Details

Time bar (total: 1.1m)

sample101.0ms

Algorithm
intervals
Results
60.0ms65×body1280valid
14.0ms43×body640valid
10.0ms121×body80valid
4.0ms16×body320valid
2.0ms11×body160valid

simplify67.0ms

Calls
1 calls:
Slowest
67.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.5b

localize26.0ms

Local error

Found 3 expressions with local error:

2.8b
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
0.0b
(/ (+ x 1) (- x 1))
0.0b
(/ x (+ x 1))

rewrite42.0ms

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)))
17.0ms
(/ (+ x 1) (- x 1))
1.0ms
(/ x (+ x 1))

series78.0ms

Calls
3 calls:
Slowest
50.0ms
(- (/ x (+ x 1)) (/ (+ x 1) (- x 1)))
16.0ms
(/ (+ x 1) (- x 1))
12.0ms
(/ x (+ x 1))

simplify49.7s

Calls
235 calls:
Slowest
793.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))
791.0ms
(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)))))
716.0ms
(fma (/ x (- (* x x) (* 1 1))) (- x 1) (- (* (sqrt (/ (+ x 1) (- x 1))) (sqrt (/ (+ x 1) (- x 1))))))
715.0ms
(fma (- (+ x 1)) (/ (+ x 1) (- (* x x) (* 1 1))) (* (+ x 1) (/ (+ x 1) (- (* x x) (* 1 1)))))

prune1.3s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize26.0ms

Local error

Found 4 expressions with local error:

5.0b
(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)))

series80.0ms

Calls
4 calls:
Slowest
44.0ms
(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))

simplify507.0ms

Calls
14 calls:
Slowest
134.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
111.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
97.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (/ 1 (pow x 2))))
18.0ms
(/ -1 (pow x 3))
16.0ms
(/ -1 (pow x 2))

prune616.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

32.4b
(fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
0.1b
(* (/ 1 (- x 1)) (+ x 1))
0.0b
(/ 1 (+ x 1))
0.0b
(/ 1 (- x 1))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
10×add-exp-log
8×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
6×associate-/r* add-cbrt-cube associate-*l* associate-/r/
4×expm1-log1p-u insert-posit16 log1p-expm1-u add-log-exp
3×rec-exp flip3-+ associate-*r* flip-+ div-inv
2×frac-times clear-num frac-2neg flip3-- prod-exp associate-*r/ pow-flip flip-- inv-pow
1×distribute-rgt-in distribute-lft-in pow-prod-down associate-*l/ *-commutative cbrt-unprod fma-udef
Calls
4 calls:
Slowest
10.0ms
(* (/ 1 (- x 1)) (+ x 1))
2.0ms
(/ 1 (+ x 1))
1.0ms
(/ 1 (- x 1))
0.0ms
(fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))

series60.0ms

Calls
4 calls:
Slowest
35.0ms
(fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
11.0ms
(* (/ 1 (- x 1)) (+ x 1))
8.0ms
(/ 1 (- x 1))
7.0ms
(/ 1 (+ x 1))

simplify3.3s

Calls
44 calls:
Slowest
914.0ms
(* (* (* (/ 1 (- x 1)) (/ 1 (- x 1))) (/ 1 (- x 1))) (* (* (+ x 1) (+ x 1)) (+ x 1)))
298.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
282.0ms
(- (+ (* 2 x) (+ (* 2 (pow x 2)) 1)))
252.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
205.0ms
(* (- x 1) (+ (* x x) (- (* 1 1) (* x 1))))

prune682.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 4 expressions with local error:

32.4b
(fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
0.1b
(* (/ 1 (- x 1)) (+ x 1))
0.0b
(/ 1 (+ x 1))
0.0b
(expm1 (log1p (fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))))

rewrite14.0ms

Algorithm
rewrite-expression-head
Rules
9×add-exp-log
7×add-sqr-sqrt pow1 *-un-lft-identity add-cube-cbrt
6×add-cbrt-cube associate-*l*
4×expm1-log1p-u associate-/r/ insert-posit16 log1p-expm1-u add-log-exp
3×associate-/r* flip3-+ associate-*r* flip-+
2×frac-times rec-exp prod-exp associate-*r/ div-inv
1×distribute-rgt-in expm1-log1p clear-num frac-2neg distribute-lft-in flip3-- pow-prod-down associate-*l/ *-commutative cbrt-unprod fma-udef pow-flip flip-- inv-pow expm1-udef
Calls
4 calls:
Slowest
10.0ms
(* (/ 1 (- x 1)) (+ x 1))
2.0ms
(/ 1 (+ x 1))
0.0ms
(fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
0.0ms
(expm1 (log1p (fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))))

series170.0ms

Calls
4 calls:
Slowest
110.0ms
(expm1 (log1p (fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))))
37.0ms
(fma x (/ 1 (+ x 1)) (- (* (/ 1 (- x 1)) (+ x 1))))
13.0ms
(* (/ 1 (- x 1)) (+ x 1))
10.0ms
(/ 1 (+ x 1))

simplify3.7s

Calls
38 calls:
Slowest
879.0ms
(* (* (* (/ 1 (- x 1)) (/ 1 (- x 1))) (/ 1 (- x 1))) (* (* (+ x 1) (+ x 1)) (+ x 1)))
317.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
287.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
271.0ms
(- (+ (* 3 (/ 1 (pow x 3))) (+ (/ 1 (pow x 2)) (* 3 (/ 1 x)))))
256.0ms
(- (+ (* 2 x) (+ (* 2 (pow x 2)) 1)))

prune860.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

regimes46.0ms

Accuracy

100% (0.0b remaining)

Error of 0.2b against oracle of 0.2b and baseline of 31.6b

bsearch177.0ms

end0.0ms

sample2.6s

Algorithm
intervals
Results
861.0ms4104×body80valid
822.0ms1717×body1280valid
582.0ms1236×body640valid
152.0ms592×body320valid
58.0ms351×body160valid