Details

Time bar (total: 9.1s)

sample19.0ms

Algorithm
intervals
Results
6.0ms57×body1280valid
3.0ms39×body640valid
3.0ms133×body80valid
1.0ms18×body320valid
0.0ms9×body160valid

simplify116.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (1.0ms)

IterNodesCost
0713
11213
21613
31913
42113
52713
63913
76013
87813
99913
1014713
1119013
1220513
done20513

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 28.5b

localize6.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
2.7b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite146.0ms

Algorithm
rewrite-expression-head
Rules
981×*-un-lft-identity
736×times-frac
585×add-sqr-sqrt
468×prod-diff
419×add-cube-cbrt
189×distribute-lft-out
94×associate-/r/
90×distribute-lft-out--
81×difference-of-squares
47×div-inv
29×flip3-+ flip-+
20×flip3-- flip--
18×fma-neg
9×associate-/r*
7×add-exp-log add-cbrt-cube associate-/l*
5×add-log-exp
3×pow1 expm1-log1p-u log1p-expm1-u
2×cbrt-undiv frac-2neg div-exp clear-num associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 596
Calls
3 calls:
5.0ms
(/ x (+ x 1.0))
10.0ms
(/ (+ x 1.0) (- x 1.0))
75.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series193.0ms

Counts
3 → 9
Calls
3 calls:
32.0ms
(/ x (+ x 1.0))
38.0ms
(/ (+ x 1.0) (- x 1.0))
123.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify1.4s

Counts
605 → 605
Iterations

Useful iterations: done (1.3s)

IterNodesCost
052334216
1120330851
2365922683
done500022489

prune679.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 0.1b

localize15.0ms

Local error

Found 4 expressions with local error:

14.8b
(/ x (- (* x x) (* 1.0 1.0)))
14.8b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
14.8b
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
29.0b
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

rewrite33.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
44×times-frac
33×add-sqr-sqrt add-cube-cbrt
14×difference-of-squares
12×associate-/r*
11×associate-/l*
10×add-exp-log add-cbrt-cube distribute-lft-out
6×associate-/r/
4×pow1 expm1-log1p-u log1p-expm1-u associate-/l/ add-log-exp
3×cbrt-undiv flip3-- frac-2neg div-exp clear-num flip-- div-inv
2×flip3-+ flip-+
1×fma-udef
Counts
4 → 129
Calls
4 calls:
5.0ms
(/ x (- (* x x) (* 1.0 1.0)))
11.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
14.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
0.0ms
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

series316.0ms

Counts
4 → 12
Calls
4 calls:
67.0ms
(/ x (- (* x x) (* 1.0 1.0)))
35.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
39.0ms
(/ (+ x 1.0) (- (* x x) (* 1.0 1.0)))
174.0ms
(fma (/ x (- (* x x) (* 1.0 1.0))) (- x 1.0) (- (* (+ x 1.0) (/ (+ x 1.0) (- (* x x) (* 1.0 1.0))))))

simplify485.0ms

Counts
141 → 141
Iterations

Useful iterations: done (481.0ms)

IterNodesCost
01692601
13982521
215412066
done50002008

prune401.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.1b

localize13.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
0.3b
(cbrt (- x 1.0))
2.7b
(- (/ x (+ x 1.0)) (* (/ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0)))))

rewrite43.0ms

Algorithm
rewrite-expression-head
Rules
41×*-un-lft-identity
29×add-sqr-sqrt
24×times-frac
23×add-cube-cbrt
18×fma-neg prod-diff
15×cbrt-prod
6×cbrt-div distribute-lft-out add-log-exp
4×pow1 add-exp-log expm1-log1p-u flip3-- associate-/r/ add-cbrt-cube flip-- log1p-expm1-u
3×pow1/3 frac-sub distribute-lft-out-- difference-of-squares
2×flip3-+ flip-+ div-inv
1×frac-times sub-neg diff-log associate-*r/ associate-*l/
Counts
4 → 104
Calls
4 calls:
2.0ms
(cbrt (- x 1.0))
2.0ms
(cbrt (- x 1.0))
2.0ms
(cbrt (- x 1.0))
34.0ms
(- (/ x (+ x 1.0)) (* (/ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0)))))

series453.0ms

Counts
4 → 12
Calls
4 calls:
94.0ms
(cbrt (- x 1.0))
94.0ms
(cbrt (- x 1.0))
95.0ms
(cbrt (- x 1.0))
171.0ms
(- (/ x (+ x 1.0)) (* (/ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (/ (cbrt (+ x 1.0)) (cbrt (- x 1.0)))))

simplify472.0ms

Counts
116 → 116
Iterations

Useful iterations: done (468.0ms)

IterNodesCost
01934086
14873977
216352192
done50002172

prune356.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.1b

localize24.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
21.6b
(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt x) (cbrt (+ x 1.0))) (- (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0)))))

rewrite2.0ms

Algorithm
rewrite-expression-head
Rules
9×cbrt-prod
7×add-sqr-sqrt add-cube-cbrt *-un-lft-identity
4×pow1 add-exp-log expm1-log1p-u add-cbrt-cube log1p-expm1-u add-log-exp
3×pow1/3
1×fma-udef
Counts
4 → 49
Calls
4 calls:
0.0ms
(cbrt x)
0.0ms
(cbrt x)
0.0ms
(cbrt x)
0.0ms
(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt x) (cbrt (+ x 1.0))) (- (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0)))))

series1.0s

Counts
4 → 12
Calls
4 calls:
178.0ms
(cbrt x)
170.0ms
(cbrt x)
173.0ms
(cbrt x)
513.0ms
(fma (/ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ (cbrt x) (cbrt (+ x 1.0))) (- (/ (/ (+ x 1.0) (* (cbrt (- x 1.0)) (cbrt (- x 1.0)))) (cbrt (- x 1.0)))))

simplify2.0s

Counts
61 → 61
Iterations

Useful iterations: 3 (335.0ms)

IterNodesCost
0102926
1270893
2901539
34669481
done5000481

prune232.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.1b

regimes48.0ms

Accuracy

99.9% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 29.4b

bsearch91.0ms

Steps
ItersRangePoint
6
2942.2625356967415
22276.40736340321
9041.27052044922
10
-155084744.97222546
-0.0009113054925467739
-9750.60840574548

simplify8.0ms

Iterations

Useful iterations: 1 (2.0ms)

IterNodesCost
043132
16496
27296
37496
done7496

end0.0ms

sample515.0ms

Algorithm
intervals
Results
170.0ms1656×body1280valid
108.0ms1212×body640valid
91.0ms4102×body80valid
43.0ms663×body320valid
15.0ms367×body160valid