(cbrt (pow (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 3))
7.0ms	(pow (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 3)

series348.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(* (cbrt (pow (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 3)) 6.0)
71.0ms	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))
84.0ms	(cbrt (pow (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 3))
98.0ms	(pow (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 3)

simplify94.0ms

Algorithm

egg-herbie

Counts

239 → 239

Iterations

Useful iterations: 2 (68.0ms)

Iter	Nodes	Cost
0	634	2404
1	2765	2269
2	5001	2250

prune387.0ms

Filtered

239 candidates to 132 candidates (55.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	239	0	239
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	239	3	242

Merged error: 0b

Counts

242 → 3

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))))

rewrite106.0ms

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))
10.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
69.0ms	(* (/ (* (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))))

series554.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(cbrt (- x 1.0))
103.0ms	(cbrt (- x 1.0))
117.0ms	(* (cbrt (- x 1.0)) (cbrt (- x 1.0)))
240.0ms	(* (/ (* (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))))

simplify85.0ms

Algorithm

egg-herbie

Counts

312 → 312

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1522	6020
1	5002	5674

prune925.0ms

Filtered

312 candidates to 222 candidates (71.2%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	312	0	312
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	312	3	315

Merged error: 0b

Counts

315 → 3

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	12	6
1	12	6

end0.0ms

sample791.0ms

Algorithm

intervals

Results

310.0ms	8000×	body	80	valid
290.0ms	8059×	body	80	nan