Details

Time bar (total: 21.2s)

sample61.0ms

Algorithm
intervals
Results
25.0ms88×body1280valid
7.0ms172×body80valid
7.0ms37×body640valid
3.0ms23×body320valid
2.0ms18×body160valid

simplify4.2s

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
066
1116
2186
3276
4516
51186
64536
736076
done50026

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.8b

localize8.0ms

Local error

Found 2 expressions with local error:

0.0b
(exp (* a x))
4.6b
(- (exp (* a x)) 1.0)

rewrite27.0ms

Algorithm
rewrite-expression-head
Rules
11×add-sqr-sqrt *-un-lft-identity
9×add-cube-cbrt prod-diff
6×add-log-exp
3×fma-neg
2×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u
1×sub-neg exp-prod flip3-- exp-to-pow diff-log flip-- rem-exp-log distribute-lft-out-- difference-of-squares
Counts
2 → 40
Calls
2 calls:
8.0ms
(exp (* a x))
17.0ms
(- (exp (* a x)) 1.0)

series75.0ms

Counts
2 → 6
Calls
2 calls:
15.0ms
(exp (* a x))
60.0ms
(- (exp (* a x)) 1.0)

simplify2.4s

Counts
46 → 46
Iterations

Useful iterations: done (2.4s)

IterNodesCost
079557
1183460
2598386
33356328
done5000325

prune176.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 6.7b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
0.0b
(* 2 (* a x))
0.0b
(+ (exp (* a x)) 1.0)
4.5b
(- (exp (* 2 (* a x))) (* 1.0 1.0))

rewrite215.0ms

Algorithm
rewrite-expression-head
Rules
30×*-un-lft-identity
24×add-sqr-sqrt
18×add-cube-cbrt
16×times-frac
11×add-exp-log add-cbrt-cube
9×pow1
8×add-log-exp
6×distribute-lft-out difference-of-squares
4×expm1-log1p-u associate-/r* log1p-expm1-u associate-/l*
3×fma-def fma-neg associate-*l* prod-diff pow-prod-down prod-exp cbrt-unprod
2×flip3-- flip3-+ associate-/r/ flip-- flip-+ associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg diff-log div-sub div-exp associate-*r* clear-num sum-log *-commutative div-inv
Counts
4 → 101
Calls
4 calls:
117.0ms
(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
35.0ms
(* 2 (* a x))
25.0ms
(+ (exp (* a x)) 1.0)
32.0ms
(- (exp (* 2 (* a x))) (* 1.0 1.0))

series250.0ms

Counts
4 → 12
Calls
4 calls:
122.0ms
(/ (- (exp (* 2 (* a x))) (* 1.0 1.0)) (+ (exp (* a x)) 1.0))
30.0ms
(* 2 (* a x))
20.0ms
(+ (exp (* a x)) 1.0)
77.0ms
(- (exp (* 2 (* a x))) (* 1.0 1.0))

simplify1.5s

Counts
113 → 113
Iterations

Useful iterations: done (1.5s)

IterNodesCost
01721938
14451874
218161713
done50001649

prune627.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 6.6b

localize50.0ms

Local error

Found 4 expressions with local error:

0.0b
(+ (exp (* a x)) 1.0)
0.0b
(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (fma 1.0 1.0 (exp (* 2 (* a x)))))
0.0b
(* (* a x) 4)
4.5b
(- (exp (* (* a x) 4)) (pow 1.0 4))

rewrite121.0ms

Algorithm
rewrite-expression-head
Rules
57×add-sqr-sqrt
44×*-un-lft-identity
32×add-cube-cbrt
21×times-frac prod-diff
15×difference-of-squares
14×unpow-prod-down
11×add-exp-log add-cbrt-cube
9×pow1
8×add-log-exp sqr-pow
7×associate-/l*
5×distribute-lft-out--
4×expm1-log1p-u log1p-expm1-u
3×fma-def fma-neg associate-*r* pow-prod-down prod-exp associate-/r* cbrt-unprod
2×flip3-- flip-- associate-/l/
1×cbrt-undiv +-commutative sub-neg frac-2neg flip3-+ diff-log div-sub div-exp associate-*l* clear-num sum-log *-commutative flip-+ div-inv distribute-lft-out
Counts
4 → 127
Calls
4 calls:
11.0ms
(+ (exp (* a x)) 1.0)
54.0ms
(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (fma 1.0 1.0 (exp (* 2 (* a x)))))
29.0ms
(* (* a x) 4)
21.0ms
(- (exp (* (* a x) 4)) (pow 1.0 4))

series251.0ms

Counts
4 → 12
Calls
4 calls:
26.0ms
(+ (exp (* a x)) 1.0)
106.0ms
(/ (- (exp (* (* a x) 4)) (pow 1.0 4)) (fma 1.0 1.0 (exp (* 2 (* a x)))))
35.0ms
(* (* a x) 4)
83.0ms
(- (exp (* (* a x) 4)) (pow 1.0 4))

simplify2.4s

Counts
139 → 139
Iterations

Useful iterations: done (2.4s)

IterNodesCost
02583353
16343002
230162663
done50012603

prune983.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 6.6b

localize53.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ (pow 1.0 4) (fma 1.0 1.0 (exp (* 2 (* a x)))))
0.0b
(/ (exp (* (* a x) 4)) (fma 1.0 1.0 (exp (* 2 (* a x)))))
0.0b
(* (* a x) 4)
4.5b
(- (/ (exp (* (* a x) 4)) (fma 1.0 1.0 (exp (* 2 (* a x))))) (/ (pow 1.0 4) (fma 1.0 1.0 (exp (* 2 (* a x))))))

rewrite241.0ms

Algorithm
rewrite-expression-head
Rules
553×times-frac
419×add-sqr-sqrt
403×*-un-lft-identity
395×add-cube-cbrt
325×prod-diff
131×unpow-prod-down
45×sqr-pow
43×div-inv
15×add-exp-log
13×fma-neg add-cbrt-cube
10×associate-/l*
9×pow1
8×difference-of-squares
6×associate-/r* add-log-exp
4×expm1-log1p-u div-exp log1p-expm1-u distribute-lft-out--
3×associate-*r* pow-prod-down prod-exp cbrt-unprod
2×cbrt-undiv frac-2neg clear-num
1×pow-to-exp sub-neg flip3-- distribute-rgt-out-- diff-log associate-*l* pow-exp *-commutative frac-sub flip-- sub-div
Counts
4 → 463
Calls
4 calls:
15.0ms
(/ (pow 1.0 4) (fma 1.0 1.0 (exp (* 2 (* a x)))))
29.0ms
(/ (exp (* (* a x) 4)) (fma 1.0 1.0 (exp (* 2 (* a x)))))
35.0ms
(* (* a x) 4)
115.0ms
(- (/ (exp (* (* a x) 4)) (fma 1.0 1.0 (exp (* 2 (* a x))))) (/ (pow 1.0 4) (fma 1.0 1.0 (exp (* 2 (* a x))))))

series473.0ms

Counts
4 → 12
Calls
4 calls:
93.0ms
(/ (pow 1.0 4) (fma 1.0 1.0 (exp (* 2 (* a x)))))
76.0ms
(/ (exp (* (* a x) 4)) (fma 1.0 1.0 (exp (* 2 (* a x)))))
27.0ms
(* (* a x) 4)
276.0ms
(- (/ (exp (* (* a x) 4)) (fma 1.0 1.0 (exp (* 2 (* a x))))) (/ (pow 1.0 4) (fma 1.0 1.0 (exp (* 2 (* a x))))))

simplify925.0ms

Counts
475 → 475
Iterations

Useful iterations: done (864.0ms)

IterNodesCost
065546085
1151842661
done500134855

prune3.2s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 6.3b

regimes669.0ms

Accuracy

94.6% (1.3b remaining)

Error of 7.2b against oracle of 5.9b and baseline of 29.6b

bsearch2.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
039132
154132
done54132

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.3s2756×body1280valid
266.0ms1365×body640valid
224.0ms5402×body80valid
121.0ms751×body320valid
26.0ms355×body160valid