Details

Time bar (total: 29.3s)

sample243.0ms

Algorithm
intervals
Results
60.0ms73×body10240exit
51.0ms20×body320valid
42.0ms60×body1280valid
32.0ms314×body80valid
21.0ms45×body640valid
3.0ms12×body160valid

simplify1.5s

Counts
1 → 1
Iterations
IterNodes
done5005
41357
3352
2122
146
019

prune15.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.9b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
0.0b
(* (- 1.0 eps) x)
0.0b
(* (+ 1.0 eps) x)
2.4b
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

rewrite218.0ms

Algorithm
rewrite-expression-head
Rules
81×frac-sub
76×exp-neg frac-times
57×neg-sub0 exp-diff
42×associate-*l/
38×associate-*r/
32×flip3-- flip--
28×flip3-+ flip-+
23×add-sqr-sqrt
19×un-div-inv
16×*-un-lft-identity
15×associate-*l*
10×pow1 add-cbrt-cube add-cube-cbrt
9×associate-*r* add-exp-log
6×add-log-exp
3×pow-prod-down prod-exp *-commutative cbrt-unprod difference-of-squares unswap-sqr
2×distribute-lft-out--
1×sub-neg times-frac diff-log distribute-lft-out
Counts
4 → 166
Calls
4 calls:
63.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
27.0ms
(* (- 1.0 eps) x)
39.0ms
(* (+ 1.0 eps) x)
73.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series471.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
44.0ms
(* (- 1.0 eps) x)
46.0ms
(* (+ 1.0 eps) x)
287.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify3.4s

Counts
178 → 178
Iterations
IterNodes
done5001
24796
11222
0396

prune1.3s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.9b

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) x)
0.1b
(* 0.6666666666666667 (* (* x x) x))
0.2b
(/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0)
4.0b
(+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x)))

rewrite175.0ms

Algorithm
rewrite-expression-head
Rules
32×pow1
20×add-cbrt-cube add-exp-log
15×add-sqr-sqrt
14×*-un-lft-identity add-cube-cbrt
9×times-frac pow-prod-down prod-exp cbrt-unprod add-log-exp
6×pow-plus pow-prod-up
4×associate-*r* associate-*l*
3×associate-/r* associate-/l*
2×pow2 associate-+l+ sum-log flip3-+ pow-sqr *-commutative associate-+l- flip-+ associate-/l/
1×cbrt-undiv +-commutative clear-num sub-neg frac-2neg diff-log div-sub div-exp pow3 div-inv unswap-sqr
Counts
4 → 94
Calls
4 calls:
25.0ms
(* (* x x) x)
38.0ms
(* 0.6666666666666667 (* (* x x) x))
80.0ms
(/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0)
28.0ms
(+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x)))

series213.0ms

Counts
4 → 12
Calls
4 calls:
41.0ms
(* (* x x) x)
52.0ms
(* 0.6666666666666667 (* (* x x) x))
67.0ms
(/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0)
53.0ms
(+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x)))

simplify3.0s

Counts
106 → 106
Iterations
IterNodes
done5004
34465
21047
1363
0141

prune474.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize106.0ms

Local error

Found 4 expressions with local error:

4.0b
(+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x)))
7.6b
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
7.6b
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
7.6b
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))

rewrite107.0ms

Algorithm
rewrite-expression-head
Rules
39×cbrt-prod
27×times-frac
25×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
9×add-log-exp
4×pow1 add-cbrt-cube add-exp-log
3×cbrt-div pow1/3 div-inv
2×associate-+l+ sum-log
1×+-commutative sub-neg flip3-+ diff-log associate-+l- flip-+
Counts
4 → 81
Calls
4 calls:
44.0ms
(+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x)))
18.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
22.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
19.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))

series938.0ms

Counts
4 → 12
Calls
4 calls:
68.0ms
(+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x)))
260.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
276.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
334.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))

simplify2.5s

Counts
93 → 93
Iterations
IterNodes
done5001
21345
1372
0154

prune780.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize144.0ms

Local error

Found 4 expressions with local error:

7.6b
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
7.6b
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
7.6b
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
7.6b
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
52×cbrt-prod
36×times-frac
32×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×pow1 cbrt-div add-cbrt-cube pow1/3 add-exp-log div-inv add-log-exp
Counts
4 → 88
Calls
4 calls:
14.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
10.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
9.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
11.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))

series1.2s

Counts
4 → 12
Calls
4 calls:
277.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
280.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
324.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
277.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))

simplify2.5s

Counts
100 → 100
Iterations
IterNodes
done5013
33365
2791
1266
0126

prune910.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.9b

regimes235.0ms

Accuracy

96.1% (0.6b remaining)

Error of 1.1b against oracle of 0.5b and baseline of 16.0b

bsearch262.0ms

Steps
ItersRangePoint
8
20.852008069825544
573579.0075499975
381.9625649006934

simplify9.0ms

Iterations
IterNodes
done48
148
035

end0.0ms

sample8.5s

Algorithm
intervals
Results
2.6s2000×body10240exit
2.1s10052×body80valid
1.9s1723×body1280valid
740.0ms1285×body640valid
342.0ms669×body320valid
191.0ms347×body160valid