Details

Time bar (total: 8.7s)

sample152.0ms

Algorithm
intervals
Results
97.0ms110×body1280valid
32.0ms81×body640valid
7.0ms38×body320valid
3.0ms256×pre80true
2.0ms19×body160valid
0.0ms8×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: 61.8b

localize7.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
5.4b
(log (+ 1.0 x))
5.4b
(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:
7.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
2.0ms
(log (+ 1.0 x))
3.0ms
(log (- 1.0 x))

series208.0ms

Counts
3 → 9
Calls
3 calls:
122.0ms
(/ (log (- 1.0 x)) (log (+ 1.0 x)))
39.0ms
(log (+ 1.0 x))
45.0ms
(log (- 1.0 x))

simplify45.0ms

Algorithm
egg-herbie
Counts
84 → 84
Iterations

Useful iterations: 2 (37.0ms)

IterNodesCost
0452686
11669638
25001623

prune212.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 59.3b

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))))))
5.4b
(log (- 1.0 x))

rewrite46.0ms

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:
28.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
7.0ms
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
3.0ms
(log (- 1.0 x))

series233.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
138.0ms
(/ (log (- 1.0 x)) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
42.0ms
(log (- 1.0 x))

simplify89.0ms

Algorithm
egg-herbie
Counts
174 → 174
Iterations

Useful iterations: 1 (20.0ms)

IterNodesCost
09281453
138371286
250011286

prune486.0ms

Pruning

3 alts after pruning (3 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))))))

rewrite96.0ms

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:
28.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
26.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
28.0ms
(/ (- (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))))))

series234.0ms

Counts
3 → 9
Calls
3 calls:
54.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
54.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
126.0ms
(/ (- (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)

IterNodesCost
07532429
131742138
250012135

prune784.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize18.0ms

Local error

Found 4 expressions with local error:

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

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
134×times-frac
124×add-sqr-sqrt
100×*-un-lft-identity
70×add-cube-cbrt
68×associate-*r*
56×unpow-prod-down
44×exp-prod
33×log-pow
29×add-exp-log
24×unpow2 sqr-pow
20×distribute-lft-out--
17×pow1 unswap-sqr
11×add-cbrt-cube
10×div-exp prod-exp difference-of-squares
6×pow-to-exp pow-exp associate-/l*
5×add-log-exp
4×expm1-log1p-u log1p-expm1-u div-inv
3×log-prod div-sub associate-*l* associate-/r*
2×cbrt-undiv exp-diff cbrt-unprod associate-/l/
1×log-div flip3-- frac-2neg associate-*r/ rem-log-exp pow-prod-down clear-num *-commutative flip-- rem-exp-log
Counts
4 → 226
Calls
4 calls:
26.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
28.0ms
(log (exp (/ (- (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))))))))
29.0ms
(exp (/ (- (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)))))))
24.0ms
(/ (- (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))))))

series459.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
123.0ms
(log (exp (/ (- (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))))))))
159.0ms
(exp (/ (- (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)))))))
125.0ms
(/ (- (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))))))

simplify101.0ms

Algorithm
egg-herbie
Counts
238 → 238
Iterations

Useful iterations: 2 (66.0ms)

IterNodesCost
08673117
134662850
250022841

prune739.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.1b

regimes34.0ms

Accuracy

0% (0.4b 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
02419
12419

end0.0ms

sample4.5s

Algorithm
intervals
Results
2.9s3404×body1280valid
989.0ms2438×body640valid
262.0ms1274×body320valid
96.0ms8000×pre80true
72.0ms645×body160valid
11.0ms239×body80valid