Details

sample144.0ms

Algorithm

intervals

Results

79.0ms	93×	body	1280	valid
37.0ms	94×	body	640	valid
10.0ms	38×	body	320	valid
4.0ms	256×	pre	80	true
2.0ms	21×	body	160	valid
0.0ms	10×	body	80	valid

simplify6.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	5
1	11	5
2	11	5

prune2.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 60.6b

Counts

2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.1b	(log (- 1.0 x))
6.2b	(log (+ 1.0 x))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

19×	`*-un-lft-identity`
17×	`add-sqr-sqrt`
16×	`times-frac`
15×	`pow1` `add-cube-cbrt`
12×	`log-pow`
9×	`log-prod`
7×	`add-exp-log`
6×	`log-div`
5×	`add-cbrt-cube`
4×	`associate-/r` `associate-/l`
3×	`add-log-exp`
2×	`flip3--` `div-sub` `rem-log-exp` `flip--`
1×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `flip-+` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 69

Calls

3 calls:

6.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
3.0ms	(log (- 1.0 x))
3.0ms	(log (+ 1.0 x))

series215.0ms

Counts

3 → 9

Calls

3 calls:

128.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
42.0ms	(log (- 1.0 x))
45.0ms	(log (+ 1.0 x))

simplify46.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	425	668
1	1561	624
2	5001	599

prune170.0ms

Filtered

78 candidates to 55 candidates (70.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	71	7	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	7	79

Merged error: 58.3b

Counts

79 → 7

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
6.1b	(log (- 1.0 x))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

92×	`times-frac`
83×	`add-sqr-sqrt`
68×	`associate-r`
56×	`unpow-prod-down`
49×	`*-un-lft-identity`
47×	`add-cube-cbrt`
29×	`add-exp-log`
24×	`unpow2` `sqr-pow`
17×	`unswap-sqr`
10×	`pow1` `div-exp` `prod-exp` `add-cbrt-cube`
6×	`pow-to-exp` `pow-exp`
5×	`log-prod` `log-pow`
4×	`log-div` `associate-/r/` `associate-/l*`
3×	`flip3--` `associate-r/` `associate-l` `associate-/r` `flip--` `add-log-exp`
2×	`cbrt-undiv` `div-sub` `frac-sub` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `flip3-+` `rem-log-exp` `pow-prod-down` `clear-num` `*-commutative` `flip-+` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 163

Calls

3 calls:

20.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
14.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
3.0ms	(log (- 1.0 x))

series239.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
135.0ms	(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
48.0ms	(log (- 1.0 x))

simplify108.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	995	1550
1	4213	1389
2	5001	1389

prune411.0ms

Filtered

172 candidates to 114 candidates (66.3%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	171	1	172
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	173	6	179

Merged error: 0.0b

Counts

179 → 6

localize13.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

178×	`times-frac`
158×	`add-sqr-sqrt`
136×	`associate-r`
112×	`unpow-prod-down`
94×	`*-un-lft-identity`
82×	`add-cube-cbrt`
51×	`add-exp-log`
48×	`unpow2` `sqr-pow`
34×	`unswap-sqr`
20×	`prod-exp`
19×	`div-exp`
15×	`add-cbrt-cube`
12×	`pow-to-exp` `pow-exp`
11×	`pow1`
8×	`distribute-lft-out--`
6×	`associate-l` `associate-/l*`
4×	`associate-*r/` `associate-/r/` `log-pow` `cbrt-unprod` `difference-of-squares`
3×	`cbrt-undiv` `associate-/r*` `div-inv` `add-log-exp`
2×	`flip3--` `pow-prod-down` `*-commutative` `frac-sub` `flip--` `associate-/l/`
1×	`frac-2neg` `flip3-+` `div-sub` `clear-num` `flip-+`

Counts

3 → 266

Calls

3 calls:

20.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
24.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
14.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series237.0ms

Counts

3 → 9

Calls

3 calls:

55.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
50.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
132.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify106.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 2 (78.0ms)

Iter	Nodes	Cost
0	855	2533
1	3688	2254
2	5001	2253

prune611.0ms

Filtered

275 candidates to 171 candidates (62.2%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	275	0	275
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	275	6	281

Merged error: 0.0b

Counts

281 → 6

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(cbrt (pow (/ (log (- 1.0 x)) (log (+ 1.0 x))) 3))
0.1b	(pow (/ (log (- 1.0 x)) (log (+ 1.0 x))) 3)
6.1b	(log (- 1.0 x))
6.2b	(log (+ 1.0 x))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

64×	`times-frac`
48×	`*-un-lft-identity`
46×	`cbrt-prod` `add-sqr-sqrt`
44×	`add-cube-cbrt`
40×	`unpow-prod-down` `cube-prod`
39×	`pow1`
34×	`log-pow`
9×	`add-exp-log` `log-prod`
7×	`add-cbrt-cube`
4×	`log-div` `div-inv` `add-log-exp`
3×	`pow-unpow`
2×	`cube-div` `cube-mult` `unpow3` `rem-log-exp` `pow-exp` `rem-cube-cbrt` `sqr-pow`
1×	`cbrt-undiv` `pow-to-exp` `cbrt-div` `flip3--` `pow-pow` `flip3-+` `pow1/3` `div-exp` `flip--` `rem-cbrt-cube` `flip-+` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 147

Calls

4 calls:

6.0ms	(cbrt (pow (/ (log (- 1.0 x)) (log (+ 1.0 x))) 3))
6.0ms	(pow (/ (log (- 1.0 x)) (log (+ 1.0 x))) 3)
3.0ms	(log (- 1.0 x))
3.0ms	(log (+ 1.0 x))

series415.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt (pow (/ (log (- 1.0 x)) (log (+ 1.0 x))) 3))
204.0ms	(pow (/ (log (- 1.0 x)) (log (+ 1.0 x))) 3)
46.0ms	(log (- 1.0 x))
40.0ms	(log (+ 1.0 x))

simplify99.0ms

Algorithm

egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 2 (81.0ms)

Iter	Nodes	Cost
0	902	1782
1	4246	1664
2	5003	1654

prune238.0ms

Filtered

159 candidates to 76 candidates (47.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	159	0	159
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	159	6	165

Merged error: 0.0b

Counts

165 → 6

regimes47.0ms

Accuracy

0% (0.4b remaining)

Error of 0.4b against oracle of 0.0b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	17
1	19	17

end0.0ms

sample4.4s

Algorithm

intervals

Results

2.9s	3396×	body	1280	valid
998.0ms	2527×	body	640	valid
246.0ms	1271×	body	320	valid
97.0ms	8000×	pre	80	true
66.0ms	606×	body	160	valid
9.0ms	200×	body	80	valid