Details

Time bar (total: 9.5s)

sample53.0ms

Algorithm
intervals
Results
27.0ms59×body1280valid
10.0ms51×body640valid
4.0ms39×body320valid
2.0ms91×body80valid
1.0ms80×body80nan
1.0ms16×body160valid

simplify4.0ms

Algorithm
egg-herbie
Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
052
152

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 38.8b

localize3.0ms

Local error

Found 1 expressions with local error:

5.5b
(log (+ 1.0 x))

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
4×log-prod *-un-lft-identity
2×pow1 add-exp-log add-sqr-sqrt add-cube-cbrt log-div
1×flip3-+ rem-log-exp log-pow add-cbrt-cube flip-+ distribute-lft-out add-log-exp
Counts
1 → 15
Calls
1 calls:
5.0ms
(log (+ 1.0 x))

series43.0ms

Counts
1 → 3
Calls
1 calls:
43.0ms
(log (+ 1.0 x))

simplify38.0ms

Algorithm
egg-herbie
Counts
18 → 18
Iterations

Useful iterations: 3 (35.0ms)

IterNodesCost
012295
132786
2116181
3500278

prune37.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.1b

localize10.0ms

Local error

Found 2 expressions with local error:

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

rewrite94.0ms

Algorithm
rewrite-expression-head
Rules
80×times-frac
70×add-sqr-sqrt
68×associate-*r*
56×unpow-prod-down
36×add-cube-cbrt *-un-lft-identity
25×add-exp-log
24×unpow2 sqr-pow
17×unswap-sqr
10×prod-exp
9×div-exp
7×add-cbrt-cube
6×pow-to-exp pow-exp add-log-exp
4×pow1
3×associate-*r/ associate-*l*
2×diff-log frac-sub cbrt-unprod
1×cbrt-undiv sub-neg flip3-- flip3-+ pow-prod-down associate--l+ sum-log *-commutative flip-- flip-+ div-inv
Counts
2 → 126
Calls
2 calls:
36.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
52.0ms
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

series89.0ms

Counts
2 → 6
Calls
2 calls:
47.0ms
(* 1/2 (/ (pow x 2) (pow 1.0 2)))
42.0ms
(- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2))))

simplify77.0ms

Algorithm
egg-herbie
Counts
132 → 132
Iterations

Useful iterations: 2 (62.0ms)

IterNodesCost
0676882
12962760
25001756

prune281.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize19.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1.0 x) (log 1.0))))
0.2b
(pow (* 1/2 (/ (pow x 2) (pow 1.0 2))) 3)
13.3b
(- (pow (+ (* 1.0 x) (log 1.0)) 3) (pow (* 1/2 (/ (pow x 2) (pow 1.0 2))) 3))
39.9b
(/ (- (pow (+ (* 1.0 x) (log 1.0)) 3) (pow (* 1/2 (/ (pow x 2) (pow 1.0 2))) 3)) (+ (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1.0 x) (log 1.0)))) (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0)))))

rewrite599.0ms

Algorithm
rewrite-expression-head
Rules
140×associate-*r/
108×frac-add
93×flip3-+ flip-+
74×add-sqr-sqrt associate-/r/
72×frac-times
65×add-exp-log
40×difference-of-squares
39×times-frac
34×*-un-lft-identity
31×prod-exp sqr-pow
27×associate-*l/
24×add-cube-cbrt
23×pow-exp
21×add-cbrt-cube
19×div-exp
13×pow-to-exp associate-/l*
12×pow1
11×unpow-prod-down cube-prod
9×cube-div
7×cbrt-unprod
6×add-log-exp
5×difference-cubes distribute-lft-out--
4×pow-prod-down frac-sub associate-/l/
3×cbrt-undiv pow-unpow associate-*r* associate-/r* rem-cube-cbrt
2×flip3-- pow-pow flip--
1×distribute-rgt-in cube-mult sub-neg frac-2neg distribute-lft-in diff-log unpow3 div-sub associate-*l* clear-num *-commutative div-inv
Counts
4 → 242
Calls
4 calls:
120.0ms
(* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1.0 x) (log 1.0))))
14.0ms
(pow (* 1/2 (/ (pow x 2) (pow 1.0 2))) 3)
104.0ms
(- (pow (+ (* 1.0 x) (log 1.0)) 3) (pow (* 1/2 (/ (pow x 2) (pow 1.0 2))) 3))
344.0ms
(/ (- (pow (+ (* 1.0 x) (log 1.0)) 3) (pow (* 1/2 (/ (pow x 2) (pow 1.0 2))) 3)) (+ (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1.0 x) (log 1.0)))) (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0)))))

series524.0ms

Counts
4 → 12
Calls
4 calls:
79.0ms
(* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1.0 x) (log 1.0))))
75.0ms
(pow (* 1/2 (/ (pow x 2) (pow 1.0 2))) 3)
125.0ms
(- (pow (+ (* 1.0 x) (log 1.0)) 3) (pow (* 1/2 (/ (pow x 2) (pow 1.0 2))) 3))
244.0ms
(/ (- (pow (+ (* 1.0 x) (log 1.0)) 3) (pow (* 1/2 (/ (pow x 2) (pow 1.0 2))) 3)) (+ (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1.0 x) (log 1.0)))) (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0)))))

simplify133.0ms

Algorithm
egg-herbie
Counts
254 → 254
Iterations

Useful iterations: 1 (44.0ms)

IterNodesCost
0203510347
1500210125

prune991.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

localize37.0ms

Local error

Found 4 expressions with local error:

0.2b
(pow (* 1/2 (pow x 2)) 3)
19.1b
(- (* (pow (+ (pow (* 1.0 x) 3) (pow (log 1.0) 3)) 3) (pow (pow 1.0 2) 3)) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (* 1/2 (pow x 2)) 3)))
39.9b
(/ (/ (- (* (pow (+ (pow (* 1.0 x) 3) (pow (log 1.0) 3)) 3) (pow (pow 1.0 2) 3)) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (* 1/2 (pow x 2)) 3))) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (pow 1.0 2) 3))) (+ (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1.0 x) (log 1.0)))) (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0)))))
55.1b
(/ (- (* (pow (+ (pow (* 1.0 x) 3) (pow (log 1.0) 3)) 3) (pow (pow 1.0 2) 3)) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (* 1/2 (pow x 2)) 3))) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (pow 1.0 2) 3)))

rewrite1.1s

Algorithm
rewrite-expression-head
Rules
122×associate-*r/
104×frac-add
100×add-exp-log flip3-+ flip-+
84×associate-/r/
68×frac-times
52×associate-*l/
50×times-frac
49×div-exp
39×pow-exp
33×prod-exp
26×cube-div add-sqr-sqrt add-cube-cbrt *-un-lft-identity
24×pow-to-exp
21×add-cbrt-cube
14×pow-prod-down associate-/l*
8×frac-sub
7×difference-cubes cbrt-undiv associate-/l/
6×div-inv add-log-exp
5×pow1
4×associate-/r*
3×pow-unpow div-sub cbrt-unprod
2×flip3-- frac-2neg clear-num flip-- rem-cube-cbrt
1×cube-mult sub-neg unpow-prod-down pow-pow diff-log unpow3 cube-prod sqr-pow
Counts
4 → 235
Calls
4 calls:
7.0ms
(pow (* 1/2 (pow x 2)) 3)
141.0ms
(- (* (pow (+ (pow (* 1.0 x) 3) (pow (log 1.0) 3)) 3) (pow (pow 1.0 2) 3)) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (* 1/2 (pow x 2)) 3)))
498.0ms
(/ (/ (- (* (pow (+ (pow (* 1.0 x) 3) (pow (log 1.0) 3)) 3) (pow (pow 1.0 2) 3)) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (* 1/2 (pow x 2)) 3))) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (pow 1.0 2) 3))) (+ (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1.0 x) (log 1.0)))) (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0)))))
388.0ms
(/ (- (* (pow (+ (pow (* 1.0 x) 3) (pow (log 1.0) 3)) 3) (pow (pow 1.0 2) 3)) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (* 1/2 (pow x 2)) 3))) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (pow 1.0 2) 3)))

series1.9s

Counts
4 → 12
Calls
4 calls:
52.0ms
(pow (* 1/2 (pow x 2)) 3)
375.0ms
(- (* (pow (+ (pow (* 1.0 x) 3) (pow (log 1.0) 3)) 3) (pow (pow 1.0 2) 3)) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (* 1/2 (pow x 2)) 3)))
645.0ms
(/ (/ (- (* (pow (+ (pow (* 1.0 x) 3) (pow (log 1.0) 3)) 3) (pow (pow 1.0 2) 3)) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (* 1/2 (pow x 2)) 3))) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (pow 1.0 2) 3))) (+ (* (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1/2 (/ (pow x 2) (pow 1.0 2))) (+ (* 1.0 x) (log 1.0)))) (* (+ (* 1.0 x) (log 1.0)) (+ (* 1.0 x) (log 1.0)))))
808.0ms
(/ (- (* (pow (+ (pow (* 1.0 x) 3) (pow (log 1.0) 3)) 3) (pow (pow 1.0 2) 3)) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (* 1/2 (pow x 2)) 3))) (* (pow (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 3) (pow (pow 1.0 2) 3)))

simplify194.0ms

Algorithm
egg-herbie
Counts
247 → 247
Iterations

Useful iterations: 1 (48.0ms)

IterNodesCost
0230818037
1500217336

prune1.5s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes79.0ms

Accuracy

99.3% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 21.8b

bsearch1.0ms

simplify1.0ms

Algorithm
egg-herbie
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
02111
12111

end0.0ms

sample1.7s

Algorithm
intervals
Results
986.0ms2291×body1280valid
328.0ms1607×body640valid
88.0ms882×body320valid
63.0ms2820×body80valid
32.0ms2614×body80nan
23.0ms400×body160valid