Details

Time bar (total: 3.4m)

sample81.0ms

Algorithm
intervals
Results
28.0ms67×body640valid
18.0ms17×body1280valid
12.0ms123×body80valid
8.0ms32×body320valid
3.0ms17×body160valid

simplify126.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
126.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 10.3b

localize20.0ms

Local error

Found 4 expressions with local error:

3.5b
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
0.0b
(- (/ 1 (+ x 1)) (/ 2 x))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite382.0ms

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:
Slowest
229.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
78.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
18.0ms
(/ 1 (- x 1))
17.0ms
(/ 1 (+ x 1))

series171.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
114.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
25.0ms
(- (/ 1 (+ x 1)) (/ 2 x))
18.0ms
(/ 1 (+ x 1))
14.0ms
(/ 1 (- x 1))

simplify2.2m

Counts
879 → 660
Calls
879 calls:
Slowest
785.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
779.0ms
(fma (/ (sqrt 1) 1) (/ (sqrt 1) (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
746.0ms
(fma (- (/ (cbrt 2) (cbrt x))) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x))) (* (/ (cbrt 2) (cbrt x)) (/ (* (cbrt 2) (cbrt 2)) (* (cbrt x) (cbrt x)))))
602.0ms
(fma (/ (sqrt 1) (* (cbrt (+ x 1)) (cbrt (+ x 1)))) (/ (sqrt 1) (cbrt (+ x 1))) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))
597.0ms
(fma (/ (* (cbrt 1) (cbrt 1)) 1) (/ (cbrt 1) (+ x 1)) (- (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))))

prune3.9s

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize48.0ms

Local error

Found 4 expressions with local error:

60.5b
(fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
3.5b
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
0.6b
(cbrt x)
0.6b
(cbrt x)

rewrite179.0ms

Algorithm
rewrite-expression-head
Rules
353×*-un-lft-identity
329×times-frac
254×add-sqr-sqrt
237×add-cube-cbrt
236×associate-+l+
234×prod-diff
55×distribute-lft-out
38×div-inv
26×associate-/r/
17×flip3-+ flip-+
16×add-log-exp
13×fma-def
10×distribute-lft-out--
6×cbrt-prod sum-log frac-add difference-of-squares
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u
2×flip3-- pow1/3 diff-log frac-sub flip--
1×+-commutative associate-+r+ sub-neg associate-+l- fma-udef
Counts
4 → 322
Calls
4 calls:
Slowest
168.0ms
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
1.0ms
(cbrt x)
1.0ms
(cbrt x)
0.0ms
(fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))

series1.3s

Counts
4 → 12
Calls
4 calls:
Slowest
718.0ms
(fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))
222.0ms
(+ (- (/ 1 (+ 1 x)) (/ 2 x)) (+ (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))
197.0ms
(cbrt x)
196.0ms
(cbrt x)

simplify40.0s

Counts
291 → 334
Calls
291 calls:
Slowest
605.0ms
(+ (* (- (* (/ 1 (+ 1 x)) (/ 1 (+ 1 x))) (* (/ 2 x) (/ 2 x))) (+ (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))) (* (+ (/ 1 (+ 1 x)) (/ 2 x)) (+ (pow (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) 3) (pow (/ 1 (- x 1)) 3))))
473.0ms
(+ (* (- (* 1 x) (* (+ 1 x) 2)) (+ (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1)))))) (* (* (+ 1 x) x) (+ (pow (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) 3) (pow (/ 1 (- x 1)) 3))))
441.0ms
(fma 1 (/ 1 (+ 1 x)) (- (* (/ (cbrt 2) x) (/ (* (cbrt 2) (cbrt 2)) 1))))
394.0ms
(fma (sqrt (/ 1 (+ 1 x))) (sqrt (/ 1 (+ 1 x))) (- (* (cbrt (/ 2 x)) (* (cbrt (/ 2 x)) (cbrt (/ 2 x))))))
384.0ms
(* (+ (* (/ 1 (+ 1 x)) (/ 1 (+ 1 x))) (+ (* (/ 2 x) (/ 2 x)) (* (/ 1 (+ 1 x)) (/ 2 x)))) (+ (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x)))))) (- (* (/ 1 (- x 1)) (/ 1 (- x 1))) (* (fma (- (/ 2 (cbrt x))) (/ 1 (* (cbrt x) (cbrt x))) (* (/ 2 (cbrt x)) (/ 1 (* (cbrt x) (cbrt x))))) (/ 1 (- x 1))))))

prune3.2s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b
(/ 2 (pow x 7))
0.1b
(/ 2 (pow x 5))
0.1b
(/ (/ 2 x) (* x x))
0.0b
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))

rewrite53.0ms

Algorithm
rewrite-expression-head
Rules
95×times-frac
60×*-un-lft-identity
58×add-sqr-sqrt add-cube-cbrt
26×add-exp-log
24×unpow-prod-down
20×add-cbrt-cube
19×associate-/l*
17×fma-def
15×associate-/r*
12×div-exp
8×cbrt-undiv sqr-pow
7×div-inv
6×add-log-exp
4×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u
3×clear-num frac-2neg
2×pow-to-exp pow-exp prod-exp cbrt-unprod
1×+-commutative sum-log flip3-+ frac-add flip-+ distribute-lft-out associate-/l/
Counts
4 → 178
Calls
4 calls:
Slowest
31.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
10.0ms
(/ (/ 2 x) (* x x))
5.0ms
(/ 2 (pow x 7))
5.0ms
(/ 2 (pow x 5))

series297.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
135.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
68.0ms
(/ 2 (pow x 7))
51.0ms
(/ 2 (pow x 5))
43.0ms
(/ (/ 2 x) (* x x))

simplify7.8s

Counts
187 → 190
Calls
187 calls:
Slowest
236.0ms
(/ (* (* 2 2) 2) (* (* (pow x 5) (pow x 5)) (pow x 5)))
234.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))
175.0ms
(* (exp (/ (/ 2 x) (* x x))) (exp (/ 2 (pow x 5))))
173.0ms
(+ (/ (/ 2 x) (* x x)) (/ 2 (pow x 5)))
168.0ms
(/ (* (cbrt 2) (cbrt 2)) (* (cbrt (pow x 7)) (cbrt (pow x 7))))

prune1.3s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.4b
(/ 1 (* x x))
0.2b
(/ 2 (pow x 7))
0.1b
(/ 2 (pow x 5))
0.1b
(fma (/ 2 x) (/ 1 (* x x)) (/ 2 (pow x 5)))

rewrite21.0ms

Algorithm
rewrite-expression-head
Rules
45×times-frac
38×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
25×add-exp-log
24×unpow-prod-down
15×associate-/r*
13×add-cbrt-cube
12×pow1
10×div-exp
9×associate-/l*
8×sqr-pow
6×pow-flip
4×expm1-log1p-u cbrt-undiv insert-posit16 log1p-expm1-u add-log-exp
3×clear-num frac-2neg prod-exp div-inv
2×pow-to-exp rec-exp 1-exp pow-exp
1×pow2 pow-plus pow-prod-down pow-sqr pow-prod-up cbrt-unprod fma-udef inv-pow
Counts
4 → 142
Calls
4 calls:
Slowest
9.0ms
(/ 1 (* x x))
5.0ms
(/ 2 (pow x 5))
5.0ms
(/ 2 (pow x 7))
0.0ms
(fma (/ 2 x) (/ 1 (* x x)) (/ 2 (pow x 5)))

series275.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
134.0ms
(fma (/ 2 x) (/ 1 (* x x)) (/ 2 (pow x 5)))
62.0ms
(/ 2 (pow x 7))
55.0ms
(/ 2 (pow x 5))
23.0ms
(/ 1 (* x x))

simplify6.5s

Counts
142 → 154
Calls
142 calls:
Slowest
294.0ms
(- (log 2) (log (pow x 7)))
240.0ms
(/ (* (* 1 1) 1) (* (* (* x x) (* x x)) (* x x)))
233.0ms
(/ (* (* 2 2) 2) (* (* (pow x 5) (pow x 5)) (pow x 5)))
231.0ms
(/ (* (* 2 2) 2) (* (* (pow x 7) (pow x 7)) (pow x 7)))
166.0ms
(/ (* (cbrt 2) (cbrt 2)) (* (cbrt (pow x 7)) (cbrt (pow x 7))))

prune1.2s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

regimes42.0ms

Accuracy

99.2% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 19.2b

bsearch161.0ms

end0.0ms

sample1.9s

Algorithm
intervals
Results
885.0ms1912×body640valid
392.0ms4134×body80valid
272.0ms534×body1280valid
192.0ms963×body320valid
61.0ms460×body160valid