Details

Time bar (total: 32.7s)

sample51.0ms

Algorithm
intervals
Results
12.0ms45×body1280valid
9.0ms44×body640valid
8.0ms149×body80valid
2.0ms13×body320valid
1.0ms5×body160valid

simplify596.0ms

Counts
1 → 1
Iterations
IterNodes
done350
14350
13346
12340
11329
10222
996
875
758
639
527
421
319
216
112
07

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize22.0ms

Local error

Found 3 expressions with local error:

0.0b
(/ x (+ x 1.0))
0.0b
(/ (+ x 1.0) (- x 1.0))
1.6b
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

rewrite456.0ms

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-cbrt-cube add-exp-log associate-/l*
5×add-log-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
2×cbrt-undiv clear-num frac-2neg div-exp associate-/l/
1×sub-neg diff-log frac-sub
Counts
3 → 599
Calls
3 calls:
30.0ms
(/ x (+ x 1.0))
42.0ms
(/ (+ x 1.0) (- x 1.0))
210.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

series339.0ms

Counts
3 → 9
Calls
3 calls:
48.0ms
(/ x (+ x 1.0))
66.0ms
(/ (+ x 1.0) (- x 1.0))
224.0ms
(- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))

simplify5.5s

Counts
608 → 608
Iterations
IterNodes
done5002
23309
11253
0526

prune4.4s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize174.0ms

Local error

Found 4 expressions with local error:

0.0b
(cbrt (/ (+ x 1.0) (- x 1.0)))
0.0b
(cbrt (/ (+ x 1.0) (- x 1.0)))
2.7b
(fma (- (cbrt (/ (+ x 1.0) (- x 1.0)))) (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (* (cbrt (/ (+ x 1.0) (- x 1.0))) (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0))))))
25.5b
(fma x (/ 1 (+ x 1.0)) (- (* (cbrt (/ (+ x 1.0) (- x 1.0))) (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))))))

rewrite50.0ms

Algorithm
rewrite-expression-head
Rules
60×*-un-lft-identity
52×cbrt-prod
40×add-sqr-sqrt times-frac
24×add-cube-cbrt
10×distribute-lft-out
8×distribute-lft-out-- difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
2×cbrt-div flip3-- pow1/3 fma-udef div-inv flip--
Counts
4 → 98
Calls
4 calls:
12.0ms
(cbrt (/ (+ x 1.0) (- x 1.0)))
25.0ms
(cbrt (/ (+ x 1.0) (- x 1.0)))
2.0ms
(fma (- (cbrt (/ (+ x 1.0) (- x 1.0)))) (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (* (cbrt (/ (+ x 1.0) (- x 1.0))) (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0))))))
2.0ms
(fma x (/ 1 (+ x 1.0)) (- (* (cbrt (/ (+ x 1.0) (- x 1.0))) (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))))))

series2.5s

Counts
4 → 12
Calls
4 calls:
256.0ms
(cbrt (/ (+ x 1.0) (- x 1.0)))
561.0ms
(cbrt (/ (+ x 1.0) (- x 1.0)))
1.3s
(fma (- (cbrt (/ (+ x 1.0) (- x 1.0)))) (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))) (* (cbrt (/ (+ x 1.0) (- x 1.0))) (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0))))))
300.0ms
(fma x (/ 1 (+ x 1.0)) (- (* (cbrt (/ (+ x 1.0) (- x 1.0))) (* (cbrt (/ (+ x 1.0) (- x 1.0))) (cbrt (/ (+ x 1.0) (- x 1.0)))))))

simplify3.6s

Counts
110 → 110
Iterations
IterNodes
done5000
21413
1467
0216

prune1.3s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize33.0ms

Local error

Found 2 expressions with local error:

0.0b
(- (/ x (+ x 1.0)) (- (fma 2.0 (+ x (* x x)) 1.0)))
0.0b
(/ x (+ x 1.0))

rewrite196.0ms

Algorithm
rewrite-expression-head
Rules
231×*-un-lft-identity
180×prod-diff
158×add-sqr-sqrt
153×add-cube-cbrt
145×times-frac
55×distribute-rgt-neg-in
54×distribute-lft-neg-in
37×distribute-lft-out
24×associate-/r/
18×neg-mul-1 fma-neg
12×flip3-+ flip-+ div-inv
6×add-log-exp
4×associate-/r* add-cbrt-cube add-exp-log
3×associate-/l*
2×expm1-log1p-u pow1 diff-log insert-posit16 log1p-expm1-u distribute-lft-out-- difference-of-squares
1×neg-sub0 cbrt-undiv distribute-neg-in clear-num sub-neg frac-2neg flip3-- div-exp neg-log fma-udef flip-- associate--r+ associate--r-
Counts
2 → 256
Calls
2 calls:
140.0ms
(- (/ x (+ x 1.0)) (- (fma 2.0 (+ x (* x x)) 1.0)))
14.0ms
(/ x (+ x 1.0))

series162.0ms

Counts
2 → 6
Calls
2 calls:
85.0ms
(- (/ x (+ x 1.0)) (- (fma 2.0 (+ x (* x x)) 1.0)))
77.0ms
(/ x (+ x 1.0))

simplify3.7s

Counts
262 → 262
Iterations
IterNodes
done5002
21724
1714
0302

prune2.2s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.0b

localize74.0ms

Local error

Found 4 expressions with local error:

0.1b
(* (* x x) x)
0.3b
(/ 3.0 (* (* x x) x))
0.5b
(/ 1.0 (* x x))
8.4b
(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

rewrite450.0ms

Algorithm
rewrite-expression-head
Rules
98×*-un-lft-identity
72×prod-diff
55×add-sqr-sqrt
52×add-cube-cbrt
37×distribute-rgt-neg-in
36×times-frac
35×distribute-lft-neg-in
23×pow1 add-cbrt-cube add-exp-log
20×distribute-lft-out
18×fma-neg
14×add-log-exp
12×div-inv
7×prod-exp cbrt-unprod
6×pow-plus pow-prod-up associate-/l*
5×cbrt-undiv neg-mul-1 div-exp
4×expm1-log1p-u diff-log insert-posit16 log1p-expm1-u distribute-lft-out--
3×associate-*r* pow-prod-down frac-sub distribute-neg-frac
2×pow2 clear-num associate-/r* sum-log frac-2neg neg-log pow-sqr
1×associate--l- neg-sub0 sub-neg flip3-+ flip3-- associate-*l* pow3 frac-add *-commutative flip-+ flip-- associate--r+ difference-of-squares unswap-sqr
Counts
4 → 199
Calls
4 calls:
49.0ms
(* (* x x) x)
34.0ms
(/ 3.0 (* (* x x) x))
10.0ms
(/ 1.0 (* x x))
338.0ms
(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

series200.0ms

Counts
4 → 12
Calls
4 calls:
50.0ms
(* (* x x) x)
52.0ms
(/ 3.0 (* (* x x) x))
58.0ms
(/ 1.0 (* x x))
40.0ms
(- (- (/ 3.0 (* (* x x) x))) (+ (/ 3.0 x) (/ 1.0 (* x x))))

simplify4.1s

Counts
211 → 211
Iterations
IterNodes
done5004
22291
1672
0258

prune951.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes165.0ms

Accuracy

98.6% (0.4b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 30.0b

bsearch141.0ms

Steps
ItersRangePoint
10
1.508099977930646e-06
2590629949647.022
1.020834055947729
10
-26711381.42537418
-6.803810524357175e-07
-1.311384526318253

simplify37.0ms

Iterations
IterNodes
done33
133
024

end0.0ms

sample1.2s

Algorithm
intervals
Results
387.0ms1713×body1280valid
327.0ms4072×body80valid
194.0ms1254×body640valid
70.0ms639×body320valid
66.0ms322×body160valid