Details

Time bar (total: 10.3s)

sample36.0ms

Algorithm
intervals
Results
7.0ms185×body80valid
5.0ms21×body640valid
5.0ms25×body1280valid
3.0ms113×body80nan
2.0ms14×body1280nan
2.0ms19×body320valid
1.0ms9×body640nan
1.0ms8×body320nan
0.0ms6×body160valid
0.0ms1×body160nan

simplify78.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0912
11912
22912
34112
45812
56312
67112
78612
811412
912712
1012912
done12912

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 17.7b

localize9.0ms

Local error

Found 4 expressions with local error:

0.0b
(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
0.0b
(/ (- x y) (- 1.0 y))
2.1b
(- 1.0 (/ (- x y) (- 1.0 y)))
5.6b
(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite82.0ms

Algorithm
rewrite-expression-head
Rules
59×add-sqr-sqrt
51×*-un-lft-identity
28×times-frac
19×difference-of-squares
18×add-cube-cbrt
17×distribute-lft-out--
12×log-prod
7×add-exp-log add-log-exp
6×pow1 flip3-- add-cbrt-cube flip-- associate--r+
5×associate-/r* associate-/l*
4×log-div
3×associate--r-
2×sub-neg diff-log div-sub associate-/r/ log-pow associate-/l/
1×cbrt-undiv frac-2neg div-exp rem-log-exp clear-num div-inv
Counts
4 → 108
Calls
4 calls:
25.0ms
(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
11.0ms
(/ (- x y) (- 1.0 y))
20.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
22.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

series269.0ms

Counts
4 → 12
Calls
4 calls:
92.0ms
(- 1.0 (log (- 1.0 (/ (- x y) (- 1.0 y)))))
40.0ms
(/ (- x y) (- 1.0 y))
51.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
85.0ms
(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify1.2s

Counts
120 → 120
Iterations

Useful iterations: done (1.2s)

IterNodesCost
02051894
14881792
211981680
331561671
done50001670

prune297.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- 1.0 y))
0.1b
(* (- x y) (/ 1 (- 1.0 y)))
4.5b
(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))
5.6b
(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
48×add-sqr-sqrt
42×*-un-lft-identity
32×times-frac
25×add-cube-cbrt
21×associate-*r*
18×add-exp-log
11×add-cbrt-cube
8×pow1 distribute-lft-out-- difference-of-squares
6×flip3-- flip-- add-log-exp
5×associate-*l* associate-/r*
4×div-exp prod-exp associate-/r/
3×log-prod associate-/l* unswap-sqr
2×cbrt-undiv frac-times log-div rec-exp 1-exp associate-*l/ cbrt-unprod div-inv
1×sub-neg pow-flip frac-2neg diff-log associate-*r/ rem-log-exp pow-prod-down clear-num log-pow un-div-inv *-commutative inv-pow
Counts
4 → 117
Calls
4 calls:
6.0ms
(/ 1 (- 1.0 y))
28.0ms
(* (- x y) (/ 1 (- 1.0 y)))
2.0ms
(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))
2.0ms
(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))

series204.0ms

Counts
4 → 12
Calls
4 calls:
23.0ms
(/ 1 (- 1.0 y))
41.0ms
(* (- x y) (/ 1 (- 1.0 y)))
51.0ms
(- 1.0 (* (- x y) (/ 1 (- 1.0 y))))
88.0ms
(log (- 1.0 (* (- x y) (/ 1 (- 1.0 y)))))

simplify2.4s

Counts
129 → 129
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02051754
14801422
213321277
343251271
done50001270

prune244.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize16.0ms

Local error

Found 4 expressions with local error:

2.1b
(- 1.0 (/ (- x y) (- 1.0 y)))
2.1b
(- 1.0 (/ (- x y) (- 1.0 y)))
5.7b
(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
5.7b
(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))

rewrite88.0ms

Algorithm
rewrite-expression-head
Rules
28×add-sqr-sqrt
18×log-prod
16×*-un-lft-identity
12×cbrt-prod
8×add-cube-cbrt add-log-exp difference-of-squares
6×pow1 add-exp-log
4×log-div cbrt-div flip3-- times-frac log-pow add-cbrt-cube flip-- distribute-lft-out--
2×sub-neg pow1/3 diff-log div-sub rem-log-exp associate--r-
Counts
4 → 74
Calls
4 calls:
23.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
21.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
21.0ms
(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
21.0ms
(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))

series334.0ms

Counts
4 → 12
Calls
4 calls:
53.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
55.0ms
(- 1.0 (/ (- x y) (- 1.0 y)))
112.0ms
(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))
114.0ms
(log (cbrt (- 1.0 (/ (- x y) (- 1.0 y)))))

simplify1.2s

Counts
86 → 86
Iterations

Useful iterations: 4 (506.0ms)

IterNodesCost
01191594
12401540
24961412
311501360
436041356
done50001356

prune284.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b
(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (+ (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)))))
2.0b
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
12.0b
(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
13.4b
(log (+ (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0))))

rewrite250.0ms

Algorithm
rewrite-expression-head
Rules
148×add-sqr-sqrt
73×difference-of-squares
72×log-prod
54×unpow-prod-down cube-prod
42×*-un-lft-identity
33×associate--l+
30×sqr-pow
24×times-frac
19×distribute-lft-out--
10×pow1
8×add-cube-cbrt log-div
6×add-exp-log log-pow add-log-exp
4×flip3-- add-cbrt-cube flip--
3×difference-cubes associate--r+
2×associate--l- sub-neg flip3-+ diff-log rem-log-exp flip-+ associate--r-
Counts
4 → 157
Calls
4 calls:
83.0ms
(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (+ (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)))))
78.0ms
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
76.0ms
(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
5.0ms
(log (+ (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0))))

series1.0s

Counts
4 → 12
Calls
4 calls:
364.0ms
(- (log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))) (log (+ (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0)))))
178.0ms
(- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3))
326.0ms
(log (- (pow 1.0 3) (pow (/ (- x y) (- 1.0 y)) 3)))
165.0ms
(log (+ (* 1.0 1.0) (* (/ (- x y) (- 1.0 y)) (+ (/ (- x y) (- 1.0 y)) 1.0))))

simplify582.0ms

Counts
169 → 169
Iterations

Useful iterations: done (575.0ms)

IterNodesCost
02635772
16045433
216675240
done50015222

prune485.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.1b

regimes143.0ms

Accuracy

99.3% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 18.0b

bsearch1.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02240
12740
done2740

end0.0ms

sample972.0ms

Algorithm
intervals
Results
215.0ms5677×body80valid
160.0ms833×body1280valid
98.0ms731×body640valid
91.0ms3682×body80nan
56.0ms370×body1280nan
45.0ms484×body320valid
40.0ms363×body640nan
18.0ms230×body320nan
17.0ms275×body160valid
6.0ms122×body160nan