Details

Time bar (total: 32.6s)

sample291.0ms

Algorithm
intervals
Results
181.0ms91×body640valid
87.0ms105×body1280valid
5.0ms26×body320valid
3.0ms256×pre80true
3.0ms27×body160valid
0.0ms7×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 (0.0%)
Pruning

2 alts after pruning (2 fresh and 0 done)

PrunedKeptTotal
New011
Fresh011
Picked000
Done000
Total022

Merged error: 60.7b

Counts
2 → 1

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
7.2b
(log (- 1.0 x))
7.3b
(log (+ 1.0 x))

rewrite16.0ms

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

series219.0ms

Counts
3 → 9
Calls
3 calls:
129.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
47.0ms
(log (- 1.0 x))
42.0ms
(log (+ 1.0 x))

simplify47.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (39.0ms)

IterNodesCost
0448686
11648638
25002619

prune184.0ms

Filtered
84 candidates to 61 candidates (72.6%)
Pruning

9 alts after pruning (8 fresh and 1 done)

PrunedKeptTotal
New76884
Fresh000
Picked011
Done000
Total76985

Merged error: 58.0b

Counts
85 → 9

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))))))
7.2b
(log (- 1.0 x))

rewrite44.0ms

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:
25.0ms
(* 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))

series240.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
142.0ms
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
48.0ms
(log (- 1.0 x))

simplify103.0ms

Algorithm
egg-herbie
Counts
194 → 194
Iterations

Useful iterations: 1 (22.0ms)

IterNodesCost
09651510
140471337
250021337

prune468.0ms

Filtered
194 candidates to 130 candidates (67.0%)
Pruning

6 alts after pruning (5 fresh and 1 done)

PrunedKeptTotal
New1931194
Fresh347
Picked101
Done011
Total1976203

Merged error: 0.1b

Counts
203 → 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))))))

rewrite145.0ms

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:
24.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
24.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
74.0ms
(/ (- (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))))))

series236.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
51.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
131.0ms
(/ (- (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))))))

simplify109.0ms

Algorithm
egg-herbie
Counts
351 → 351
Iterations

Useful iterations: 2 (71.0ms)

IterNodesCost
08043333
134623030
250013029

prune776.0ms

Filtered
351 candidates to 203 candidates (57.8%)
Pruning

6 alts after pruning (4 fresh and 2 done)

PrunedKeptTotal
New3501351
Fresh134
Picked011
Done011
Total3516357

Merged error: 0.0b

Counts
357 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
0.0b
(/ (* 1.0 x) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
0.0b
(- (/ (- (log 1.0) (* 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)))))) (/ (* 1.0 x) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
29.7b
(/ (- (log 1.0) (* 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))))))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
11502×add-sqr-sqrt
8497×times-frac
4161×*-un-lft-identity
3214×add-cube-cbrt
3160×prod-diff
2758×unswap-sqr
2616×difference-of-squares
1222×unpow-prod-down
1186×unpow2 sqr-pow
1142×associate-*l*
892×associate-/l*
890×associate-*r*
635×distribute-lft-out--
594×frac-sub
308×pow1
302×log-pow
275×*-commutative
175×associate-/r*
125×div-inv
79×fma-neg
56×frac-2neg
55×clear-num
38×associate-/l/
34×add-exp-log
20×flip3-- flip--
19×associate-*r/
16×add-cbrt-cube
12×div-exp
11×prod-exp
7×sub-div
6×pow-to-exp pow-exp add-log-exp
4×cbrt-undiv expm1-log1p-u log1p-expm1-u
3×cbrt-unprod
2×div-sub un-div-inv
1×associate--l- sub-neg distribute-rgt-out-- diff-log pow-prod-down
Counts
4 → 4212
Calls
4 calls:
24.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
7.0ms
(/ (* 1.0 x) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
295.0ms
(- (/ (- (log 1.0) (* 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)))))) (/ (* 1.0 x) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
75.0ms
(/ (- (log 1.0) (* 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))))))

series589.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
146.0ms
(/ (* 1.0 x) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
272.0ms
(- (/ (- (log 1.0) (* 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)))))) (/ (* 1.0 x) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
117.0ms
(/ (- (log 1.0) (* 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))))))

simplify3.4s

Algorithm
egg-herbie
Counts
4224 → 4224
Iterations

Useful iterations: 0 (60.0ms)

IterNodesCost
05001361313

prune20.1s

Filtered
4224 candidates to 3195 candidates (75.6%)
Pruning

6 alts after pruning (3 fresh and 3 done)

PrunedKeptTotal
New422404224
Fresh033
Picked011
Done022
Total422464230

Merged error: 0.0b

Counts
4230 → 6

regimes53.0ms

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
01724
11724

end0.0ms

sample4.4s

Algorithm
intervals
Results
2.9s3342×body1280valid
1.0s2515×body640valid
248.0ms1262×body320valid
100.0ms8000×pre80true
71.0ms651×body160valid
11.0ms230×body80valid