Details

sample183.0ms

Algorithm

intervals

Results

113.0ms	107×	body	1280	valid
40.0ms	77×	body	640	valid
11.0ms	43×	body	320	valid
5.0ms	256×	pre	80	true
3.0ms	22×	body	160	valid
0.0ms	7×	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: 61.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.4b	(log (+ 1.0 x))
6.4b	(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×	`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)))
3.0ms	(log (+ 1.0 x))
4.0ms	(log (- 1.0 x))

series212.0ms

Counts

3 → 9

Calls

3 calls:

127.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
40.0ms	(log (+ 1.0 x))
45.0ms	(log (- 1.0 x))

simplify45.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	452	686
1	1669	638
2	5001	623

prune179.0ms

Filtered

84 candidates to 61 candidates (72.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	79	5	84
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	79	6	85

Merged error: 59.4b

Counts

85 → 6

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)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
6.4b	(log (- 1.0 x))

rewrite37.0ms

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))

series264.0ms

Counts

3 → 9

Calls

3 calls:

49.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
167.0ms	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
47.0ms	(log (- 1.0 x))

simplify91.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 1 (21.0ms)

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

prune425.0ms

Filtered

174 candidates to 116 candidates (66.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	173	1	174
Fresh	2	2	4
Picked	1	0	1
Done	1	0	1
Total	177	3	180

Merged error: 0.0b

Counts

180 → 3

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

rewrite67.0ms

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:

21.0ms	(* 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))))))

series258.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
80.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
124.0ms	(/ (- (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))))))

simplify89.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 2 (62.0ms)

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

prune650.0ms

Filtered

277 candidates to 173 candidates (62.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	275	2	277
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	275	5	280

Merged error: 0.0b

Counts

280 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b	(cbrt (pow (/ (- (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)))))) 3))
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))))))
0.0b	(pow (/ (- (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)))))) 3)

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

170×	`times-frac`
157×	`add-sqr-sqrt`
139×	`*-un-lft-identity`
100×	`unpow-prod-down`
91×	`add-cube-cbrt`
68×	`associate-r`
50×	`cbrt-prod`
44×	`cube-prod`
32×	`add-exp-log` `distribute-lft-out--`
26×	`sqr-pow`
24×	`unpow2`
23×	`pow1`
17×	`unswap-sqr`
16×	`log-pow` `difference-of-squares`
14×	`add-cbrt-cube`
11×	`div-exp`
10×	`prod-exp`
8×	`pow-exp`
7×	`pow-to-exp`
6×	`div-inv` `associate-/l*`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `pow-unpow` `associate-l` `associate-/r*`
2×	`cube-div` `cube-mult` `unpow3` `cbrt-unprod` `associate-/l/` `rem-cube-cbrt`
1×	`cbrt-div` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--` `rem-cbrt-cube`

Counts

4 → 284

Calls

4 calls:

19.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
13.0ms	(cbrt (pow (/ (- (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)))))) 3))
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))))))
9.0ms	(pow (/ (- (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)))))) 3)

series507.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
149.0ms	(cbrt (pow (/ (- (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)))))) 3))
128.0ms	(/ (- (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))))))
175.0ms	(pow (/ (- (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)))))) 3)

simplify149.0ms

Algorithm

egg-herbie

Counts

296 → 296

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1071	5491
1	4892	5180
2	5001	5180

prune694.0ms

Filtered

296 candidates to 157 candidates (53.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	295	1	296
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	297	4	301

Merged error: 0.0b

Counts

301 → 4

regimes25.0ms

Accuracy

0% (0.3b remaining)

Error of 0.4b against oracle of 0.1b and baseline of 0.4b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	20
1	23	20

end0.0ms

sample4.9s

Algorithm

intervals

Results

3.1s	3386×	body	1280	valid
1.1s	2470×	body	640	valid
295.0ms	1271×	body	320	valid
137.0ms	8000×	pre	80	true
90.0ms	666×	body	160	valid
14.0ms	207×	body	80	valid