Details

Time bar (total: 14.5s)

sample128.0ms

Algorithm
intervals
Results
69.0ms66×body10240exit
29.0ms263×body80valid
4.0ms6×body640valid
3.0ms8×body320valid
3.0ms2×body1280valid
2.0ms6×body160valid

simplify12.0ms

Counts
1 → 1
Iterations
IterNodes
done21
221
114
08

prune22.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.5b

localize14.0ms

Local error

Found 3 expressions with local error:

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

rewrite18.0ms

Algorithm
rewrite-expression-head
Rules
11×*-un-lft-identity
8×log-prod
6×add-log-exp
5×add-sqr-sqrt add-cube-cbrt
4×pow1 log-div associate--l+ add-exp-log
3×flip3-+ add-cbrt-cube flip-+ insert-posit16 distribute-lft-out
2×associate--l-
1×+-commutative sum-log sub-neg flip3-- diff-log rem-log-exp log-pow flip--
Counts
3 → 48
Calls
3 calls:
5.0ms
(+ 1 (exp x))
9.0ms
(- (log (+ 1 (exp x))) (* x y))
4.0ms
(log (+ 1 (exp x)))

series159.0ms

Counts
3 → 9
Calls
3 calls:
15.0ms
(+ 1 (exp x))
74.0ms
(- (log (+ 1 (exp x))) (* x y))
70.0ms
(log (+ 1 (exp x)))

simplify806.0ms

Counts
57 → 57
Iterations
IterNodes
done5000
2778
1203
084

prune261.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.4b

localize53.0ms

Local error

Found 4 expressions with local error:

0.7b
(* (* (cbrt (log (+ 1 (exp x)))) (cbrt (log (+ 1 (exp x))))) (cbrt (log (+ 1 (exp x)))))
1.1b
(cbrt (log (+ 1 (exp x))))
1.1b
(cbrt (log (+ 1 (exp x))))
1.1b
(cbrt (log (+ 1 (exp x))))

rewrite24.0ms

Algorithm
rewrite-expression-head
Rules
27×pow1
17×cbrt-prod
12×pow1/3
11×add-sqr-sqrt
9×*-un-lft-identity add-exp-log pow-prod-up add-cube-cbrt
7×associate-*r*
6×pow-plus
5×add-cbrt-cube pow-prod-down
4×log-pow insert-posit16 add-log-exp
3×prod-exp pow-sqr cbrt-unprod
2×pow2 unswap-sqr
1×associate-*l* pow3 *-commutative
Counts
4 → 76
Calls
4 calls:
20.0ms
(* (* (cbrt (log (+ 1 (exp x)))) (cbrt (log (+ 1 (exp x))))) (cbrt (log (+ 1 (exp x)))))
1.0ms
(cbrt (log (+ 1 (exp x))))
1.0ms
(cbrt (log (+ 1 (exp x))))
1.0ms
(cbrt (log (+ 1 (exp x))))

series1.2s

Counts
4 → 12
Calls
4 calls:
86.0ms
(* (* (cbrt (log (+ 1 (exp x)))) (cbrt (log (+ 1 (exp x))))) (cbrt (log (+ 1 (exp x)))))
270.0ms
(cbrt (log (+ 1 (exp x))))
568.0ms
(cbrt (log (+ 1 (exp x))))
228.0ms
(cbrt (log (+ 1 (exp x))))

simplify1.4s

Counts
88 → 88
Iterations
IterNodes
done5000
2950
1210
085

prune344.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(* 1/2 (* x x))
0.0b
(+ (+ 2 x) (* 1/2 (* x x)))
0.0b
(- (log (+ (+ 2 x) (* 1/2 (* x x)))) (* x y))
7.5b
(log (+ (+ 2 x) (* 1/2 (* x x))))

rewrite87.0ms

Algorithm
rewrite-expression-head
Rules
10×pow1 add-exp-log add-log-exp
9×add-cbrt-cube
8×add-sqr-sqrt
7×*-un-lft-identity add-cube-cbrt
6×log-prod
4×log-div insert-posit16
3×sum-log flip3-+ associate-*l* pow-prod-down prod-exp associate--l+ cbrt-unprod flip-+
2×associate--l-
1×+-commutative associate-+l+ sub-neg flip3-- diff-log rem-log-exp associate-*r* log-pow *-commutative flip-- unswap-sqr
Counts
4 → 67
Calls
4 calls:
13.0ms
(* 1/2 (* x x))
36.0ms
(+ (+ 2 x) (* 1/2 (* x x)))
19.0ms
(- (log (+ (+ 2 x) (* 1/2 (* x x)))) (* x y))
18.0ms
(log (+ (+ 2 x) (* 1/2 (* x x))))

series223.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(* 1/2 (* x x))
34.0ms
(+ (+ 2 x) (* 1/2 (* x x)))
94.0ms
(- (log (+ (+ 2 x) (* 1/2 (* x x)))) (* x y))
44.0ms
(log (+ (+ 2 x) (* 1/2 (* x x))))

simplify1.4s

Counts
79 → 79
Iterations
IterNodes
done5001
21634
1359
0132

prune432.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize85.0ms

Local error

Found 4 expressions with local error:

0.5b
(log (+ 1 (exp x)))
0.7b
(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
0.7b
(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
12.5b
(/ (+ (- (* (* x y) (* (* x y) (* x y)))) (* (log (+ 1 (exp x))) (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))))) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))))

rewrite254.0ms

Algorithm
rewrite-expression-head
Rules
39×*-un-lft-identity
31×pow1
29×add-sqr-sqrt
25×add-cube-cbrt
20×log-prod
13×log-pow
12×swap-sqr
11×add-exp-log
10×add-cbrt-cube
9×times-frac
8×distribute-rgt-in distribute-lft-in associate-*r* associate-*l*
5×distribute-lft-out
4×insert-posit16 add-log-exp
3×associate-/r* flip3-+ flip-+ associate-/l*
2×pow2 log-div pow-plus pow-prod-down prod-exp associate-/r/ pow-sqr *-commutative pow-prod-up cbrt-unprod unswap-sqr associate-/l/
1×neg-sub0 cbrt-undiv clear-num frac-2neg div-sub div-exp rem-log-exp associate-+l- div-inv
Counts
4 → 127
Calls
4 calls:
7.0ms
(log (+ 1 (exp x)))
24.0ms
(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
20.0ms
(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
201.0ms
(/ (+ (- (* (* x y) (* (* x y) (* x y)))) (* (log (+ 1 (exp x))) (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))))) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))))

series507.0ms

Counts
4 → 12
Calls
4 calls:
78.0ms
(log (+ 1 (exp x)))
83.0ms
(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
104.0ms
(* (log (+ 1 (exp x))) (log (+ 1 (exp x))))
240.0ms
(/ (+ (- (* (* x y) (* (* x y) (* x y)))) (* (log (+ 1 (exp x))) (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))))) (+ (* (log (+ 1 (exp x))) (log (+ 1 (exp x)))) (+ (* (* x y) (* x y)) (* (log (+ 1 (exp x))) (* x y)))))

simplify2.1s

Counts
139 → 139
Iterations
IterNodes
done5002
22391
1433
0160

prune718.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

regimes118.0ms

Accuracy

82.3% (0.2b remaining)

Error of 0.5b against oracle of 0.2b and baseline of 1.5b

bsearch134.0ms

Steps
ItersRangePoint
10
4.3052657707541446e-11
32.81305289360078
8.156195176767745e-07
8
-0.00010358510568112945
-3.3482176662224007e-07
-1.4952609597112308e-05

simplify6.0ms

Iterations
IterNodes
done41
141
030

end0.0ms

sample4.0s

Algorithm
intervals
Results
2.1s2386×body10240exit
1.3s8495×body80valid
133.0ms258×body640valid
94.0ms107×body1280valid
70.0ms202×body320valid
19.0ms90×body160valid