Details

Time bar (total: 54.8s)

sample1.7s

Algorithm
intervals
Results
1.6s3281×body80valid

simplify709.0ms

Calls
1 calls:
Slowest
708.0ms
(* (* (/ 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))))))

prune23.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.9b

localize71.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.4b
(* (/ (/ 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)))))
0.4b
(* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))
0.3b
(/ (/ 1 (fabs x)) (fabs x))

rewrite108.0ms

Algorithm
rewrite-expression-head
Rules
108×times-frac
63×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
56×associate-*r*
29×add-exp-log
22×div-inv
20×add-cbrt-cube
17×associate-*l*
14×associate-*r/
11×pow1
10×associate-*l/
9×div-exp
8×frac-times
7×prod-exp
6×frac-add
5×cbrt-undiv cbrt-unprod
4×insert-posit16 associate-/l* add-log-exp
3×rec-exp associate-/r*
2×flip3-+ pow-prod-down *-commutative flip-+ pow-div
1×distribute-rgt-in clear-num frac-2neg distribute-lft-in distribute-rgt-out pow1/2 pow-flip inv-pow associate-/l/
Calls
4 calls:
Slowest
69.0ms
(* (/ (/ 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)))))
22.0ms
(* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))
10.0ms
(/ (/ 1 (fabs x)) (fabs x))
0.0ms
(sqrt PI)

series143.0ms

Calls
4 calls:
Slowest
97.0ms
(* (/ (/ 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)))))
30.0ms
(* (* (/ (/ 1 (fabs x)) (fabs x)) 15/8) (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))
16.0ms
(/ (/ 1 (fabs x)) (fabs x))
0.0ms
(sqrt PI)

simplify18.0s

Calls
154 calls:
Slowest
1.4s
(* (/ (* (* (/ 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))))))
1.3s
(* (* (* (/ (/ 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))))))
723.0ms
(* (/ 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))))))
660.0ms
(* (/ 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))))))
660.0ms
(* (/ 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))))))

prune2.7s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.4b
(/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x)))
0.3b
(/ (/ 1 (fabs x)) (fabs x))
0.3b
(/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))

rewrite99.0ms

Algorithm
rewrite-expression-head
Rules
112×times-frac
68×*-un-lft-identity
64×add-sqr-sqrt add-cube-cbrt
24×associate-/l*
23×div-inv
21×add-exp-log
16×add-cbrt-cube
12×pow1
9×div-exp
7×associate-/r*
6×cbrt-undiv pow-div
5×associate-/l/
4×insert-posit16 add-log-exp
3×clear-num frac-2neg
2×rec-exp pow-flip distribute-lft-out inv-pow
1×flip3-+ pow1/2 frac-add prod-exp cbrt-unprod flip-+
Calls
4 calls:
Slowest
84.0ms
(/ (+ (/ (/ 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))
4.0ms
(/ (/ 1 (fabs x)) (fabs x))
0.0ms
(sqrt PI)

series154.0ms

Calls
4 calls:
Slowest
121.0ms
(/ (+ (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) (/ 15/8 (pow (fabs x) 5))) (* (fabs x) (fabs x)))
19.0ms
(/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))
13.0ms
(/ (/ 1 (fabs x)) (fabs x))
0.0ms
(sqrt PI)

simplify8.2s

Calls
188 calls:
Slowest
703.0ms
(- (* (/ (/ 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))))
405.0ms
(/ (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
396.0ms
(/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (fabs x) (fabs x)) (fabs x)))
307.0ms
(/ (* (* (+ (/ (/ 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))))
283.0ms
(+ (pow (/ (/ 3/4 (* (fabs x) (fabs x))) (fabs x)) 3) (pow (/ 15/8 (pow (fabs x) 5)) 3))

prune2.8s

Pruning

13 alts after pruning (13 fresh and 0 done)

Merged error: 0.1b

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.4b
(* (/ (/ 1 (fabs x)) (fabs x)) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))))
0.3b
(/ (/ 1 (fabs x)) (fabs x))
0.3b
(/ (/ 1 (fabs x)) (fabs x))

rewrite28.0ms

Algorithm
rewrite-expression-head
Rules
36×times-frac
31×add-sqr-sqrt *-un-lft-identity add-cube-cbrt
20×add-exp-log
16×associate-*l*
14×div-inv
13×add-cbrt-cube
12×pow1
8×associate-/l*
6×associate-/r* div-exp
5×associate-*r/
4×insert-posit16 add-log-exp pow-div
3×frac-times cbrt-undiv rec-exp associate-*r* prod-exp
2×clear-num frac-2neg flip3-+ frac-add cbrt-unprod flip-+ pow-flip inv-pow associate-/l/
1×distribute-rgt-in distribute-lft-in pow1/2 pow-prod-down associate-*l/ *-commutative
Calls
4 calls:
Slowest
14.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))))
6.0ms
(/ (/ 1 (fabs x)) (fabs x))
4.0ms
(/ (/ 1 (fabs x)) (fabs x))
0.0ms
(sqrt PI)

series172.0ms

Calls
4 calls:
Slowest
140.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))))
19.0ms
(/ (/ 1 (fabs x)) (fabs x))
13.0ms
(/ (/ 1 (fabs x)) (fabs x))
0.0ms
(sqrt PI)

simplify7.8s

Calls
118 calls:
Slowest
805.0ms
(* (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (fabs x) (fabs x)) (fabs x))) (* (* (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))))) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))))))
517.0ms
(* (* (* (/ (/ 1 (fabs x)) (fabs x)) (/ (/ 1 (fabs x)) (fabs x))) (/ (/ 1 (fabs x)) (fabs x))) (* (* (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))))) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))))))
505.0ms
(* (/ 1 (fabs x)) (+ (* 15/8 (fabs x)) (* (pow (fabs x) 5) (* 3/4 (/ (/ 1 (fabs x)) (fabs x))))))
447.0ms
(* (/ 1 (fabs x)) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))))
430.0ms
(* (/ (/ 1 (fabs x)) (fabs x)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))))

prune2.2s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 0.1b

localize27.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.4b
(* (/ 1 (fabs x)) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))))
0.3b
(/ (/ 1 (fabs x)) (fabs x))
0.3b
(/ (/ 1 (fabs x)) (fabs x))

rewrite41.0ms

Algorithm
rewrite-expression-head
Rules
24×add-sqr-sqrt *-un-lft-identity times-frac add-cube-cbrt
16×add-exp-log
12×pow1
11×div-inv
10×add-cbrt-cube
8×associate-/l*
6×associate-/r*
5×associate-*r/
4×div-exp associate-*l* insert-posit16 add-log-exp pow-div
3×frac-times rec-exp associate-*r*
2×cbrt-undiv clear-num frac-2neg flip3-+ frac-add prod-exp flip-+ pow-flip inv-pow associate-/l/
1×distribute-rgt-in distribute-lft-in pow1/2 pow-prod-down associate-*l/ *-commutative cbrt-unprod
Calls
4 calls:
Slowest
22.0ms
(* (/ 1 (fabs x)) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))))
9.0ms
(/ (/ 1 (fabs x)) (fabs x))
8.0ms
(/ (/ 1 (fabs x)) (fabs x))
0.0ms
(sqrt PI)

series133.0ms

Calls
4 calls:
Slowest
106.0ms
(* (/ 1 (fabs x)) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))))
14.0ms
(/ (/ 1 (fabs x)) (fabs x))
13.0ms
(/ (/ 1 (fabs x)) (fabs x))
0.0ms
(sqrt PI)

simplify7.1s

Calls
103 calls:
Slowest
672.0ms
(* 1 (+ (* 15/8 (fabs x)) (* (pow (fabs x) 5) (* 3/4 (/ (/ 1 (fabs x)) (fabs x))))))
567.0ms
(* (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))))) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))))))
440.0ms
(* (/ 1 (fabs x)) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))))
434.0ms
(* 1 (- (* (/ 15/8 (pow (fabs x) 5)) (/ 15/8 (pow (fabs x) 5))) (* (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x))))))
414.0ms
(* (/ 1 (fabs x)) (+ (/ 15/8 (pow (fabs x) 5)) (* 3/4 (/ (/ (/ 1 (fabs x)) (fabs x)) (fabs x)))))

prune2.2s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

regimes384.0ms

bsearch10.0ms

end0.0ms