Details

rewrite14.7m (42.3%)

Algorithm
153×rewrite-expression-head
Calls

446 calls:

3.5m
(* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp (+ (+ (- z 1.0) 7.0) 0.5))) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))
2.0m
(* (* (/ (cbrt (* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5))) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (* (* PI 2.0) (sqrt (* PI 2.0))))) (exp z)) (exp (- (- 1.0 7.0) 0.5))) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))
2.0m
(* (* (/ (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)) (sqrt (* PI 2.0))) (exp z)) (exp (- (- 1.0 7.0) 0.5))) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))
53.6s
(* (* (/ 1.0 (sqrt PI)) (exp (* (fabs x) (fabs x)))) (+ (+ (+ (/ 1.0 (fabs x)) (* (/ 1.0 2.0) (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 3.0 4.0) (* (* (* (* (/ 1.0 (fabs x)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))) (* (/ 15.0 8.0) (* (* (* (* (* (/ 1.0 (pow (fabs x) 2)) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))) (/ 1.0 (fabs x))))))
35.4s
(+ (+ (/ 1.5056327351493116e-07 (+ (- z) 8.0)) (/ 12.507343278686905 (+ 5.0 (- z)))) (+ (/ -1259.1392167224028 (+ 2.0 (- z))) (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (- 1.0 z))) (/ -176.6150291621406 (+ (- z) 4.0))) (/ 771.3234287776531 (+ 3.0 (- z)))) (+ (/ 9.984369578019572e-06 (+ (- z) 7.0)) (/ -0.13857109526572012 (+ 6.0 (- z)))))))
Rules
1655357×frac-times
1295974×associate-*l/
876704×associate-*r/
789555×frac-add
20212×times-frac
18270×flip-+ flip3-+
16088×*-un-lft-identity
12621×add-sqr-sqrt
10190×add-cube-cbrt
5339×sqrt-prod
3259×distribute-rgt-neg-in
3241×distribute-lft-neg-in
2845×distribute-lft-out
2075×add-exp-log
1640×add-cbrt-cube
1396×associate-*l*
1250×pow1
1114×prod-diff
1074×associate-*r*
802×associate-/l*
736×add-log-exp
689×div-inv
639×prod-exp
621×difference-of-squares
493×div-exp
475×exp-diff
466×neg-mul-1
461×associate-/r*
447×log1p-expm1-u
446×expm1-log1p-u
429×cbrt-unprod
369×distribute-lft-out--
356×cbrt-prod
348×cbrt-undiv
333×unswap-sqr
298×unpow-prod-down
292×associate-/r/
285×pow-prod-down
242×swap-sqr
215×fma-def
184×cube-prod
163×sum-log
153×fma-neg
151×exp-sum
148×log-pow
133×*-commutative
128×distribute-rgt-in distribute-lft-in
119×flip3-- flip--
111×sqrt-pow1
96×pow1/3 sqrt-div
92×clear-num frac-2neg
91×sqr-pow pow-exp
89×associate-/l/
78×log-prod
75×fma-udef
71×pow1/2
70×associate--r+
68×pow-unpow
64×pow-prod-up
61×pow-to-exp cbrt-div
59×associate--l+
56×exp-prod sub-neg
46×associate-+l+
45×pow-sqr
41×rec-exp 1-exp diff-log
29×pow-plus
28×rem-sqrt-square
27×unpow3 cube-mult
25×pow2
23×+-commutative
21×pow-pow
17×div-sub
13×rem-cube-cbrt
12×associate-+l-
11×frac-sub
rem-log-exp log-div
cos-sum distribute-neg-frac
cube-div unpow-prod-up sqrt-undiv
log1p-udef sqrt-unprod log1p-expm1 expm1-log1p pow-flip expm1-udef associate--l-
rem-exp-log un-div-inv sin-sum distribute-neg-in pow-sub associate-+r+ rem-square-sqrt
inv-pow unpow2 hypot-udef distribute-frac-neg distribute-rgt-neg-out rem-cbrt-cube
sqrt-pow2 distribute-lft-neg-out neg-sub0 hypot-def associate--r-
pow3 distribute-rgt-out

simplify9.4m (27.2%)

prune5.2m (14.9%)

sample3.6m (10.3%)

Algorithm
98×intervals
Results
1.2m12136×body10240exit
50.4s437645×body80valid
27.3s26654×body1280valid
12.9s21309×body640valid
6.5s68580×body80nan
4.6s1635×body1280nan
3.9s10483×body320valid
3.3s9401×body160valid
2.4s1328×body640nan
2.3s49536×pre80true
849.0ms1515×body2560valid
759.0ms660×body320nan
664.0ms315×body160nan
318.0ms599×body5120valid

series1.6m (4.6%)

Calls

444 calls:

3.7s
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta)))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0)))
3.6s
(* (/ (/ (* i (+ (+ alpha beta) i)) (fma 2.0 i (+ alpha beta))) (+ (+ alpha beta) (fma i 2.0 (sqrt 1.0)))) (/ (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma 2.0 i (+ alpha beta))) (- (fma 2.0 i (+ alpha beta)) (sqrt 1.0))))
1.6s
(/ (/ (* (* i (+ (+ alpha beta) i)) (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i)))) (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0))
1.4s
(* (/ 1.0 6.0) (pow (* -2.0 (log u1)) 0.5))
1.3s
(* (* (/ (cbrt (* (* (pow (+ (+ (- z 1.0) 7.0) 0.5) (* 2 (+ (- z 1.0) 0.5))) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (* (* PI 2.0) (sqrt (* PI 2.0))))) (exp z)) (exp (- (- 1.0 7.0) 0.5))) (+ (+ (+ (/ 12.507343278686905 (+ (- z 1.0) 5.0)) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (+ (+ (+ (/ -1259.1392167224028 (+ (- z 1.0) 2.0)) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (+ (/ 676.5203681218851 z) 0.9999999999998099))) (+ (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0)) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0)))))

regimes8.0s (0.4%)

Accuracy

Total 31.8b remaining (23.2%)

Threshold costs 5.5b (4%)

10.2b25.7%_divideComplex, imaginary part
7.7b32.2%_divideComplex, real part
3.0b77.3%Octave 3.8, jcobi/1
2.3b39.9%Octave 3.8, jcobi/4
2.1b18.6%Octave 3.8, jcobi/3

localize5.0s (0.2%)

bsearch1.0s (0.0%)

end1.0ms (0.0%)