Details

Time bar (total: 2.7m)

sample1.3s

Algorithm
intervals
Results
1.2s3316×body80valid

simplify727.0ms

Counts
1 → 1
Calls
1 calls:
Slowest
727.0ms
(* (* (/ 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: 0.8b

localize77.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.4b
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
0.3b
(* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
0.3b
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))

rewrite168.0ms

Algorithm
rewrite-expression-head
Rules
182×add-exp-log
140×times-frac
110×add-cbrt-cube
103×pow1
90×div-exp
64×pow-div
57×add-sqr-sqrt
55×prod-exp
50×cbrt-undiv
48×*-un-lft-identity
45×add-cube-cbrt
31×cbrt-unprod
30×associate-/l*
21×associate-*l*
16×pow2 pow-plus pow-sqr pow-prod-up pow-flip inv-pow
11×div-inv
8×rec-exp 1-exp
5×unswap-sqr
4×associate-*r* insert-posit16 add-log-exp
3×sqrt-prod
2×frac-times clear-num associate-/r* frac-2neg flip3-+ associate-*r/ flip-+ associate-/l/
1×distribute-rgt-in rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ *-commutative distribute-lft-out
Counts
4 → 245
Calls
4 calls:
Slowest
99.0ms
(* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
41.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
14.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series222.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
107.0ms
(* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))
72.0ms
(/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))
42.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify40.6s

Counts
278 → 255
Calls
278 calls:
Slowest
1.5s
(* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
1.4s
(* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
1.3s
(* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (* (fabs x) (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
1.3s
(* (/ (/ (* (* (/ 1 (fabs x)) (/ 1 (fabs x))) (/ 1 (fabs x))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))
1.2s
(* (/ (* (* (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))) (/ (/ 1 (fabs x)) (* (fabs x) (fabs x)))) (* (* (* (fabs x) (fabs x)) (fabs x)) (* (* (fabs x) (fabs x)) (fabs x)))) (* (* (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x))))))

prune4.4s

Pruning

15 alts after pruning (15 fresh and 0 done)

Merged error: 0.2b

localize52.0ms

Local error

Found 4 expressions with local error:

1.0b
(sqrt PI)
0.4b
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
0.3b
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.3b
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x))))

rewrite1.4s

Algorithm
rewrite-expression-head
Rules
79×times-frac
75×*-un-lft-identity
60×add-sqr-sqrt
51×add-cube-cbrt
25×add-exp-log
23×add-cbrt-cube
22×associate-*l*
17×associate-/l*
15×unpow-prod-down
14×distribute-lft-out
13×sqrt-prod
10×div-exp
8×cbrt-undiv associate-/r* frac-add
7×pow1 associate-*r* div-inv
5×frac-times flip3-+ associate-*r/ flip-+ sqr-pow
4×prod-exp cbrt-unprod insert-posit16 add-log-exp
3×unswap-sqr associate-/l/
2×clear-num frac-2neg
1×distribute-rgt-in pow-to-exp rem-sqrt-square distribute-lft-in sqrt-pow1 pow1/2 pow-prod-down associate-*l/ pow-exp *-commutative
Counts
4 → 176
Calls
4 calls:
Slowest
1.3s
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x))))
66.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
26.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
2.0ms
(sqrt PI)

series635.0ms

Counts
4 → 10
Calls
4 calls:
Slowest
469.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x))))
131.0ms
(/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))
34.0ms
(/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))
0.0ms
(sqrt PI)

simplify34.0s

Counts
188 → 186
Calls
188 calls:
Slowest
1.4s
(* (/ (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (fabs x)))) (* (* (sqrt PI) (sqrt PI)) (sqrt PI))) (* (* (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x))) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x)))) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x)))))
1.1s
(* (* (* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (/ (exp (* (fabs x) (fabs x))) (sqrt PI))) (/ (exp (* (fabs x) (fabs x))) (sqrt PI))) (* (* (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x))) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x)))) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x)))))
783.0ms
(* (exp (* (fabs x) (fabs x))) (+ (* (+ (pow (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) 3) (pow (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5)) 3)) (fabs x)) (* (+ (* (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x)))) (- (* (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5)) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (* (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))))) 1)))
631.0ms
(* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (/ 1 (fabs x)))
549.0ms
(* (sqrt (/ (exp (* (fabs x) (fabs x))) (sqrt PI))) (sqrt (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (/ (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))) (pow (fabs x) 5))) (/ 1 (fabs x)))))

prune3.1s

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 0.1b

localize97.0ms

Local error

Found 4 expressions with local error:

0.3b
(/ 15/8 (pow (fabs x) 7))
0.3b
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(* (sqrt (/ 1 PI)) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
0.3b
(* (* (fabs x) (fabs x)) (fabs x))

rewrite2.4s

Algorithm
rewrite-expression-head
Rules
47×*-un-lft-identity
42×add-sqr-sqrt
35×times-frac
32×add-cube-cbrt
25×pow1 add-exp-log
22×add-cbrt-cube
18×frac-add
17×associate-*l*
16×sqrt-prod
12×unpow-prod-down
11×associate-*r* distribute-lft-out
8×associate-/r* sqrt-div
7×frac-times prod-exp associate-*r/ cbrt-unprod
6×flip3-+ pow-plus div-exp pow-prod-up flip-+ associate-/l*
5×div-inv unswap-sqr
4×cbrt-undiv pow-prod-down insert-posit16 add-log-exp sqr-pow
2×pow2 clear-num frac-2neg pow-sqr *-commutative
1×distribute-rgt-in pow-to-exp distribute-lft-in pow3 associate-*l/ pow-exp
Counts
4 → 156
Calls
4 calls:
Slowest
2.3s
(* (sqrt (/ 1 PI)) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
40.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
34.0ms
(* (* (fabs x) (fabs x)) (fabs x))
12.0ms
(/ 15/8 (pow (fabs x) 7))

series882.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
725.0ms
(* (sqrt (/ 1 PI)) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
85.0ms
(/ 15/8 (pow (fabs x) 7))
37.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
35.0ms
(* (* (fabs x) (fabs x)) (fabs x))

simplify26.0s

Counts
165 → 168
Calls
165 calls:
Slowest
1.4s
(* (* (* (sqrt (/ 1 PI)) (sqrt (/ 1 PI))) (sqrt (/ 1 PI))) (* (* (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))))
769.0ms
(* (pow (fabs x) 7) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (pow (fabs x) 5)) (fabs x)))
688.0ms
(* (sqrt PI) (* (pow (fabs x) 7) (* (- (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (fabs x))))
633.0ms
(* (sqrt 1) (+ (* 15/8 (+ (* (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5)))) (- (* (/ 1 (fabs x)) (/ 1 (fabs x))) (* (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))) (* (pow (fabs x) 7) (+ (pow (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) 3) (pow (/ 1 (fabs x)) 3)))))
616.0ms
(* (sqrt PI) (+ (* (/ 15/8 (pow (fabs x) 7)) (/ 15/8 (pow (fabs x) 7))) (- (* (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))) (* (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))))

prune3.2s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 0.1b

localize108.0ms

Local error

Found 4 expressions with local error:

0.3b
(* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7)))
0.3b
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
0.3b
(* (sqrt (/ 1 PI)) (+ (* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
0.3b
(* (* (fabs x) (fabs x)) (fabs x))

rewrite2.6s

Algorithm
rewrite-expression-head
Rules
91×add-sqr-sqrt
68×times-frac
53×sqrt-prod
52×associate-*r*
46×*-un-lft-identity
45×add-cube-cbrt
30×add-exp-log
27×pow1
25×add-cbrt-cube
23×associate-*l*
22×unpow-prod-down
19×unswap-sqr
18×frac-add associate-*r/
11×prod-exp
10×sqr-pow
9×cbrt-unprod
8×sqrt-div
7×frac-times
6×flip3-+ pow-plus div-exp pow-prod-up flip-+
5×pow-prod-down
4×cbrt-undiv insert-posit16 add-log-exp
3×*-commutative div-inv associate-/l*
2×pow2 pow-sqr
1×distribute-rgt-in pow-to-exp clear-num associate-/r* frac-2neg distribute-lft-in pow3 associate-*l/ pow-exp
Counts
4 → 188
Calls
4 calls:
Slowest
2.5s
(* (sqrt (/ 1 PI)) (+ (* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
39.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
34.0ms
(* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7)))
18.0ms
(* (* (fabs x) (fabs x)) (fabs x))

series670.0ms

Counts
4 → 12
Calls
4 calls:
Slowest
427.0ms
(* (sqrt (/ 1 PI)) (+ (* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
168.0ms
(* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7)))
48.0ms
(/ 1/2 (* (* (fabs x) (fabs x)) (fabs x)))
27.0ms
(* (* (fabs x) (fabs x)) (fabs x))

simplify37.7s

Counts
192 → 200
Calls
192 calls:
Slowest
1.6s
(* (* (* (sqrt (/ 1 PI)) (sqrt (/ 1 PI))) (sqrt (/ 1 PI))) (* (* (+ (* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))) (+ (* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))) (+ (* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))))
813.0ms
(* (pow (fabs x) 7) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (pow (fabs x) 5)) (fabs x)))
733.0ms
(* (sqrt PI) (* (pow (fabs x) 7) (* (- (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (fabs x))))
714.0ms
(cbrt (+ (* (sqrt 15/8) (/ (sqrt 15/8) (pow (fabs x) 7))) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))
641.0ms
(* (sqrt 1) (+ (* (* (sqrt 15/8) (sqrt 15/8)) (+ (* (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5)))) (- (* (/ 1 (fabs x)) (/ 1 (fabs x))) (* (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x)))))) (* (pow (fabs x) 7) (+ (pow (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) 3) (pow (/ 1 (fabs x)) 3)))))

prune4.0s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 0.1b

regimes279.0ms

bsearch10.0ms

end0.0ms