Details

sample145.0ms

Algorithm

intervals

Results

87.0ms	100×	body	1280	valid
33.0ms	87×	body	640	valid
8.0ms	40×	body	320	valid
3.0ms	256×	pre	80	true
3.0ms	23×	body	160	valid
0.0ms	6×	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

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.4b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
7.8b	(log (- 1.0 x))
7.8b	(log (+ 1.0 x))

rewrite29.0ms

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:

16.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.0ms	(log (- 1.0 x))
5.0ms	(log (+ 1.0 x))

series201.0ms

Counts

3 → 9

Calls

3 calls:

118.0ms	(/ (log (- 1.0 x)) (log (+ 1.0 x)))
39.0ms	(log (- 1.0 x))
44.0ms	(log (+ 1.0 x))

simplify53.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (40.0ms)

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

prune219.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 59.0b

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))))))
7.8b	(log (- 1.0 x))

rewrite68.0ms

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:

38.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
16.0ms	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
6.0ms	(log (- 1.0 x))

series221.0ms

Counts

3 → 9

Calls

3 calls:

46.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
134.0ms	(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
40.0ms	(log (- 1.0 x))

simplify99.0ms

Algorithm

egg-herbie

Counts

174 → 174

Iterations

Useful iterations: 1 (20.0ms)

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

prune498.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

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))))))

rewrite150.0ms

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:

36.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
38.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
58.0ms	(/ (- (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))))))

series217.0ms

Counts

3 → 9

Calls

3 calls:

54.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
47.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
116.0ms	(/ (- (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))))))

simplify90.0ms

Algorithm

egg-herbie

Counts

277 → 277

Iterations

Useful iterations: 2 (65.0ms)

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

prune798.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 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	(/ 1 (/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
0.0b	(/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

rewrite163.0ms

Algorithm

rewrite-expression-head

Rules

322×	`times-frac`
248×	`add-sqr-sqrt`
196×	`*-un-lft-identity`
148×	`add-cube-cbrt`
136×	`associate-r`
112×	`unpow-prod-down`
63×	`add-exp-log`
48×	`unpow2` `sqr-pow`
34×	`unswap-sqr`
32×	`distribute-lft-out--`
30×	`associate-/r*`
26×	`div-exp`
25×	`pow1`
21×	`add-cbrt-cube`
20×	`prod-exp`
16×	`log-pow` `difference-of-squares`
12×	`pow-to-exp` `pow-exp`
11×	`associate-/r/`
8×	`div-inv`
6×	`cbrt-undiv` `associate-l` `associate-/l*`
5×	`flip3--` `flip--`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
2×	`rec-exp` `frac-2neg` `1-exp` `associate-r/` `pow-prod-down` `clear-num` `-commutative`
1×	`pow-flip` `inv-pow`

Counts

4 → 389

Calls

4 calls:

37.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
37.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
35.0ms	(/ 1 (/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
31.0ms	(/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

series331.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
52.0ms	(* 1/2 (/ (pow x 2) (pow 1.0 2)))
112.0ms	(/ 1 (/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
114.0ms	(/ (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))

simplify81.0ms

Algorithm

egg-herbie

Counts

401 → 401

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1053	6079
1	5001	5411

prune1.1s

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes27.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	17
1	22	17

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.9s	3435×	body	1280	valid
1.0s	2542×	body	640	valid
239.0ms	1216×	body	320	valid
95.0ms	8000×	pre	80	true
66.0ms	586×	body	160	valid
10.0ms	221×	body	80	valid