Details

simplify4.1m (24.2%)

rewrite4.0m (23.6%)

Algorithm
153×rewrite-expression-head
Calls

468 calls:

1.1m
(* (* (sqrt (* PI 2.0)) (/ (pow (- (+ 7.0 (+ z 0.5)) 1.0) (+ (- z 1.0) 0.5)) (exp (- z (- (- 1.0 0.5) 7.0))))) (+ (/ -1259.1392167224028 (+ 2.0 (- z 1.0))) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (+ (/ -0.13857109526572012 (+ 6.0 (- z 1.0))) (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (+ (/ 9.984369578019572e-06 (+ 7.0 (- z 1.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))))))
1.1m
(/ (+ (/ 9.984369578019572e-06 (+ 7.0 (- z))) (+ (+ (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (/ -176.6150291621406 (+ (- z) 4.0)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))))) (exp (+ (+ 0.5 7.0) (- z))))
45.2s
(* (+ (+ (/ -1259.1392167224028 (- (+ 2.0 z) 1.0)) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ 3.0 (- z 1.0))))) (+ (+ (+ (/ 12.507343278686905 (- z (- 1.0 5.0))) (/ 9.984369578019572e-06 (- (+ 7.0 z) 1.0))) (/ 1.5056327351493116e-07 (- z (- 1.0 8.0)))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0)))) (* (pow (+ 7.0 (- (+ z 0.5) 1.0)) (+ 0.5 (- z 1.0))) (sqrt (* PI 2.0))))
19.6s
(/ (* (+ (+ (/ -1259.1392167224028 (- (+ 2.0 z) 1.0)) (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 z)) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 771.3234287776531 (+ 3.0 (- z 1.0))))) (+ (+ (+ (/ 12.507343278686905 (- z (- 1.0 5.0))) (/ 9.984369578019572e-06 (- (+ 7.0 z) 1.0))) (/ 1.5056327351493116e-07 (- z (- 1.0 8.0)))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0)))) (* (pow (+ 7.0 (- (+ z 0.5) 1.0)) (+ 0.5 (- z 1.0))) (sqrt (* PI 2.0)))) (exp (- z (- (- 1.0 0.5) 7.0))))
7.9s
(+ (+ (+ (/ 771.3234287776531 (+ 3.0 (- z))) (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z)))) (+ (/ -1259.1392167224028 (+ (- z) 2.0)) (/ -176.6150291621406 (+ (- z) 4.0)))) (+ (+ (/ -0.13857109526572012 (+ 6.0 (- z))) (/ 12.507343278686905 (+ 5.0 (- z)))) (/ 1.5056327351493116e-07 (+ 8.0 (- z)))))
Rules
27115×times-frac
20594×*-un-lft-identity
14683×add-sqr-sqrt
12811×add-cube-cbrt
5435×sqrt-prod
3822×distribute-lft-out
2376×add-exp-log
1796×frac-add
1704×prod-diff
1648×add-cbrt-cube
1495×associate-/l*
1286×pow1
1017×associate-*r*
954×unpow-prod-down
921×associate-*l*
797×associate-/r*
786×flip-+ flip3-+
776×prod-exp
773×add-log-exp
770×div-inv
737×difference-of-squares
677×associate-/r/
602×div-exp
576×exp-sum
484×log-pow
469×expm1-log1p-u log1p-expm1-u
420×cbrt-unprod distribute-lft-out--
414×distribute-rgt-in distribute-lft-in
395×cbrt-prod
381×cbrt-undiv
359×associate-*l/
350×unswap-sqr
321×pow-exp
289×exp-prod
272×pow-prod-down
263×associate-/l/
261×frac-times
239×sqr-pow
230×sqrt-pow1
208×flip3-- flip--
206×associate-*r/
185×swap-sqr
176×fma-def
175×distribute-rgt-neg-in
163×pow-to-exp
160×sum-log
137×fma-neg
128×log-prod
123×associate-+r-
120×pow-sub
113×sqrt-div
108×*-commutative
104×frac-2neg clear-num
99×cube-prod
97×pow-unpow
96×associate-+r+
81×sub-neg
79×pow1/3
78×cbrt-div
76×1-exp
73×fma-udef
71×pow1/2
70×associate--r+
68×rec-exp
63×associate--l+
44×distribute-lft-neg-in diff-log
41×pow-pow
37×pow-prod-up
35×+-commutative
27×pow-sqr
26×unpow-prod-up
22×pow-flip rem-sqrt-square
20×inv-pow
18×associate-+l+ associate--r-
17×hypot-udef
14×neg-mul-1
13×pow2 unpow3 pow-plus cube-mult
12×rem-cube-cbrt div-sub
11×rem-log-exp
10×sin-sum
9×exp-diff
7×cube-div un-div-inv
6×rem-exp-log cos-sum distribute-neg-in
5×associate--l-
4×distribute-lft-neg-out sqrt-undiv distribute-rgt-neg-out sqrt-unprod unpow2 associate-+l- rem-square-sqrt log-div
3×frac-sub unpow1/3
2×neg-sub0 expm1-log1p expm1-udef log1p-expm1 log1p-udef hypot-def unsub-neg
1×neg-log sqrt-pow2

sample3.7m (21.9%)

Algorithm
100×intervals
Results
1.1m16026×body10240exit
53.0s447618×body80valid
29.7s30265×body1280valid
14.4s23103×body640valid
6.7s70594×body80nan
6.6s11982×body320valid
6.0s3149×body1280nan
4.1s10065×body160valid
3.1s2647×body640nan
2.2s49536×pre80true
1.4s1463×body2560valid
1.3s1309×body320nan
411.0ms664×body160nan
392.0ms615×body5120valid

prune3.2m (19.1%)

series1.5m (8.7%)

Calls

468 calls:

3.1s
(* (/ (/ (fma i (+ i (+ alpha beta)) (* beta alpha)) (+ (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (fma i 2.0 (+ alpha beta))) (* (/ (+ i (+ alpha beta)) (- (fma i 2.0 (+ alpha beta)) (sqrt 1.0))) (/ i (fma i 2.0 (+ alpha beta)))))
2.2s
(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)
1.5s
(* (pow (* (pow -1 1.0) (pow -2.0 1.0)) 0.5) (pow (pow (- (log u1)) 1.0) 0.5))
1.3s
(- (fma (/ (exp (- (pow (fabs x) 2))) (pow (fma 0.3275911 (fabs x) 1.0) 4)) 1.453152027 (fma (/ (exp (- (pow (fabs x) 2))) (pow (fma 0.3275911 (fabs x) 1.0) 2)) 0.284496736 1.0)) (fma 1.061405429 (/ (exp (- (pow (fabs x) 2))) (pow (fma 0.3275911 (fabs x) 1.0) 5)) (fma (/ (exp (- (pow (fabs x) 2))) (fma 0.3275911 (fabs x) 1.0)) 0.254829592 (/ (* 1.421413741 (exp (- (pow (fabs x) 2)))) (pow (fma 0.3275911 (fabs x) 1.0) 3)))))
1.3s
(- 1.0 (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 0.254829592 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -0.284496736 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ 1.421413741 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (log (exp (/ 1.0 (fma (fabs x) 0.3275911 1.0)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

regimes13.3s (1.3%)

Accuracy

Total 46.0b remaining (38.3%)

Threshold costs 5.7b (4.7%)

10.0b30.9%_divideComplex, real part
7.6b-13%Octave 3.8, jcobi/2
7.4b32.6%_divideComplex, imaginary part
4.0b20%powComplex, real part
3.3b73.2%Octave 3.8, jcobi/1

localize10.0s (1.0%)

bsearch1.6s (0.2%)

end1.0ms (0.0%)