Details

Time bar (total: 14.6s)

sample62.0ms

Algorithm
intervals
Results
22.0ms58×body640valid
15.0ms147×body80valid
9.0ms33×body320valid
3.0ms8×body1280valid
2.0ms10×body160valid

simplify243.0ms

Counts
1 → 1
Iterations
IterNodes
done475
9475
8357
7164
6102
581
465
345
235
121
010

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 8.1b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- x 1))
0.0b
(/ 1 (+ x 1))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))
2.7b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

rewrite306.0ms

Algorithm
rewrite-expression-head
Rules
743×*-un-lft-identity
715×times-frac
544×add-sqr-sqrt
494×add-cube-cbrt
468×prod-diff
236×associate-+l+
99×distribute-lft-out
72×div-inv
58×associate-/r/
29×flip3-+ flip-+
22×distribute-lft-out--
20×difference-of-squares
18×fma-neg
13×fma-def
12×add-exp-log
11×associate-/r* add-log-exp
8×add-cbrt-cube
6×pow1 associate-/l*
4×expm1-log1p-u difference-of-sqr-1 div-exp insert-posit16 log1p-expm1-u
3×flip3-- frac-add flip--
2×cbrt-undiv rec-exp clear-num sum-log sub-neg frac-2neg diff-log 1-exp frac-sub pow-flip inv-pow
1×+-commutative associate-+l-
Counts
4 → 648
Calls
4 calls:
16.0ms
(/ 1 (- x 1))
8.0ms
(/ 1 (+ x 1))
57.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
189.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

series214.0ms

Counts
4 → 12
Calls
4 calls:
15.0ms
(/ 1 (- x 1))
21.0ms
(/ 1 (+ x 1))
41.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
138.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

simplify1.3s

Counts
660 → 660
Iterations
IterNodes
done2000
22000
11149
0495

prune2.7s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b
(/ 1 (- x 1))
0.0b
(/ 1 (+ x 1))
0.0b
(fma 1 (/ 1 (+ x 1)) (- (* (/ 1 x) 2)))
2.7b
(+ (fma 1 (/ 1 (+ x 1)) (- (* (/ 1 x) 2))) (+ (fma (- (/ 1 x)) 2 (* (/ 1 x) 2)) (/ 1 (- x 1))))

rewrite75.0ms

Algorithm
rewrite-expression-head
Rules
53×*-un-lft-identity
42×add-sqr-sqrt
33×times-frac
26×add-cube-cbrt
12×add-exp-log
11×associate-/r*
9×distribute-lft-out add-log-exp
8×add-cbrt-cube difference-of-squares
6×pow1 associate-/l*
4×expm1-log1p-u difference-of-sqr-1 div-exp associate-/r/ insert-posit16 log1p-expm1-u distribute-lft-out--
3×sum-log fma-def div-inv
2×cbrt-undiv rec-exp clear-num frac-2neg flip3-+ 1-exp flip-+ fma-udef pow-flip inv-pow
1×+-commutative associate-+l+ associate-+r+ flip3-- flip--
Counts
4 → 126
Calls
4 calls:
17.0ms
(/ 1 (- x 1))
16.0ms
(/ 1 (+ x 1))
0.0ms
(fma 1 (/ 1 (+ x 1)) (- (* (/ 1 x) 2)))
39.0ms
(+ (fma 1 (/ 1 (+ x 1)) (- (* (/ 1 x) 2))) (+ (fma (- (/ 1 x)) 2 (* (/ 1 x) 2)) (/ 1 (- x 1))))

series302.0ms

Counts
4 → 12
Calls
4 calls:
25.0ms
(/ 1 (- x 1))
24.0ms
(/ 1 (+ x 1))
51.0ms
(fma 1 (/ 1 (+ x 1)) (- (* (/ 1 x) 2)))
201.0ms
(+ (fma 1 (/ 1 (+ x 1)) (- (* (/ 1 x) 2))) (+ (fma (- (/ 1 x)) 2 (* (/ 1 x) 2)) (/ 1 (- x 1))))

simplify1.2s

Counts
138 → 138
Iterations
IterNodes
done2004
32004
21379
1445
0193

prune540.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize87.0ms

Local error

Found 4 expressions with local error:

0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))
0.3b
(cbrt (+ x 1))
16.8b
(+ (fma 1 (* (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1)))) (- (* (/ 1 x) 2))) (+ (fma (- (/ 1 x)) 2 (* (/ 1 x) 2)) (/ 1 (- x 1))))

rewrite70.0ms

Algorithm
rewrite-expression-head
Rules
21×*-un-lft-identity
12×cbrt-prod
9×add-log-exp
8×add-sqr-sqrt add-cube-cbrt distribute-lft-out
6×cbrt-div
4×expm1-log1p-u pow1 flip3-+ add-cbrt-cube add-exp-log flip-+ insert-posit16 log1p-expm1-u
3×sum-log fma-def pow1/3
1×+-commutative associate-+l+ associate-+r+ fma-udef div-inv
Counts
4 → 74
Calls
4 calls:
5.0ms
(cbrt (+ x 1))
5.0ms
(cbrt (+ x 1))
5.0ms
(cbrt (+ x 1))
53.0ms
(+ (fma 1 (* (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1)))) (- (* (/ 1 x) 2))) (+ (fma (- (/ 1 x)) 2 (* (/ 1 x) 2)) (/ 1 (- x 1))))

series359.0ms

Counts
4 → 12
Calls
4 calls:
45.0ms
(cbrt (+ x 1))
46.0ms
(cbrt (+ x 1))
58.0ms
(cbrt (+ x 1))
211.0ms
(+ (fma 1 (* (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1)))) (- (* (/ 1 x) 2))) (+ (fma (- (/ 1 x)) 2 (* (/ 1 x) 2)) (/ 1 (- x 1))))

simplify1.2s

Counts
86 → 86
Iterations
IterNodes
done2009
32009
21050
1322
0123

prune634.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize53.0ms

Local error

Found 4 expressions with local error:

0.1b
(/ 2 (* x (* x x)))
0.1b
(* x (* x x))
0.2b
(/ 2 (pow x 7))
0.2b
(/ 2 (pow x 5))

rewrite84.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
40×add-sqr-sqrt
39×*-un-lft-identity add-cube-cbrt
28×add-exp-log
24×unpow-prod-down
22×add-cbrt-cube
18×pow1
15×associate-/r*
9×div-exp associate-/l*
8×sqr-pow
6×prod-exp cbrt-unprod
5×cbrt-undiv pow-prod-up
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg associate-*l* pow-prod-down div-inv
2×pow-to-exp pow-exp
1×pow2 pow-plus cube-unmult associate-*r* pow-sqr *-commutative unswap-sqr
Counts
4 → 149
Calls
4 calls:
25.0ms
(/ 2 (* x (* x x)))
29.0ms
(* x (* x x))
16.0ms
(/ 2 (pow x 7))
10.0ms
(/ 2 (pow x 5))

series282.0ms

Counts
4 → 12
Calls
4 calls:
51.0ms
(/ 2 (* x (* x x)))
48.0ms
(* x (* x x))
101.0ms
(/ 2 (pow x 7))
82.0ms
(/ 2 (pow x 5))

simplify926.0ms

Counts
161 → 161
Iterations
IterNodes
done2007
32007
21502
1430
0218

prune564.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0b

regimes88.0ms

Accuracy

99% (0.2b remaining)

Error of 0.3b against oracle of 0.0b and baseline of 25.2b

bsearch203.0ms

Steps
ItersRangePoint
10
3.4946005567744297e-15
48819.349325626084
89.72182339181649
9
-6838974.188497498
-0.005838610583870787
-94.31796734081924

simplify11.0ms

Iterations
IterNodes
done58
258
156
037

end0.0ms

sample3.0s

Algorithm
intervals
Results
1.4s1914×body640valid
531.0ms4168×body80valid
377.0ms566×body1280valid
336.0ms912×body320valid
160.0ms442×body160valid