Details

Time bar (total: 22.8s)

sample182.0ms

Algorithm
intervals
Results
44.0ms313×body80valid
43.0ms63×body10240exit
33.0ms51×body1280valid
18.0ms44×body640valid
7.0ms25×body320valid
2.0ms8×body160valid

simplify1.4s

Counts
1 → 1
Iterations
IterNodes
done5000
42266
3377
2122
146
019

prune20.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (+ 1.0 eps) x)
0.0b
(exp (- (* (- 1.0 eps) x)))
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
2.0b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite167.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
77×exp-neg
76×frac-times
58×neg-sub0 exp-diff
40×associate-*l/
38×associate-*r/
31×flip3-- flip--
28×flip3-+ flip-+
19×un-div-inv
18×add-sqr-sqrt
13×*-un-lft-identity
10×associate-*l*
9×add-cube-cbrt
8×pow1 add-cbrt-cube add-log-exp
7×add-exp-log
6×exp-prod associate-*r*
2×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr rem-exp-log
1×distribute-lft-neg-in neg-mul-1 sub-neg distribute-rgt-neg-in times-frac diff-log neg-log distribute-lft-out distribute-lft-out--
Counts
4 → 161
Calls
4 calls:
32.0ms
(* (+ 1.0 eps) x)
13.0ms
(exp (- (* (- 1.0 eps) x)))
61.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
42.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series459.0ms

Counts
4 → 12
Calls
4 calls:
31.0ms
(* (+ 1.0 eps) x)
53.0ms
(exp (- (* (- 1.0 eps) x)))
75.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
300.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify1.2s

Counts
173 → 173
Iterations
IterNodes
done5000
11245
0392

prune1.1s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 3 expressions with local error:

0.1b
(* 0.6666666666666667 (* (* x x) x))
0.1b
(* (* x x) x)
5.4b
(- (+ (* 0.6666666666666667 (* (* x x) x)) 2.0) (* (* 1.0 x) x))

rewrite534.0ms

Algorithm
rewrite-expression-head
Rules
31×pow1
17×add-cbrt-cube add-exp-log
9×pow-prod-down prod-exp cbrt-unprod
8×add-log-exp
6×add-sqr-sqrt pow-plus pow-prod-up
5×*-un-lft-identity add-cube-cbrt
4×associate-*r* associate-*l*
2×pow2 diff-log pow-sqr *-commutative
1×sum-log sub-neg flip3-- pow3 associate--l+ flip-- unswap-sqr
Counts
3 → 63
Calls
3 calls:
73.0ms
(* 0.6666666666666667 (* (* x x) x))
28.0ms
(* (* x x) x)
429.0ms
(- (+ (* 0.6666666666666667 (* (* x x) x)) 2.0) (* (* 1.0 x) x))

series180.0ms

Counts
3 → 9
Calls
3 calls:
44.0ms
(* 0.6666666666666667 (* (* x x) x))
61.0ms
(* (* x x) x)
75.0ms
(- (+ (* 0.6666666666666667 (* (* x x) x)) 2.0) (* (* 1.0 x) x))

simplify1.5s

Counts
72 → 72
Iterations
IterNodes
done5001
21919
1272
092

prune249.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) (* x 0.6666666666666667))
0.4b
(exp (log (+ (* (* x x) (* x 0.6666666666666667)) (- 2.0 (* (* x x) 1.0)))))
5.4b
(+ (* (* x x) (* x 0.6666666666666667)) (- 2.0 (* (* x x) 1.0)))
8.8b
(log (+ (* (* x x) (* x 0.6666666666666667)) (- 2.0 (* (* x x) 1.0))))

rewrite147.0ms

Algorithm
rewrite-expression-head
Rules
18×pow1
17×add-exp-log
16×add-cbrt-cube
9×add-log-exp
8×pow-prod-down prod-exp cbrt-unprod
7×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
6×log-prod
4×log-div exp-prod
3×flip3-+ exp-sum flip-+
2×associate-+r+ sum-log exp-diff log-pow
1×+-commutative associate-+r- sub-neg diff-log rem-log-exp associate-*r* associate-*l* *-commutative rem-exp-log
Counts
4 → 68
Calls
4 calls:
23.0ms
(* (* x x) (* x 0.6666666666666667))
57.0ms
(exp (log (+ (* (* x x) (* x 0.6666666666666667)) (- 2.0 (* (* x x) 1.0)))))
39.0ms
(+ (* (* x x) (* x 0.6666666666666667)) (- 2.0 (* (* x x) 1.0)))
26.0ms
(log (+ (* (* x x) (* x 0.6666666666666667)) (- 2.0 (* (* x x) 1.0))))

series279.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(* (* x x) (* x 0.6666666666666667))
50.0ms
(exp (log (+ (* (* x x) (* x 0.6666666666666667)) (- 2.0 (* (* x x) 1.0)))))
55.0ms
(+ (* (* x x) (* x 0.6666666666666667)) (- 2.0 (* (* x x) 1.0)))
129.0ms
(log (+ (* (* x x) (* x 0.6666666666666667)) (- 2.0 (* (* x x) 1.0))))

simplify1.7s

Counts
80 → 80
Iterations
IterNodes
done5000
21952
1354
0139

prune415.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.2b

localize34.0ms

Local error

Found 4 expressions with local error:

0.0b
(* x (- eps 1.0))
0.0b
(* (+ 1.0 eps) x)
0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
2.0b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (* x (- eps 1.0)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite221.0ms

Algorithm
rewrite-expression-head
Rules
26×associate-*l/
23×add-sqr-sqrt
18×frac-sub
16×*-un-lft-identity
13×associate-*l*
12×exp-neg frac-times
11×flip3-- associate-*r* flip--
10×pow1 flip3-+ add-cbrt-cube add-cube-cbrt flip-+
9×neg-sub0 exp-diff add-exp-log
8×associate-*r/
6×add-log-exp
3×sub-neg pow-prod-down prod-exp un-div-inv *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×distribute-rgt-in distribute-lft-in distribute-lft-out--
1×times-frac diff-log distribute-lft-out
Counts
4 → 107
Calls
4 calls:
16.0ms
(* x (- eps 1.0))
18.0ms
(* (+ 1.0 eps) x)
108.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
76.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (* x (- eps 1.0)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series579.0ms

Counts
4 → 12
Calls
4 calls:
33.0ms
(* x (- eps 1.0))
42.0ms
(* (+ 1.0 eps) x)
66.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
437.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (* x (- eps 1.0)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify2.6s

Counts
119 → 119
Iterations
IterNodes
done5001
24112
1745
0261

prune1.0s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes116.0ms

Accuracy

96.3% (0.6b remaining)

Error of 1.0b against oracle of 0.4b and baseline of 16.8b

bsearch258.0ms

Steps
ItersRangePoint
9
5.1798647897020696e-05
7.830610238325062
0.8522439107470308

simplify25.0ms

Iterations
IterNodes
done60
260
148
033

end0.0ms

sample8.3s

Algorithm
intervals
Results
2.6s1964×body10240exit
2.0s1723×body1280valid
2.0s10200×body80valid
740.0ms1223×body640valid
202.0ms607×body320valid
69.0ms333×body160valid