Details

Time bar (total: 44.4s)

sample1.6s

Algorithm
intervals
Results
1.6s3460×body80valid

simplify682.0ms

Calls
1 calls:
Slowest
681.0ms
(* (* (/ 1 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1 (fabs x)) (* (/ 1 2) (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 3 4) (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))) (* (/ 15 8) (* (* (* (* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))))

prune31.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize83.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.3b
(* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))
0.3b
(* (/ (/ 1 (fabs x)) (fabs x)) (+ (* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))))
0.3b
(* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))

rewrite102.0ms

Algorithm
rewrite-expression-head
Rules
180×times-frac
108×associate-*r*
95×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
30×div-inv
25×add-exp-log
18×add-cbrt-cube
17×associate-*l*
15×associate-*r/
10×associate-*l/
8×frac-times pow1
7×div-exp prod-exp
6×frac-add
5×cbrt-unprod
4×cbrt-undiv insert-posit16 add-log-exp
3×*-commutative
2×rec-exp flip3-+ pow-prod-down flip-+
1×distribute-rgt-in distribute-lft-in distribute-rgt-out pow1/2
Calls
4 calls:
Slowest
51.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (+ (* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))))
40.0ms
(* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))
7.0ms
(* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

series168.0ms

Calls
4 calls:
Slowest
102.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (+ (* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))))
36.0ms
(* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))
30.0ms
(* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))
0.0ms
(sqrt PI)

simplify19.5s

Calls
171 calls:
Slowest
1.4s
(* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (* (* (+ (* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))) (+ (* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))))) (+ (* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))))))
1.3s
(* (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (+ (* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))) (+ (* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))))) (+ (* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))))))
754.0ms
(* (/ 1 (fabs x)) (+ (* (* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ 1 (fabs x)) (fabs x))) (fabs x)) (* (fabs x) (* 3/4 (/ (/ 1 (fabs x)) (fabs x))))))
653.0ms
(* (/ 1 (fabs x)) (+ (* (* (* (/ 1 (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))) (fabs x)) (* (fabs x) (* 3/4 (/ (/ 1 (fabs x)) (fabs x))))))
630.0ms
(* (/ 1 (fabs x)) (+ (* (* (* (/ 1 (fabs x)) 15/8) (/ (/ 1 (fabs x)) (fabs x))) (fabs x)) (* (* (fabs x) (fabs x)) (* 3/4 (/ (/ 1 (fabs x)) (fabs x))))))

prune3.2s

Pruning

16 alts after pruning (16 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.3b
(/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x)))
0.3b
(/ 3/4 (* (fabs x) (fabs x)))
0.3b
(/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))

rewrite77.0ms

Algorithm
rewrite-expression-head
Rules
100×times-frac
59×*-un-lft-identity
55×add-sqr-sqrt add-cube-cbrt
20×associate-/l*
19×div-inv
17×add-exp-log
14×add-cbrt-cube
9×pow1
7×div-exp
5×cbrt-undiv associate-/r*
4×insert-posit16 add-log-exp pow-div associate-/l/
3×clear-num frac-2neg
2×distribute-lft-out
1×rec-exp flip3-+ pow1/2 frac-add prod-exp cbrt-unprod flip-+ pow-flip inv-pow
Calls
4 calls:
Slowest
65.0ms
(/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x)))
8.0ms
(/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))
1.0ms
(/ 3/4 (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

series158.0ms

Calls
4 calls:
Slowest
100.0ms
(/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x)))
33.0ms
(/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))
24.0ms
(/ 3/4 (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify7.7s

Calls
153 calls:
Slowest
804.0ms
(/ (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
376.0ms
(/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
312.0ms
(/ (* (* (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5)))) (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))))
301.0ms
(- (* (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x))) (* (/ 15/8 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 5))))
282.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x))) (+ (/ (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) 2) (/ 1 (fabs x)))))

prune2.5s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
1.0b
(sqrt PI)
0.3b
(/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x)))
0.3b
(/ 3/4 (* (fabs x) (fabs x)))

rewrite71.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-cbrt-cube add-exp-log
6×add-sqr-sqrt add-cube-cbrt
4×pow1 times-frac insert-posit16 associate-/l* add-log-exp
3×associate-/l/
2×cbrt-undiv clear-num associate-/r* frac-2neg pow1/2 div-exp div-inv distribute-lft-out
1×flip3-+ frac-add prod-exp cbrt-unprod flip-+
Calls
4 calls:
Slowest
68.0ms
(/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x)))
1.0ms
(/ 3/4 (* (fabs x) (fabs x)))
1.0ms
(sqrt PI)
1.0ms
(sqrt PI)

series110.0ms

Calls
4 calls:
Slowest
96.0ms
(/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x)))
14.0ms
(/ 3/4 (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify2.2s

Calls
25 calls:
Slowest
345.0ms
(- (* (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x))) (* (/ 15/8 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 5))))
273.0ms
(+ (pow (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) 3) (pow (/ 15/8 (pow (fabs x) 5)) 3))
269.0ms
(/ (* (* (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5)))) (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))))
251.0ms
(/ (* (* (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5)))) (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5)))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))))
118.0ms
(- (log (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5)))) (+ (log (fabs x)) (log (fabs x))))

prune1.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize6.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
1.0b
(sqrt PI)
0.3b
(/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x)))
0.3b
(/ 3/4 (* (fabs x) (fabs x)))

rewrite101.0ms

Algorithm
rewrite-expression-head
Rules
10×*-un-lft-identity
9×add-cbrt-cube add-exp-log
6×add-sqr-sqrt add-cube-cbrt
4×pow1 times-frac insert-posit16 associate-/l* add-log-exp
3×associate-/l/
2×cbrt-undiv clear-num associate-/r* frac-2neg pow1/2 div-exp div-inv distribute-lft-out
1×flip3-+ frac-add prod-exp cbrt-unprod flip-+
Calls
4 calls:
Slowest
96.0ms
(/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x)))
3.0ms
(/ 3/4 (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

series123.0ms

Calls
4 calls:
Slowest
109.0ms
(/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x)))
14.0ms
(/ 3/4 (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)
0.0ms
(sqrt PI)

simplify3.3s

Calls
27 calls:
Slowest
542.0ms
(* (/ (exp (* (fabs x) (fabs x))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (+ (/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x))) (+ (/ (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) 2) (/ 1 (fabs x)))))
485.0ms
(* (/ (exp (* (fabs x) (fabs x))) (* (sqrt (sqrt PI)) (sqrt (sqrt PI)))) (+ (/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x))) (+ (/ (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)) 2) (/ 1 (fabs x)))))
335.0ms
(/ (* (* (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5)))) (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5)))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))))
332.0ms
(/ (* (* (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5)))) (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x))))
299.0ms
(- (* (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x))) (* (/ 15/8 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 5))))

prune1.2s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

regimes268.0ms

bsearch8.0ms

end0.0ms