Details

Time bar (total: 5.5m)

sample123.0ms

Algorithm
intervals
Results
72.0ms78×body10240exit
26.0ms274×body80valid
5.0ms4×body1280valid
4.0ms8×body640valid
2.0ms5×body320valid
0.0ms1×body160valid

simplify41.0ms

Calls
1 calls:
Slowest
41.0ms
(- (log (+ 1 (exp x))) (* x y))

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.8b

localize52.0ms

Local error

Found 3 expressions with local error:

0.8b
(log (+ 1 (exp x)))
0.0b
(+ 1 (exp x))
0.0b
(- (log (+ 1 (exp x))) (* x y))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
17×*-un-lft-identity
10×add-sqr-sqrt
8×log-prod add-log-exp
6×pow1
5×add-cube-cbrt
4×log-div associate--l+ add-exp-log distribute-lft-out--
3×flip3-+ add-cbrt-cube log-pow flip-+ insert-posit16 distribute-lft-out
2×associate--l- diff-log associate-*l* difference-of-squares
1×+-commutative sum-log sub-neg flip3-- rem-log-exp flip-- unswap-sqr
Calls
3 calls:
Slowest
24.0ms
(- (log (+ 1 (exp x))) (* x y))
9.0ms
(+ 1 (exp x))
7.0ms
(log (+ 1 (exp x)))

series135.0ms

Calls
3 calls:
Slowest
65.0ms
(log (+ 1 (exp x)))
56.0ms
(- (log (+ 1 (exp x))) (* x y))
14.0ms
(+ 1 (exp x))

simplify1.2s

Calls
34 calls:
Slowest
201.0ms
(/ (exp (log (+ 1 (exp x)))) (exp (* x y)))
97.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))
94.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))
74.0ms
(log (+ (pow 1 3) (pow (exp x) 3)))
70.0ms
(+ (log 2) (+ (* 1/2 x) (* 1/8 (pow x 2))))

prune651.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.2b

localize71.0ms

Local error

Found 4 expressions with local error:

7.0b
(- (* (exp x) (exp x)) (* 1 (exp x)))
0.5b
(log (/ (+ (pow 1 3) (pow (exp x) 3)) (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x))))))
0.4b
(/ (+ (pow 1 3) (pow (exp x) 3)) (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x)))))
0.0b
(pow (exp x) 3)

rewrite919.0ms

Algorithm
rewrite-expression-head
Rules
3200×*-un-lft-identity
1290×distribute-lft-out
884×times-frac
765×distribute-lft-out--
761×associate-*l*
448×log-prod
283×pow-unpow unpow-prod-down cube-prod
280×sum-cubes
204×*-commutative
144×add-sqr-sqrt
122×associate-*r*
116×swap-sqr
109×add-cube-cbrt
72×cube-mult
68×associate-/r*
52×log-div
41×unswap-sqr
29×associate-/l*
15×difference-of-squares
10×add-exp-log
8×distribute-rgt-out--
7×add-cbrt-cube
6×pow1 add-log-exp
4×pow-pow flip3-+ log-rec associate-/r/ flip-+ insert-posit16 associate-/l/
3×exp-prod clear-num
2×frac-2neg div-exp rem-log-exp pow-exp div-inv
1×pow-to-exp cbrt-undiv sub-neg flip3-- diff-log unpow3 log-pow flip-- rem-cube-cbrt sqr-pow
Calls
4 calls:
Slowest
457.0ms
(log (/ (+ (pow 1 3) (pow (exp x) 3)) (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x))))))
292.0ms
(/ (+ (pow 1 3) (pow (exp x) 3)) (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x)))))
70.0ms
(- (* (exp x) (exp x)) (* 1 (exp x)))
7.0ms
(pow (exp x) 3)

series328.0ms

Calls
4 calls:
Slowest
166.0ms
(log (/ (+ (pow 1 3) (pow (exp x) 3)) (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x))))))
90.0ms
(/ (+ (pow 1 3) (pow (exp x) 3)) (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x)))))
46.0ms
(- (* (exp x) (exp x)) (* 1 (exp x)))
26.0ms
(pow (exp x) 3)

simplify3.9m

Calls
1526 calls:
Slowest
709.0ms
(log (/ (+ (* 1 1) (- (* (pow (exp x) 1) (pow (exp x) 1)) (* 1 (pow (exp x) 1)))) 1))
670.0ms
(/ (+ (pow 1 3) (pow (exp x) 3)) (+ (* 1 1) (- (* (exp x) (exp x)) (exp x))))
637.0ms
(/ (+ (* 1 1) (pow (exp x) 3)) (+ (* 1 1) (- (* (exp x) (exp x)) (exp x))))
594.0ms
(/ (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x)))) 1)
584.0ms
(/ (+ (pow 1 1) (pow (exp x) 1)) (cbrt (+ (* 1 1) (- (* (exp x) (exp x)) (* 1 (exp x))))))

prune14.0s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.2b

localize50.0ms

Local error

Found 4 expressions with local error:

7.0b
(- (* (exp x) (exp x)) (exp x))
6.9b
(log (+ 1 (- (* (exp x) (exp x)) (exp x))))
0.5b
(log (+ (* (* (exp x) (exp x)) (exp x)) 1))
0.0b
(- (log (+ (* (* (exp x) (exp x)) (exp x)) 1)) (log (+ 1 (- (* (exp x) (exp x)) (exp x)))))

rewrite516.0ms

Algorithm
rewrite-expression-head
Rules
48×*-un-lft-identity
24×add-sqr-sqrt log-prod
12×add-cube-cbrt distribute-lft-out distribute-lft-out--
11×associate-*l*
10×pow1 add-log-exp
8×log-div
6×associate--l+ add-exp-log log-pow associate--r+ difference-of-squares
5×distribute-rgt-out-- diff-log
4×flip3-+ add-cbrt-cube flip-+ insert-posit16
3×associate-*r*
2×associate--l- sub-neg flip3-- rem-log-exp *-commutative flip-- associate--r-
1×swap-sqr unswap-sqr
Calls
4 calls:
Slowest
194.0ms
(- (log (+ (* (* (exp x) (exp x)) (exp x)) 1)) (log (+ 1 (- (* (exp x) (exp x)) (exp x)))))
118.0ms
(log (+ 1 (- (* (exp x) (exp x)) (exp x))))
106.0ms
(log (+ (* (* (exp x) (exp x)) (exp x)) 1))
95.0ms
(- (* (exp x) (exp x)) (exp x))

series462.0ms

Calls
4 calls:
Slowest
182.0ms
(- (log (+ (* (* (exp x) (exp x)) (exp x)) 1)) (log (+ 1 (- (* (exp x) (exp x)) (exp x)))))
148.0ms
(log (+ 1 (- (* (exp x) (exp x)) (exp x))))
82.0ms
(log (+ (* (* (exp x) (exp x)) (exp x)) 1))
50.0ms
(- (* (exp x) (exp x)) (exp x))

simplify7.5s

Calls
83 calls:
Slowest
548.0ms
(- (log (+ (* (* (exp x) (exp x)) (exp x)) 1)) (log (+ 1 (- (* (exp x) (exp x)) (exp x)))))
501.0ms
(log (+ (pow 1 3) (pow (- (* (exp x) (exp x)) (exp x)) 3)))
408.0ms
(log (+ (pow (* (* (exp x) (exp x)) (exp x)) 3) (pow 1 3)))
377.0ms
(log (- (* (* (* (exp x) (exp x)) (exp x)) (* (* (exp x) (exp x)) (exp x))) (* 1 1)))
353.0ms
(log (+ (pow (* (* (exp x) (exp x)) (exp x)) 3) (pow 1 3)))

prune1.4s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.2b

localize55.0ms

Local error

Found 4 expressions with local error:

7.0b
(- (* (exp x) (exp x)) (exp x))
1.2b
(log (/ (sqrt (+ (pow 1 3) (pow (exp x) 3))) (+ 1 (- (* (exp x) (exp x)) (exp x)))))
1.2b
(log (/ (sqrt (+ (pow 1 3) (pow (exp x) 3))) 1))
0.5b
(/ (sqrt (+ (pow 1 3) (pow (exp x) 3))) (+ 1 (- (* (exp x) (exp x)) (exp x))))

rewrite635.0ms

Algorithm
rewrite-expression-head
Rules
645×*-un-lft-identity
240×times-frac
234×sqrt-prod
210×distribute-lft-out
154×log-prod
107×add-sqr-sqrt
97×add-cube-cbrt
72×pow-unpow unpow-prod-down cube-prod sum-cubes distribute-lft-out--
51×log-div
50×associate-/l*
37×associate-*l*
18×cube-mult
15×associate-/r*
13×add-exp-log
6×pow1 add-cbrt-cube sqrt-div add-log-exp associate-/l/
5×clear-num flip3-+ distribute-rgt-out-- rem-log-exp flip-+ difference-of-squares
4×div-exp log-rec associate-/r/ insert-posit16
3×frac-2neg associate-*r* div-inv
2×log-pow *-commutative
1×cbrt-undiv sub-neg flip3-- diff-log 1-exp swap-sqr flip-- unswap-sqr
Calls
4 calls:
Slowest
266.0ms
(log (/ (sqrt (+ (pow 1 3) (pow (exp x) 3))) (+ 1 (- (* (exp x) (exp x)) (exp x)))))
234.0ms
(/ (sqrt (+ (pow 1 3) (pow (exp x) 3))) (+ 1 (- (* (exp x) (exp x)) (exp x))))
66.0ms
(- (* (exp x) (exp x)) (exp x))
52.0ms
(log (/ (sqrt (+ (pow 1 3) (pow (exp x) 3))) 1))

series684.0ms

Calls
4 calls:
Slowest
328.0ms
(log (/ (sqrt (+ (pow 1 3) (pow (exp x) 3))) (+ 1 (- (* (exp x) (exp x)) (exp x)))))
171.0ms
(/ (sqrt (+ (pow 1 3) (pow (exp x) 3))) (+ 1 (- (* (exp x) (exp x)) (exp x))))
153.0ms
(log (/ (sqrt (+ (pow 1 3) (pow (exp x) 3))) 1))
32.0ms
(- (* (exp x) (exp x)) (exp x))

simplify1.0m

Calls
472 calls:
Slowest
639.0ms
(log (sqrt (+ (pow (pow 1 3) 3) (pow (pow (exp x) 3) 3))))
479.0ms
(log (/ (* (cbrt (sqrt (+ (pow 1 3) (pow (exp x) 3)))) (cbrt (sqrt (+ (pow 1 3) (pow (exp x) 3))))) (* (cbrt (+ 1 (- (* (exp x) (exp x)) (exp x)))) (cbrt (+ 1 (- (* (exp x) (exp x)) (exp x)))))))
357.0ms
(log (/ (sqrt (sqrt (+ (pow 1 3) (pow (exp x) 3)))) (* (cbrt (+ 1 (- (* (exp x) (exp x)) (exp x)))) (cbrt (+ 1 (- (* (exp x) (exp x)) (exp x)))))))
335.0ms
(log (/ (sqrt (+ (* (pow 1 1) (pow 1 1)) (- (* (pow (exp x) 1) (pow (exp x) 1)) (* (pow 1 1) (pow (exp x) 1))))) 1))
334.0ms
(log (/ (sqrt (+ (* 1 1) (- (* (pow (exp x) 1) (pow (exp x) 1)) (* 1 (pow (exp x) 1))))) (* (cbrt (+ 1 (- (* (exp x) (exp x)) (exp x)))) (cbrt (+ 1 (- (* (exp x) (exp x)) (exp x)))))))

prune4.7s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

regimes58.0ms

Accuracy

0% (0.2b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 0.5b

bsearch5.0ms

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.9s2425×body10240exit
656.0ms8451×body80valid
102.0ms277×body640valid
96.0ms204×body320valid
90.0ms134×body1280valid
16.0ms98×body160valid