Details

Time bar (total: 29.0s)

sample527.0ms

Algorithm
intervals
Results
384.0ms314×body80valid
52.0ms73×body10240exit
41.0ms60×body1280valid
16.0ms45×body640valid
6.0ms20×body320valid
2.0ms12×body160valid

simplify1.6s

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

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 31.9b

localize65.0ms

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)))))

rewrite259.0ms

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:
104.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
31.0ms
(* (- 1.0 eps) x)
36.0ms
(* (+ 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)))))

series456.0ms

Counts
4 → 12
Calls
4 calls:
74.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
52.0ms
(* (- 1.0 eps) x)
44.0ms
(* (+ 1.0 eps) x)
285.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify3.1s

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

localize38.0ms

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)))

rewrite245.0ms

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)
73.0ms
(* 0.6666666666666667 (* (* x x) x))
100.0ms
(/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0)
43.0ms
(+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x)))

series231.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* (* x x) x)
47.0ms
(* 0.6666666666666667 (* (* x x) x))
69.0ms
(/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0)
70.0ms
(+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x)))

simplify3.2s

Counts
106 → 106
Iterations
IterNodes
done5004
34465
21047
1363
0141

prune431.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.9b

localize79.0ms

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))

rewrite94.0ms

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))
18.0ms
(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))

series753.0ms

Counts
4 → 12
Calls
4 calls:
52.0ms
(+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x)))
246.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
230.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
224.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))

simplify2.0s

Counts
93 → 93
Iterations
IterNodes
done5001
21345
1372
0154

prune711.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.9b

localize129.0ms

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))

rewrite41.0ms

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:
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))
9.0ms
(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))

series1.1s

Counts
4 → 12
Calls
4 calls:
251.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
243.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
289.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))
317.0ms
(cbrt (/ (+ (- 2.0 (* (* x x) 1.0)) (* 0.6666666666666667 (* (* x x) x))) 2.0))

simplify2.6s

Counts
100 → 100
Iterations
IterNodes
done5013
33365
2791
1266
0126

prune989.0ms

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

bsearch269.0ms

Steps
ItersRangePoint
8
20.852008069825544
573579.0075499975
381.9625649006934

simplify18.0ms

Iterations
IterNodes
done48
148
035

end0.0ms

sample8.6s

Algorithm
intervals
Results
2.4s2000×body10240exit
2.3s1723×body1280valid
1.7s10052×body80valid
778.0ms669×body320valid
744.0ms1285×body640valid
159.0ms347×body160valid