Details

Time bar (total: 1.1m)

sample54.0ms

Algorithm
intervals
Results
21.0ms63×body1280valid
11.0ms43×body640valid
8.0ms123×body80valid
4.0ms21×body320valid
1.0ms6×body160valid

simplify63.0ms

Calls
1 calls:
Slowest
63.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize47.0ms

Local error

Found 3 expressions with local error:

2.4b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite33.0ms

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
18.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
8.0ms
(/ (+ x 1) (- x 1))
1.0ms
(/ x (+ x 1))

series60.0ms

Calls
3 calls:
Slowest
33.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
15.0ms
(/ x (+ x 1))
11.0ms
(/ (+ x 1) (- x 1))

simplify48.9s

Calls
235 calls:
Slowest
1.0s
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (sqrt (/ (+ x 1) (- x 1))) (sqrt (/ (+ x 1) (- x 1))))))
796.0ms
(fma (sqrt (/ x (+ x 1))) (sqrt (/ x (+ x 1))) (- (* (/ (cbrt (+ x 1)) (- x 1)) (/ (* (cbrt (+ x 1)) (cbrt (+ x 1))) 1))))
763.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
730.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
694.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))

prune1.4s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize38.0ms

Local error

Found 4 expressions with local error:

7.5b
(fma (/ (/ -1 (* x x)) x) 3 (/ -1 (* x x)))
0.3b
(/ -1 (* x x))
0.3b
(/ -1 (* x x))
0.1b
(/ (/ -1 (* x x)) x)

rewrite5.0ms

Algorithm
rewrite-expression-head
Rules
5×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
4×expm1-log1p-u pow1 add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u div-inv associate-/l* add-log-exp
3×clear-num frac-2neg
2×associate-/r*
1×fma-udef associate-/l/
Calls
4 calls:
Slowest
3.0ms
(/ (/ -1 (* x x)) x)
0.0ms
(/ -1 (* x x))
0.0ms
(/ -1 (* x x))
0.0ms
(fma (/ (/ -1 (* x x)) x) 3 (/ -1 (* x x)))

series74.0ms

Calls
4 calls:
Slowest
37.0ms
(fma (/ (/ -1 (* x x)) x) 3 (/ -1 (* x x)))
13.0ms
(/ (/ -1 (* x x)) x)
13.0ms
(/ -1 (* x x))
10.0ms
(/ -1 (* x x))

simplify465.0ms

Calls
14 calls:
Slowest
126.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
101.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
98.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
16.0ms
(/ -1 (pow x 3))
15.0ms
(/ -1 (pow x 2))

prune656.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize31.0ms

Local error

Found 4 expressions with local error:

7.4b
(fma (/ (log (exp (/ -1 (* x x)))) x) 3 (/ -1 (* x x)))
1.1b
(log (exp (/ -1 (* x x))))
0.3b
(/ -1 (* x x))
0.3b
(/ -1 (* x x))

rewrite8.0ms

Algorithm
rewrite-expression-head
Rules
6×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
5×pow1 log-pow
4×expm1-log1p-u exp-prod add-cbrt-cube add-exp-log insert-posit16 log1p-expm1-u add-log-exp
3×log-prod div-inv
2×clear-num associate-/r* frac-2neg
1×rem-log-exp fma-udef
Calls
4 calls:
Slowest
6.0ms
(log (exp (/ -1 (* x x))))
1.0ms
(/ -1 (* x x))
1.0ms
(/ -1 (* x x))
0.0ms
(fma (/ (log (exp (/ -1 (* x x)))) x) 3 (/ -1 (* x x)))

series72.0ms

Calls
4 calls:
Slowest
41.0ms
(fma (/ (log (exp (/ -1 (* x x)))) x) 3 (/ -1 (* x x)))
11.0ms
(log (exp (/ -1 (* x x))))
10.0ms
(/ -1 (* x x))
10.0ms
(/ -1 (* x x))

simplify473.0ms

Calls
19 calls:
Slowest
110.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
101.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
84.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
20.0ms
(log (sqrt (exp (/ -1 (* x x)))))
18.0ms
(log (* (cbrt (exp (/ -1 (* x x)))) (cbrt (exp (/ -1 (* x x))))))

prune676.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize24.0ms

Local error

Found 4 expressions with local error:

32.3b
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))
17.5b
(/ x (- (* x x) (* 1 1)))
17.5b
(/ (+ x 1) (- (* x x) (* 1 1)))
0.1b
(* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))

rewrite30.0ms

Algorithm
rewrite-expression-head
Rules
24×times-frac
23×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
18×associate-*r*
11×add-cbrt-cube add-exp-log
8×associate-/r* difference-of-squares
6×pow1 associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×flip3-+ flip3-- associate-*l* flip-+ div-inv flip-- associate-/l*
2×frac-times cbrt-undiv clear-num frac-2neg div-exp associate-*l/ prod-exp cbrt-unprod associate-/l/
1×pow-prod-down associate-*r/ *-commutative fma-udef
Calls
4 calls:
Slowest
14.0ms
(* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))
11.0ms
(/ (+ x 1) (- (* x x) (* 1 1)))
3.0ms
(/ x (- (* x x) (* 1 1)))
0.0ms
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))

series121.0ms

Calls
4 calls:
Slowest
57.0ms
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))))
26.0ms
(/ x (- (* x x) (* 1 1)))
20.0ms
(* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1))))
18.0ms
(/ (+ x 1) (- (* x x) (* 1 1)))

simplify9.6s

Calls
86 calls:
Slowest
1.1s
(* (- (* x x) (* 1 1)) (/ (+ x 1) (- (* x x) (* 1 1))))
848.0ms
(/ (* (* (+ x 1) (+ x 1)) (+ x 1)) (* (* (- (* x x) (* 1 1)) (- (* x x) (* 1 1))) (- (* x x) (* 1 1))))
665.0ms
(* (+ (* x x) (- (* 1 1) (* x 1))) (- (* x x) (* 1 1)))
602.0ms
(* (- x 1) (- (* x x) (* 1 1)))
294.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))

prune1.1s

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.0b

regimes70.0ms

Accuracy

100% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 32.2b

bsearch205.0ms

end0.0ms

sample2.3s

Algorithm
intervals
Results
1.2s1667×body1280valid
397.0ms1232×body640valid
346.0ms4174×body80valid
174.0ms640×body320valid
65.0ms287×body160valid