Details

simplify49.5m

Calls

18348 calls:

Slowest
2.0s
(* (* (* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (/ 1 (fabs x)))) (* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (/ 1 (fabs x))))) (* (/ (exp (* (fabs x) (fabs x))) (sqrt PI)) (+ (+ (/ (/ 1/2 (fabs x)) (* (fabs x) (fabs x))) (* (/ (/ (/ 1 (fabs x)) (* (fabs x) (fabs x))) (* (fabs x) (fabs x))) (+ 3/4 (/ 15/8 (* (fabs x) (fabs x)))))) (/ 1 (fabs x)))))
1.9s
(* (* (* (* (sqrt (/ 1 PI)) (sqrt (/ 1 PI))) (sqrt (/ 1 PI))) (* (* (exp (* (fabs x) (fabs x))) (exp (* (fabs x) (fabs x)))) (exp (* (fabs x) (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))))) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))))
1.7s
(* (* (* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x)))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (fabs x))))) (* (sqrt (/ 1 PI)) (exp (* (fabs x) (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))))) (+ (/ 15/8 (pow (fabs x) 7)) (+ (+ (/ 1/2 (* (* (fabs x) (fabs x)) (fabs x))) (/ 3/4 (pow (fabs x) 5))) (/ 1 (fabs x))))))
1.7s
(* (* (* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (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))))) (* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (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)))))) (* (* (sqrt (/ 1 PI)) (exp (* (fabs x) (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))))))
1.6s
(* (* (* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))) (* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))) (* (/ 1 (sqrt PI)) (+ (+ (+ (* 2 (fabs x)) (* (/ 2 3) (* (* (fabs x) (fabs x)) (fabs x)))) (* (/ 1 5) (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (* (/ 1 21) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))))

sample9.2m

Algorithm
88×intervals
Results
6.4m100341×body10240exit
1.1m387340×body80valid
26.2s22306×body1280valid
13.4s17664×body640valid
10.8s70193×body80nan
6.2s1507×body1280nan
5.7s9535×body320valid
4.0s9102×body160valid
3.7s1255×body640nan
2.8s33536×pre80true
2.1s1384×body2560valid
1.9s666×body320nan
890.0ms322×body160nan
613.0ms657×body5120valid

rewrite4.8m

Algorithm
146×rewrite-expression-head
Calls

436 calls:

Slowest
26.3s
(* (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (+ (/ -0.13857109526572012 (- z -5)) (/ 12.507343278686905 (+ z 4))) (+ (+ (/ 771.3234287776531 (+ z 2)) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1))))) (/ -176.6150291621406 (+ z 3))))) (exp (- (+ (- z -6) 0.5))))
19.6s
(* (* (pow (+ (- z -6) 0.5) (- z (- 1 0.5))) (sqrt (* PI 2))) (* (+ (+ (/ 9.984369578019572e-06 (- z -6)) (/ 1.5056327351493116e-07 (+ z 7))) (+ (+ (/ -0.13857109526572012 (- z -5)) (/ 12.507343278686905 (+ z 4))) (+ (+ (/ 771.3234287776531 (+ z 2)) (+ (/ 676.5203681218851 z) (+ 0.9999999999998099 (/ -1259.1392167224028 (- z -1))))) (/ -176.6150291621406 (+ z 3))))) (exp (- (+ (- z -6) 0.5)))))
17.5s
(log (exp (- 1 (/ (/ (+ (/ (+ -0.284496736 (/ (+ (/ (+ -1.453152027 (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911)))) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911)))) (+ 1 (* (fabs x) 0.3275911))) 0.254829592) (+ 1 (* (fabs x) 0.3275911))) (exp (* (fabs x) (fabs x)))))))
17.3s
(log (exp (- 1 (/ (/ (+ (/ (+ -0.284496736 (/ (+ (/ (+ -1.453152027 (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911)))) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911)))) (+ 1 (* (fabs x) 0.3275911))) 0.254829592) (+ 1 (* (fabs x) 0.3275911))) (exp (* (fabs x) (fabs x)))))))
17.1s
(log (exp (- 1 (/ (/ (+ (/ (+ -0.284496736 (/ (+ (/ (+ -1.453152027 (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911)))) (+ 1 (* (fabs x) 0.3275911))) 1.421413741) (+ 1 (* (fabs x) 0.3275911)))) (+ 1 (* (fabs x) 0.3275911))) 0.254829592) (+ 1 (* (fabs x) 0.3275911))) (exp (* (fabs x) (fabs x)))))))
Rules
10832×*-un-lft-identity
8650×times-frac
6006×add-sqr-sqrt
5250×pow1
4128×add-cube-cbrt
3725×add-exp-log
3551×distribute-lft-out
3094×add-cbrt-cube
2864×frac-add
2422×pow-prod-down
2293×prod-exp
1767×cbrt-unprod
1451×associate-*r*
1438×flip-+ flip3-+
1108×pow-prod-up
1080×frac-times
986×associate-*l*
915×sqrt-prod
900×associate-*l/
666×difference-of-squares
639×pow-plus
618×add-log-exp
587×associate-*r/
571×associate-/l*
547×sqrt-pow1
540×associate-/r/
436×insert-posit16
419×cbrt-div
418×cbrt-prod
340×associate-/r*
332×distribute-lft-out--
320×div-inv
317×div-exp
285×cbrt-undiv
252×pow-sqr
251×exp-diff
250×pow-exp
246×exp-neg
245×pow-sub
243×neg-sub0
220×unswap-sqr
218×flip3-- flip--
215×log-pow
186×swap-sqr
181×sqrt-div
178×pow2
151×*-commutative
134×pow1/3
130×pow-to-exp
94×associate-/l/
86×log-prod
84×pow1/2
80×unpow-prod-down
79×exp-prod
76×frac-2neg clear-num
70×sub-neg
52×distribute-rgt-in distribute-lft-in
51×diff-log
48×sum-log
45×sqr-pow
42×cube-unmult
39×rem-sqrt-square
36×+-commutative
33×pow3
26×frac-sub
20×div-sub log-div
16×exp-sum
14×1-exp rec-exp associate--l+
12×rem-log-exp
10×associate--r+
pow-flip
pow-div inv-pow
pow-unpow un-div-inv distribute-rgt-out
associate-+l+ associate--l- distribute-rgt1-in
sin-sum difference-of-sqr-1 pow-pow associate--r-
unpow-prod-up distribute-lft-neg-out sqrt-undiv distribute-lft-neg-in distribute-rgt-neg-in associate-+l-
sqrt-unprod rem-square-sqrt
neg-mul-1 rem-exp-log cos-sum difference-cubes distribute-neg-in rem-cbrt-cube

prune3.4m

series1.6m

Calls

436 calls:

Slowest
4.7s
(* rand (/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0)))))))
4.1s
(/ (- a (/ 1.0 3.0)) (sqrt (* (* 9 (+ (sqrt a) (sqrt (/ 1.0 3.0)))) (- (sqrt a) (sqrt (/ 1.0 3.0))))))
3.2s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2 i))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
3.0s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2 i))) (+ (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))) (/ (/ (+ alpha i) (/ (+ (+ alpha beta) (* 2 i)) (+ i beta))) (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
1.1s
(* (* (pow (* (log u1) -2) 0.5) (pow (* (log u1) -2) 0.5)) (pow (* (log u1) -2) 0.5))

regimes11.2s

Accuracy

Total 100.1b remaining (45.5%)

Threshold costs 3.0b (1.4%)

16.8b44.2%math.log10 on complex, real part
12.6b57.6%math.sqrt on complex, real part
12.3b45%math.log/2 on complex, real part
9.9b51.9%math.sqrt on complex, imaginary part, im greater than 0 branch
9.6b58.4%math.log/1 on complex, real part

bsearch9.1s

localize6.4s

end2.0ms