Details

Time bar (total: 9.5s)

sample143.0ms

Algorithm
intervals
Results
86.0ms100×body1280valid
32.0ms87×body640valid
8.0ms40×body320valid
3.0ms256×pre80true
3.0ms23×body160valid
0.0ms6×body80valid

simplify5.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0105
1115
2115

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 61.4b

localize7.0ms

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))

rewrite30.0ms

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×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 → 69
Calls
3 calls:
17.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.0ms
(log (- 1.0 x))
5.0ms
(log (+ 1.0 x))

series196.0ms

Counts
3 → 9
Calls
3 calls:
115.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
39.0ms
(log (- 1.0 x))
43.0ms
(log (+ 1.0 x))

simplify43.0ms

Algorithm
egg-herbie
Counts
78 → 78
Iterations

Useful iterations: 2 (36.0ms)

IterNodesCost
0425668
11561624
25001599

prune199.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 59.0b

localize17.0ms

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)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
7.8b
(log (- 1.0 x))

rewrite112.0ms

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-/r/ associate-/l*
3×flip3-- associate-*r/ associate-*l* associate-/r* flip-- add-log-exp
2×cbrt-undiv div-sub frac-sub cbrt-unprod div-inv
1×frac-2neg flip3-+ rem-log-exp pow-prod-down clear-num *-commutative flip-+ distribute-lft-out-- difference-of-squares
Counts
3 → 163
Calls
3 calls:
37.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
61.0ms
(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
5.0ms
(log (- 1.0 x))

series215.0ms

Counts
3 → 9
Calls
3 calls:
50.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
122.0ms
(/ (log (- 1.0 x)) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))
43.0ms
(log (- 1.0 x))

simplify105.0ms

Algorithm
egg-herbie
Counts
172 → 172
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09951550
142131389
250011389

prune474.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

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

rewrite187.0ms

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×associate-*r/ associate-/r/ log-pow cbrt-unprod difference-of-squares
3×cbrt-undiv associate-/r* div-inv add-log-exp
2×flip3-- pow-prod-down *-commutative frac-sub flip-- associate-/l/
1×frac-2neg flip3-+ div-sub clear-num flip-+
Counts
3 → 266
Calls
3 calls:
39.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
38.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
95.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

series204.0ms

Counts
3 → 9
Calls
3 calls:
47.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
46.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
110.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))

simplify100.0ms

Algorithm
egg-herbie
Counts
275 → 275
Iterations

Useful iterations: 2 (74.0ms)

IterNodesCost
08552533
136882254
250012253

prune719.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b
(- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))
0.1b
(* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))
0.2b
(* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))
28.6b
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))))

rewrite795.0ms

Algorithm
rewrite-expression-head
Rules
47×*-un-lft-identity
40×add-exp-log add-sqr-sqrt
36×times-frac
31×associate-*l* associate-*l/
26×add-cube-cbrt
23×add-cbrt-cube
21×prod-exp
19×flip3-- flip--
15×pow1
14×distribute-lft-out--
12×associate-/r/ frac-sub
9×cbrt-unprod
7×log-pow difference-of-squares
6×associate-/l* add-log-exp
5×div-exp
3×cbrt-undiv pow-to-exp pow-exp associate-/r*
2×frac-times associate-*r/ associate-*r* pow-prod-down *-commutative div-inv associate-/l/
1×sub-neg frac-2neg diff-log div-sub clear-num
Counts
4 → 140
Calls
4 calls:
94.0ms
(- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))
46.0ms
(* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))
484.0ms
(* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))
164.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))))

series711.0ms

Counts
4 → 12
Calls
4 calls:
104.0ms
(- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))
224.0ms
(* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))
211.0ms
(* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2))))) (* (- (* 1.0 x) (log 1.0)) (pow 1.0 2)))
171.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (- (* (* 1.0 x) (* 1.0 x)) (* (log 1.0) (log 1.0))) (pow 1.0 2)) (* (- (* 1.0 x) (log 1.0)) (* 1/2 (pow x 2)))))

simplify149.0ms

Algorithm
egg-herbie
Counts
152 → 152
Iterations

Useful iterations: 1 (24.0ms)

IterNodesCost
09424903
146794351
250024351

prune512.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 0.1b

regimes41.0ms

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)

IterNodesCost
01917
11917

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.9s3435×body1280valid
1.0s2542×body640valid
237.0ms1216×body320valid
96.0ms8000×pre80true
64.0ms586×body160valid
10.0ms221×body80valid