Details

Time bar (total: 12.9s)

sample28.0ms

Algorithm
intervals
Results
9.0ms67×body640valid
5.0ms138×body80valid
3.0ms35×body320valid
1.0ms16×body160valid

simplify5.0ms

Counts
1 → 1
Iterations

Useful iterations: 0 (0.0ms)

IterNodesCost
069
199
2129
done129

prune1.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 15.0b

localize6.0ms

Local error

Found 2 expressions with local error:

0.0b
(/ 1.0 (+ x 1.0))
1.7b
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

rewrite207.0ms

Algorithm
rewrite-expression-head
Rules
362×*-un-lft-identity
358×times-frac
265×add-sqr-sqrt
253×add-cube-cbrt
234×prod-diff
49×distribute-lft-out
35×div-inv
30×associate-/r/
18×fma-neg
15×flip3-+ flip-+
8×distribute-lft-out--
4×add-exp-log associate-/r* add-cbrt-cube add-log-exp difference-of-squares
3×associate-/l*
2×pow1 expm1-log1p-u log1p-expm1-u
1×cbrt-undiv sub-neg flip3-- frac-2neg diff-log div-exp clear-num frac-sub flip--
Counts
2 → 314
Calls
2 calls:
11.0ms
(/ 1.0 (+ x 1.0))
149.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

series169.0ms

Counts
2 → 6
Calls
2 calls:
41.0ms
(/ 1.0 (+ x 1.0))
127.0ms
(- (/ 1.0 (+ x 1.0)) (/ 1.0 x))

simplify2.0s

Counts
320 → 320
Iterations

Useful iterations: 2 (797.0ms)

IterNodesCost
038712162
191810697
232518100
done50008100

prune802.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.8b

localize58.0ms

Local error

Found 4 expressions with local error:

0.6b
(cbrt x)
0.6b
(cbrt x)
0.6b
(cbrt x)
27.6b
(fma (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ 1.0 (cbrt (+ x 1.0))) (- (/ (/ 1.0 (cbrt x)) (* (cbrt x) (cbrt x)))))

rewrite7.0ms

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:
2.0ms
(cbrt x)
2.0ms
(cbrt x)
2.0ms
(cbrt x)
1.0ms
(fma (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ 1.0 (cbrt (+ x 1.0))) (- (/ (/ 1.0 (cbrt x)) (* (cbrt x) (cbrt x)))))

series1.1s

Counts
4 → 12
Calls
4 calls:
266.0ms
(cbrt x)
278.0ms
(cbrt x)
264.0ms
(cbrt x)
279.0ms
(fma (/ 1 (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (/ 1.0 (cbrt (+ x 1.0))) (- (/ (/ 1.0 (cbrt x)) (* (cbrt x) (cbrt x)))))

simplify2.2s

Counts
61 → 61
Iterations

Useful iterations: 3 (954.0ms)

IterNodesCost
087697
1220672
2777513
33954463
done5000463

prune312.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.8b

localize35.0ms

Local error

Found 3 expressions with local error:

0.0b
(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
0.4b
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
29.5b
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (/ 1.0 x)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
57×*-un-lft-identity
27×times-frac
20×distribute-lft-out
17×add-sqr-sqrt add-cube-cbrt
16×unpow-prod-down cube-prod
9×associate-/r*
8×add-log-exp
5×add-exp-log add-cbrt-cube
4×sum-cubes
3×pow1 expm1-log1p-u associate-+r+ log1p-expm1-u associate-/l*
2×flip3-+ sum-log associate-/r/ flip-+
1×cbrt-undiv +-commutative associate-+r- sub-neg fma-def frac-2neg diff-log div-exp prod-diff clear-num fma-udef div-inv
Counts
3 → 84
Calls
3 calls:
31.0ms
(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
66.0ms
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
1.0ms
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (/ 1.0 x)))

series225.0ms

Counts
3 → 9
Calls
3 calls:
23.0ms
(+ (* x x) (- (* 1.0 1.0) (* x 1.0)))
88.0ms
(/ 1.0 (+ (pow x 3) (pow 1.0 3)))
113.0ms
(fma (/ 1.0 (+ (pow x 3) (pow 1.0 3))) (+ (* x x) (- (* 1.0 1.0) (* x 1.0))) (- (/ 1.0 x)))

simplify1.8s

Counts
93 → 93
Iterations

Useful iterations: done (1.8s)

IterNodesCost
01561582
14121352
219731236
done50021229

prune396.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.8b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1.0 (pow x 4))
0.5b
(/ 1.0 (pow x 3))
0.9b
(/ 1.0 (* x x))
10.3b
(- (/ 1.0 (pow x 3)) (+ (/ 1.0 (pow x 4)) (/ 1.0 (* x x))))

rewrite340.0ms

Algorithm
rewrite-expression-head
Rules
304×*-un-lft-identity
280×times-frac
232×add-sqr-sqrt
219×add-cube-cbrt
200×prod-diff
92×div-inv
82×distribute-lft-out
79×unpow-prod-down
67×cube-prod
40×fma-neg
27×sqr-pow
22×cube-mult unpow3
20×associate-/r*
19×add-exp-log
13×add-cbrt-cube
9×associate-/l* add-log-exp
8×div-exp
5×difference-of-squares
4×pow1 cbrt-undiv expm1-log1p-u log1p-expm1-u
3×frac-2neg clear-num frac-sub distribute-lft-out--
2×pow-to-exp diff-log pow-exp
1×sub-neg flip3-- flip3-+ frac-add prod-exp sum-log flip-- cbrt-unprod flip-+ associate--r+
Counts
4 → 404
Calls
4 calls:
7.0ms
(/ 1.0 (pow x 4))
19.0ms
(/ 1.0 (pow x 3))
16.0ms
(/ 1.0 (* x x))
270.0ms
(- (/ 1.0 (pow x 3)) (+ (/ 1.0 (pow x 4)) (/ 1.0 (* x x))))

series204.0ms

Counts
4 → 12
Calls
4 calls:
49.0ms
(/ 1.0 (pow x 4))
53.0ms
(/ 1.0 (pow x 3))
49.0ms
(/ 1.0 (* x x))
53.0ms
(- (/ 1.0 (pow x 3)) (+ (/ 1.0 (pow x 4)) (/ 1.0 (* x x))))

simplify646.0ms

Counts
416 → 416
Iterations

Useful iterations: done (626.0ms)

IterNodesCost
039918449
199512834
done500010730

prune1.1s

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

regimes51.0ms

Accuracy

99.8% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 28.7b

bsearch138.0ms

Steps
ItersRangePoint
11
0.022891638200552334
5.118117448855024e+31
9917.966055990473
10
-911936.9907706906
-4.3470241882695893e-07
-10864.733221646793

simplify6.0ms

Iterations

Useful iterations: 1 (3.0ms)

IterNodesCost
02867
13751
done3751

end0.0ms

sample967.0ms

Algorithm
intervals
Results
351.0ms1948×body640valid
243.0ms4241×body80valid
139.0ms1218×body320valid
41.0ms595×body160valid