Details

sample145.0ms

Algorithm

intervals

Results

82.0ms	93×	body	1280	valid
38.0ms	94×	body	640	valid
8.0ms	38×	body	320	valid
4.0ms	256×	pre	80	true
2.0ms	21×	body	160	valid
0.0ms	10×	body	80	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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))

rewrite15.0ms

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×	`expm1-log1p-u` `log1p-expm1-u` `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 → 75

Calls

3 calls:

6.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
4.0ms	(log (- 1.0 x))
3.0ms	(log (+ 1.0 x))

series210.0ms

Counts

3 → 9

Calls

3 calls:

122.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
47.0ms	(log (- 1.0 x))
41.0ms	(log (+ 1.0 x))

simplify53.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	452	686
1	1669	638
2	5002	623

prune186.0ms

Filtered

84 candidates to 61 candidates (72.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	77	7	84
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Merged error: 58.3b

Counts

85 → 7

localize18.0ms

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

rewrite38.0ms

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-/l*`
3×	`expm1-log1p-u` `associate-l` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `flip3--` `div-sub` `flip--` `cbrt-unprod` `div-inv`
1×	`frac-2neg` `associate-r/` `rem-log-exp` `pow-prod-down` `clear-num` `-commutative` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 165

Calls

3 calls:

20.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
6.0ms	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
4.0ms	(log (- 1.0 x))

series411.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
132.0ms	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
228.0ms	(log (- 1.0 x))

simplify89.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	928	1453
1	3837	1286
2	5001	1286

prune394.0ms

Filtered

174 candidates to 116 candidates (66.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	175	6	181

Merged error: 0.0b

Counts

181 → 6

localize17.0ms

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))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite68.0ms

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×	`log-pow` `cbrt-unprod` `difference-of-squares`
3×	`cbrt-undiv` `expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`associate-r/` `pow-prod-down` `-commutative` `associate-/l/`
1×	`flip3--` `frac-2neg` `div-sub` `clear-num` `flip--`

Counts

3 → 268

Calls

3 calls:

20.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
20.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
9.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series218.0ms

Counts

3 → 9

Calls

3 calls:

48.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
50.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
119.0ms	(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify94.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 2 (67.0ms)

Iter	Nodes	Cost
0	753	2429
1	3174	2138
2	5001	2135

prune655.0ms

Filtered

277 candidates to 173 candidates (62.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	277	0	277
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	277	6	283

Merged error: 0.0b

Counts

283 → 6

localize9.0ms

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))

rewrite26.0ms

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×	`expm1-log1p-u` `log-div` `log1p-expm1-u` `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 → 155

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)
4.0ms	(log (- 1.0 x))
3.0ms	(log (+ 1.0 x))

series416.0ms

Counts

4 → 12

Calls

4 calls:

120.0ms	(cbrt (pow (/ (log (- 1.0 x)) (log (+ 1.0 x))) 3))
210.0ms	(pow (/ (log (- 1.0 x)) (log (+ 1.0 x))) 3)
41.0ms	(log (- 1.0 x))
45.0ms	(log (+ 1.0 x))

simplify101.0ms

Algorithm

egg-herbie

Counts

167 → 167

Iterations

Useful iterations: 2 (82.0ms)

Iter	Nodes	Cost
0	948	1807
1	4450	1682
2	5001	1678

prune264.0ms

Filtered

167 candidates to 86 candidates (51.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	167	0	167
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	167	6	173

Merged error: 0.0b

Counts

173 → 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	18	16
1	18	16

end0.0ms

sample4.6s

Algorithm

intervals

Results

3.0s	3396×	body	1280	valid
1.0s	2527×	body	640	valid
261.0ms	1271×	body	320	valid
108.0ms	8000×	pre	80	true
70.0ms	606×	body	160	valid
10.0ms	200×	body	80	valid