Details

Time bar (total: 2.5m)

sample69.0ms

Algorithm
intervals
Results
26.0ms56×body1280valid
15.0ms40×body640valid
12.0ms128×body80valid
6.0ms21×body320valid
2.0ms11×body160valid

simplify102.0ms

Calls
1 calls:
Slowest
102.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 29.6b

localize25.0ms

Local error

Found 3 expressions with local error:

3.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite31.0ms

Algorithm
rewrite-expression-head
Rules
90×prod-diff
75×add-sqr-sqrt
72×*-un-lft-identity
70×add-cube-cbrt
64×times-frac
48×associate-/r/
24×div-inv
18×flip3-+ flip-+
8×flip3-- flip--
6×associate-/r* fma-neg
5×add-cbrt-cube add-exp-log add-log-exp
3×expm1-log1p-u pow1 insert-posit16 log1p-expm1-u associate-/l*
2×clear-num frac-2neg difference-of-squares associate-/l/
1×cbrt-undiv sub-neg diff-log div-exp frac-sub distribute-lft-out--
Calls
3 calls:
Slowest
17.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
7.0ms
(/ (+ x 1) (- x 1))
1.0ms
(/ x (+ x 1))

series166.0ms

Calls
3 calls:
Slowest
114.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
27.0ms
(/ x (+ x 1))
24.0ms
(/ (+ x 1) (- x 1))

simplify49.8s

Calls
235 calls:
Slowest
1.1s
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
757.0ms
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (sqrt (/ (+ x 1) (- x 1))) (sqrt (/ (+ x 1) (- x 1))))))
746.0ms
(fma (/ x (+ (pow x 3) (pow 1 3))) (+ (* x x) (- (* 1 1) (* x 1))) (- (* (/ (+ x 1) (- x 1)) 1)))
707.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
690.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))

prune1.4s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

3.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(expm1 (log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
0.0b
(log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
0.0b
(/ (+ x 1) (- x 1))

rewrite20.0ms

Algorithm
rewrite-expression-head
Rules
90×prod-diff
75×add-sqr-sqrt
72×*-un-lft-identity
70×add-cube-cbrt
64×times-frac
46×associate-/r/
23×div-inv
17×flip3-+ flip-+
8×flip3-- flip--
6×add-cbrt-cube fma-neg add-exp-log add-log-exp
5×expm1-log1p-u
4×pow1 insert-posit16 log1p-expm1-u
3×associate-/r* associate-/l*
2×difference-of-squares associate-/l/
1×cbrt-undiv log1p-udef expm1-log1p clear-num sub-neg frac-2neg diff-log div-exp log1p-expm1 frac-sub distribute-lft-out-- expm1-udef
Calls
4 calls:
Slowest
12.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
4.0ms
(/ (+ x 1) (- x 1))
0.0ms
(log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
0.0ms
(expm1 (log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))

series402.0ms

Calls
4 calls:
Slowest
156.0ms
(expm1 (log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
115.0ms
(log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))
94.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
38.0ms
(/ (+ x 1) (- x 1))

simplify50.5s

Calls
235 calls:
Slowest
807.0ms
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (/ (sqrt (+ x 1)) (- x 1)) (/ (sqrt (+ x 1)) 1))))
771.0ms
(fma (sqrt (/ x (+ x 1))) (sqrt (/ x (+ x 1))) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))
740.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
716.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
687.0ms
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (sqrt (/ (+ x 1) (- x 1))) (sqrt (/ (+ x 1) (- x 1))))))

prune1.7s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize6.0ms

Local error

Found 4 expressions with local error:

3.6b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.5b
(expm1 (expm1 (log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))))
0.0b
(log1p (expm1 (expm1 (log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))))
0.0b
(expm1 (log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
90×prod-diff
67×add-sqr-sqrt
64×*-un-lft-identity
62×add-cube-cbrt
55×times-frac
44×associate-/r/
22×div-inv
16×flip3-+ flip-+
7×flip3-- flip--
6×fma-neg add-log-exp
5×log1p-expm1-u
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16
2×expm1-log1p expm1-udef difference-of-squares
1×log1p-udef sub-neg diff-log log1p-expm1 frac-sub distribute-lft-out--
Calls
4 calls:
Slowest
9.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0ms
(expm1 (expm1 (log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))))
0.0ms
(expm1 (log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
0.0ms
(log1p (expm1 (expm1 (log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))))

series710.0ms

Calls
4 calls:
Slowest
234.0ms
(log1p (expm1 (expm1 (log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))))
193.0ms
(expm1 (log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))))
176.0ms
(expm1 (expm1 (log1p (- (/ x (+ x 1)) (/ (+ x 1) (- x 1))))))
107.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

simplify38.5s

Calls
207 calls:
Slowest
655.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
635.0ms
(fma 1 (/ x (+ x 1)) (- (* (/ (cbrt (+ x 1)) (- x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1))))
556.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
537.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
482.0ms
(fma (- (/ 1 (- x 1))) (+ x 1) (* (/ 1 (- x 1)) (+ x 1)))

prune1.1s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

30.0b
(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))
0.5b
(expm1 (expm1 (log1p (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1)))))))
0.0b
(log1p (expm1 (expm1 (log1p (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))))))
0.0b
(expm1 (log1p (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))))

rewrite1.0ms

Algorithm
rewrite-expression-head
Rules
5×log1p-expm1-u
4×add-sqr-sqrt expm1-log1p-u pow1 *-un-lft-identity add-cbrt-cube add-exp-log add-cube-cbrt insert-posit16 add-log-exp
2×expm1-log1p expm1-udef
1×log1p-udef log1p-expm1 fma-udef
Calls
4 calls:
Slowest
0.0ms
(expm1 (expm1 (log1p (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1)))))))
0.0ms
(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))
0.0ms
(log1p (expm1 (expm1 (log1p (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))))))
0.0ms
(expm1 (log1p (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))))

series527.0ms

Calls
4 calls:
Slowest
182.0ms
(log1p (expm1 (expm1 (log1p (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))))))
146.0ms
(expm1 (expm1 (log1p (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1)))))))
123.0ms
(expm1 (log1p (fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))))
76.0ms
(fma x (/ 1 (+ x 1)) (- (/ (+ x 1) (- x 1))))

simplify1.8s

Calls
14 calls:
Slowest
214.0ms
(- (+ (* 11/2 (* (pow x 2) E)) (+ E (* 3 (* x E)))) 1)
184.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
180.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
179.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
178.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune435.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes50.0ms

Accuracy

99.8% (0.1b remaining)

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

bsearch120.0ms

end0.0ms

sample1.6s

Algorithm
intervals
Results
811.0ms1669×body1280valid
369.0ms1321×body640valid
235.0ms4089×body80valid
116.0ms627×body320valid
30.0ms294×body160valid