Details

rewrite19.5m (54.3%)

Algorithm
162×rewrite-expression-head
Calls

512 calls:

3.5m
(* (* (/ 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 (* (sqrt (fabs x)) (fabs x))) (/ (cbrt 1) (sqrt (fabs x)))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))) (/ 1 (fabs x))))))
42.8s
(* (/ (sqrt (+ (* (* (* x x) (* x x)) (+ (* (* (* x x) (* (* x x) (* x x))) 0.0001789971) 0.0424060604)) (+ (* (* x x) (+ (* 0.0005064034 (* (* x x) (* (* x x) (* x x)))) 0.1049934947)) (+ (* 0.0072644182 (* (* x x) (* (* x x) (* x x)))) 1)))) 1) (/ (sqrt (+ (* (* (* x x) (* x x)) (+ (* (* (* x x) (* (* x x) (* x x))) 0.0001789971) 0.0424060604)) (+ (* (* x x) (+ (* 0.0005064034 (* (* x x) (* (* x x) (* x x)))) 0.1049934947)) (+ (* 0.0072644182 (* (* x x) (* (* x x) (* x x)))) 1)))) (+ (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (+ 0.0140005442 (* (* x x) (+ 0.0008327945 (* (* (* x x) 2) 0.0001789971))))) (+ (* (* x x) (+ (* 0.0694555761 (* (* x x) (* x x))) 0.7715471019)) (+ 1 (* 0.2909738639 (* (* x x) (* x x))))))))
41.7s
(* (* d1 (* (* (* (* (* d1 (* d1 d1)) d1) d1) (* d1 d1)) d1)) d1)
35.8s
(- 1 (/ (log (exp (+ (/ (+ (/ 1 (/ (+ 1 (* (fabs x) 0.3275911)) (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741))) -0.284496736) (+ 1 (* (fabs x) 0.3275911))) 0.254829592))) (* (+ 1 (* (fabs x) 0.3275911)) (exp (* (fabs x) (fabs x))))))
34.6s
(- 1 (/ (+ (log (exp (/ (+ (/ 1 (/ (+ 1 (* (fabs x) 0.3275911)) (+ (/ (+ (/ 1.061405429 (+ 1 (* (fabs x) 0.3275911))) -1.453152027) (+ 1 (* (fabs x) 0.3275911))) 1.421413741))) -0.284496736) (+ 1 (* (fabs x) 0.3275911))))) 0.254829592) (* (+ 1 (* (fabs x) 0.3275911)) (exp (* (fabs x) (fabs x))))))
Rules
9095×*-un-lft-identity
8547×times-frac
6069×add-sqr-sqrt
4676×add-cube-cbrt
4606×pow1
4543×add-exp-log
2957×sqrt-prod
2943×frac-times associate-*l/
2829×add-cbrt-cube
2570×cbrt-div
2453×prod-exp
2166×flip-+ flip3-+
2154×pow-prod-up
1918×distribute-lft-out
1600×frac-add
1510×associate-*r/
1325×associate-*r*
1268×associate-*l*
1208×cbrt-unprod
1037×flip3-- flip--
1020×pow-plus
977×add-log-exp
808×div-exp
742×pow-prod-down
653×associate-/r/
538×associate-/l*
515×cbrt-prod
508×insert-posit16
491×cbrt-undiv
440×swap-sqr
382×distribute-lft-out--
371×div-inv
357×unswap-sqr
355×associate-/r*
330×log-pow
284×pow-sqr
273×sqrt-div
271×sum-log
245×pow2
226×pow-exp
214×difference-of-squares
189×associate-/l/
175×pow1/3
167×sqrt-pow1
166×1-exp
156×rec-exp
149×*-commutative
131×pow-to-exp
126×pow1/2
100×unpow-prod-down
94×cube-unmult
86×frac-sub
80×frac-2neg clear-num
71×sub-neg
70×rem-sqrt-square
66×+-commutative exp-prod
65×pow-flip
64×distribute-rgt-in distribute-lft-in
60×inv-pow
51×log-prod
43×diff-log
40×sqr-pow
37×un-div-inv
29×cube-prod
28×log-div
27×pow-unpow pow3
18×associate-+l+ associate-+r+
16×exp-diff div-sub
15×exp-sum
13×pow-pow
12×sum-cubes
11×cube-div
associate-+r-
sin-sum associate--l+ rem-log-exp
pow-sub
associate--r+ rem-exp-log distribute-rgt-out
unpow-prod-up cos-sum distribute-rgt1-in
rem-cube-cbrt distribute-rgt-out-- associate-+l-
remove-posit16 unpow3 cube-mult associate--r-
rem-cbrt-cube
associate--l- sqrt-unprod difference-cubes exp-to-pow rem-square-sqrt count-2

simplify8.0m (22.3%)

sample4.0m (11.2%)

Algorithm
99×intervals
Results
1.4m15594×body10240exit
50.2s436798×body80valid
36.7s29992×body1280valid
17.4s22854×body640valid
8.7s3001×body1280nan
7.5s71455×body80nan
6.0s11914×body320valid
4.2s2456×body640nan
3.0s10239×body160valid
2.4s49536×pre80true
1.8s1237×body320nan
1.3s634×body5120valid
848.0ms1509×body2560valid
589.0ms701×body160nan

prune2.4m (6.6%)

series1.6m (4.5%)

Calls

508 calls:

3.6s
(/ (* (/ (/ (* 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)))
3.2s
(* (* (/ (/ (* 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)))) (/ 1 (- (+ (+ alpha beta) (* 2 i)) (sqrt 1.0))))
3.0s
(* (/ (/ (* 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))))
1.7s
(* (* (/ (* (pow (+ 0.5 (- z -6)) z) (sqrt (* PI 2))) (* (exp (+ 0.5 z)) (pow (+ 0.5 (- z -6)) (- 1 0.5)))) (exp -6)) (+ (+ (+ (/ 9.984369578019572e-06 (+ z 6)) (/ 1.5056327351493116e-07 (+ z 7))) (/ -0.13857109526572012 (+ z 5))) (+ (+ (+ (/ 12.507343278686905 (+ z 4)) 0.9999999999998099) (+ (+ (/ -1259.1392167224028 (+ 1 z)) (/ 676.5203681218851 z)) (/ 771.3234287776531 (+ z 2)))) (/ -176.6150291621406 (+ 3 z)))))
1.5s
(* (sqrt 1/6) (* (sqrt 1/6) (pow (* -2 (log u1)) 0.5)))

regimes13.1s (0.6%)

Accuracy

Total 87.2b remaining (31.5%)

Threshold costs 4.5b (1.6%)

10.1b57.9%math.log/2 on complex, real part
9.7b59%math.log10 on complex, real part
9.4b59.8%math.log/1 on complex, real part
9.1b58.7%math.abs on complex
9.0b56.7%math.sqrt on complex, imaginary part, im greater than 0 branch

localize9.0s (0.4%)

bsearch2.1s (0.1%)

end1.0ms (0.0%)