Details

Time bar (total: 8.9s)

sample149.0ms

Algorithm
intervals
Results
87.0ms102×body1280valid
33.0ms82×body640valid
9.0ms44×body320valid
7.0ms256×pre80true
3.0ms24×body160valid
0.0ms4×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune2.0ms

Filtered
1 candidates to 0 candidates (100.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 62.1b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
6.7b
(log (+ 1.0 x))
6.9b
(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)))
3.0ms
(log (+ 1.0 x))
4.0ms
(log (- 1.0 x))

series227.0ms

Counts
3 → 9
Calls
3 calls:
134.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
48.0ms
(log (+ 1.0 x))
44.0ms
(log (- 1.0 x))

simplify47.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (38.0ms)

IterNodesCost
0448686
11648638
25002619

prune182.0ms

Filtered
84 candidates to 61 candidates (27.4%)
Pruning

8 alts after pruning (8 fresh and 0 done)

PrunedKeptTotal
New76884
Fresh000
Picked101
Done000
Total77885

Merged error: 59.9b

Counts
85 → 8

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))))))
6.9b
(log (- 1.0 x))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
92×times-frac
87×add-sqr-sqrt
68×associate-*r*
62×unpow-prod-down
54×*-un-lft-identity
51×add-cube-cbrt
29×add-exp-log
26×unpow2 sqr-pow
19×associate-*r/
17×unswap-sqr
13×associate-/l*
11×associate-/r*
10×pow1 div-exp prod-exp add-cbrt-cube
6×pow-to-exp pow-exp
5×log-prod log-pow
4×log-div
3×expm1-log1p-u associate-*l* clear-num log1p-expm1-u add-log-exp
2×cbrt-undiv flip3-- frac-2neg div-sub un-div-inv flip-- cbrt-unprod div-inv
1×rem-log-exp pow-prod-down *-commutative distribute-lft-out-- difference-of-squares
Counts
3 → 185
Calls
3 calls:
23.0ms
(* 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))

series256.0ms

Counts
3 → 9
Calls
3 calls:
57.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
150.0ms
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
49.0ms
(log (- 1.0 x))

simplify101.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 1 (23.0ms)

IterNodesCost
09651510
140471337
250021337

prune465.0ms

Filtered
194 candidates to 130 candidates (33.0%)
Pruning

6 alts after pruning (6 fresh and 0 done)

PrunedKeptTotal
New1931194
Fresh257
Picked101
Done000
Total1966202

Merged error: 0.0b

Counts
202 → 6

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))))))

rewrite135.0ms

Algorithm
rewrite-expression-head
Rules
202×times-frac
192×*-un-lft-identity
174×add-sqr-sqrt
136×associate-*r*
124×unpow-prod-down
98×add-cube-cbrt
52×unpow2 sqr-pow
51×add-exp-log
40×distribute-lft-out--
38×associate-*r/ associate-*l*
34×unswap-sqr
32×distribute-lft-out associate-/l*
27×pow1
20×prod-exp log-pow
19×div-exp associate-/r*
15×add-cbrt-cube
12×pow-to-exp pow-exp
5×clear-num
4×un-div-inv cbrt-unprod difference-of-squares
3×cbrt-undiv expm1-log1p-u frac-2neg div-sub log1p-expm1-u div-inv add-log-exp
2×pow-prod-down *-commutative associate-/l/ associate--r+
1×+-commutative flip3-- flip--
Counts
3 → 342
Calls
3 calls:
25.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
23.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
68.0ms
(/ (- (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))))))

series245.0ms

Counts
3 → 9
Calls
3 calls:
55.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
52.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
139.0ms
(/ (- (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))))))

simplify111.0ms

Algorithm
egg-herbie
Counts
351 → 351
Iterations

Useful iterations: 2 (70.0ms)

IterNodesCost
08123479
139833026
250013025

prune768.0ms

Filtered
351 candidates to 203 candidates (42.2%)
Pruning

5 alts after pruning (5 fresh and 0 done)

PrunedKeptTotal
New3492351
Fresh235
Picked101
Done000
Total3525357

Merged error: 0.0b

Counts
357 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

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))))))
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
(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)

rewrite256.0ms

Algorithm
rewrite-expression-head
Rules
331×*-un-lft-identity
206×times-frac
154×unpow-prod-down
153×add-sqr-sqrt
100×distribute-lft-out--
99×add-cube-cbrt
83×associate-*l*
80×distribute-lft-out
68×associate-*r*
57×pow1
51×cbrt-prod
50×log-pow
32×add-exp-log
28×sqr-pow
26×unpow2
23×associate-/l*
19×associate-*r/
17×unswap-sqr
14×add-cbrt-cube
11×div-exp associate-/r*
10×prod-exp difference-of-squares
8×pow-exp
7×pow-to-exp
4×expm1-log1p-u pow-unpow log1p-expm1-u div-inv add-log-exp
3×cbrt-undiv div-sub clear-num
2×frac-2neg unpow3 un-div-inv rem-cbrt-cube cbrt-unprod associate-/l/ associate--r+ rem-cube-cbrt
1×+-commutative flip3-- pow-pow pow1/3 pow-prod-down *-commutative flip--
Counts
4 → 339
Calls
4 calls:
22.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
69.0ms
(/ (- (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))))))
72.0ms
(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))
67.0ms
(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)

series522.0ms

Counts
4 → 12
Calls
4 calls:
57.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
133.0ms
(/ (- (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))))))
140.0ms
(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))
191.0ms
(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)

simplify153.0ms

Algorithm
egg-herbie
Counts
351 → 351
Iterations

Useful iterations: 2 (87.0ms)

IterNodesCost
010586073
146645863
250015860

prune736.0ms

Filtered
351 candidates to 176 candidates (49.9%)
Pruning

5 alts after pruning (4 fresh and 1 done)

PrunedKeptTotal
New3501351
Fresh134
Picked011
Done000
Total3515356

Merged error: 0.0b

Counts
356 → 5

regimes27.0ms

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)

IterNodesCost
02118
12118

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.9s3384×body1280valid
998.0ms2513×body640valid
250.0ms1285×body320valid
102.0ms8000×pre80true
66.0ms602×body160valid
10.0ms216×body80valid