Details

Time bar (total: 27.0s)

sample218.0ms

Algorithm
intervals
Results
70.0ms44×body640valid
45.0ms63×body10240exit
36.0ms51×body1280valid
29.0ms313×body80valid
8.0ms25×body320valid
2.0ms8×body160valid

simplify2.2s

Counts
1 → 1
Iterations

Useful iterations: 4 (858.0ms)

IterNodesCost
019664
147664
2124664
3395584
42356559
done5001559

prune21.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 30.1b

localize46.0ms

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)))))

rewrite196.0ms

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*
4×expm1-log1p-u log1p-expm1-u
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 fma-neg diff-log prod-diff neg-log distribute-lft-out distribute-lft-out--
Counts
4 → 171
Calls
4 calls:
31.0ms
(* (+ 1.0 eps) x)
7.0ms
(exp (- (* (- 1.0 eps) x)))
81.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
58.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

series470.0ms

Counts
4 → 12
Calls
4 calls:
34.0ms
(* (+ 1.0 eps) x)
47.0ms
(exp (- (* (- 1.0 eps) x)))
79.0ms
(* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x))))
309.0ms
(- (* (+ 1.0 (/ 1.0 eps)) (exp (- (* (- 1.0 eps) x)))) (* (- (/ 1.0 eps) 1.0) (exp (- (* (+ 1.0 eps) x)))))

simplify2.3s

Counts
183 → 183
Iterations

Useful iterations: done (2.3s)

IterNodesCost
0405167710
11386136815
done5001133534

prune893.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize17.0ms

Local error

Found 3 expressions with local error:

0.0b
(fma 0.6666666666666667 (* (* x x) x) 2.0)
0.1b
(* (* x x) x)
5.4b
(- (fma 0.6666666666666667 (* (* x x) x) 2.0) (* 1.0 (* x x)))

rewrite42.0ms

Algorithm
rewrite-expression-head
Rules
22×pow1
8×add-cbrt-cube add-exp-log
7×add-sqr-sqrt
6×*-un-lft-identity pow-plus pow-prod-up add-cube-cbrt
5×add-log-exp
3×expm1-log1p-u fma-neg associate-*r* prod-diff pow-prod-down prod-exp cbrt-unprod log1p-expm1-u
2×pow2 pow-sqr fma-udef
1×sub-neg flip3-- diff-log associate-*l* pow3 associate--l+ *-commutative flip-- unswap-sqr
Counts
3 → 61
Calls
3 calls:
0.0ms
(fma 0.6666666666666667 (* (* x x) x) 2.0)
29.0ms
(* (* x x) x)
10.0ms
(- (fma 0.6666666666666667 (* (* x x) x) 2.0) (* 1.0 (* x x)))

series255.0ms

Counts
3 → 9
Calls
3 calls:
128.0ms
(fma 0.6666666666666667 (* (* x x) x) 2.0)
66.0ms
(* (* x x) x)
61.0ms
(- (fma 0.6666666666666667 (* (* x x) x) 2.0) (* 1.0 (* x x)))

simplify2.1s

Counts
70 → 70
Iterations

Useful iterations: done (2.1s)

IterNodesCost
08615538
125112425
2178111752
done500211680

prune304.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize28.0ms

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))))

rewrite121.0ms

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
7×add-sqr-sqrt
6×*-un-lft-identity pow-plus pow-prod-up add-cube-cbrt
5×associate-+r+
4×associate-*r* associate-*l*
3×expm1-log1p-u prod-diff log1p-expm1-u
2×pow2 sum-log pow-sqr *-commutative
1×+-commutative associate-+r- sub-neg fma-def flip3-+ diff-log pow3 flip-+ unswap-sqr
Counts
3 → 74
Calls
3 calls:
38.0ms
(* 0.6666666666666667 (* (* x x) x))
15.0ms
(* (* x x) x)
66.0ms
(+ (* 0.6666666666666667 (* (* x x) x)) (- 2.0 (* 1.0 (* x x))))

series126.0ms

Counts
3 → 9
Calls
3 calls:
46.0ms
(* 0.6666666666666667 (* (* x x) x))
36.0ms
(* (* x x) x)
44.0ms
(+ (* 0.6666666666666667 (* (* x x) x)) (- 2.0 (* 1.0 (* x x))))

simplify2.4s

Counts
83 → 83
Iterations

Useful iterations: done (2.4s)

IterNodesCost
010617929
131714126
2215713138
done500113113

prune254.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

localize62.0ms

Local error

Found 4 expressions with local error:

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

rewrite1.5s

Algorithm
rewrite-expression-head
Rules
215×*-un-lft-identity
184×prod-diff
179×add-sqr-sqrt
166×add-cube-cbrt
136×times-frac
112×exp-sum
78×distribute-rgt-in distribute-lft-in
25×associate-/l*
24×distribute-neg-in
21×distribute-lft-out
13×sub-neg
10×add-cbrt-cube associate-*r*
9×add-exp-log add-log-exp
8×pow1
6×associate-*l*
5×div-inv
4×expm1-log1p-u fma-neg associate-*r/ log1p-expm1-u distribute-lft-out-- difference-of-squares
3×associate-/r* flip3-- flip--
2×diff-log pow-prod-down prod-exp *-commutative frac-sub cbrt-unprod unswap-sqr
1×cbrt-undiv clear-num sum-log frac-2neg flip3-+ div-exp associate--l+ flip-+
Counts
4 → 311
Calls
4 calls:
18.0ms
(* x (- eps 1.0))
32.0ms
(* x (- eps 1.0))
22.0ms
(/ (exp (* x (- eps 1.0))) eps)
1.4s
(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ eps 1.0)))) eps))

series247.0ms

Counts
4 → 12
Calls
4 calls:
44.0ms
(* x (- eps 1.0))
44.0ms
(* x (- eps 1.0))
31.0ms
(/ (exp (* x (- eps 1.0))) eps)
128.0ms
(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ eps 1.0)))) eps))

simplify3.1s

Counts
323 → 323
Iterations

Useful iterations: done (2.9s)

IterNodesCost
0523211183
11186194415
24467167061
done5000166586

prune1.8s

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.2b

regimes74.0ms

Accuracy

0% (0.5b remaining)

Error of 0.9b against oracle of 0.4b and baseline of 0.9b

bsearch0.0ms

simplify15.0ms

Iterations

Useful iterations: 0 (2.0ms)

IterNodesCost
018639
127639
233639
done33639

end0.0ms

sample8.2s

Algorithm
intervals
Results
3.0s1964×body10240exit
2.0s1723×body1280valid
1.7s10200×body80valid
710.0ms1223×body640valid
303.0ms607×body320valid
70.0ms333×body160valid