Details

rewrite12.3m (46.2%)

Algorithm
155×rewrite-expression-head
Calls

481 calls:

1.0m
(/ (+ (/ 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))))
7.7s
(+ (+ (+ (/ 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)))))
6.5s
(* (/ (+ (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (fma (* x x) 0.0001789971 0.0005064034)) (fma (* 0.0072644182 (* x x)) (* (* x x) (* x x)) (fma (* (* x x) (* x x)) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))) (fma (* 2.0 0.0001789971) (* (* (* x x) (* (* x x) (* x x))) (* (* x x) (* (* x x) (* x x)))) (fma (* (* x x) (* (* x x) (* x x))) (+ (* 0.0008327945 (* (* x x) (* x x))) (* (* x x) 0.0140005442)) (fma (* (* x x) (* (* x x) (* x x))) 0.0694555761 (fma 0.2909738639 (* (* x x) (* x x)) (fma (* x x) 0.7715471019 1.0)))))) x)
6.2s
(* (/ (+ (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (fma (* x x) 0.0001789971 0.0005064034)) (fma (* (* x x) 0.0072644182) (* (* x x) (* x x)) (fma (* (* x x) (* x x)) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))) (fma (* 2.0 0.0001789971) (* (* (* x x) (* (* x x) (* x x))) (* (* x x) (* (* x x) (* x x)))) (fma (* (* x x) (* (* x x) (* x x))) (+ (* 0.0008327945 (* (* x x) (* x x))) (* (* x x) 0.0140005442)) (fma (* (* x x) (* (* x x) (* x x))) 0.0694555761 (fma 0.2909738639 (* (* x x) (* x x)) (fma (* x x) 0.7715471019 1.0)))))) (sqrt x))
6.1s
(* (* (/ (+ (* (* (* (* x x) (* x x)) (* (* x x) (* x x))) (fma (* x x) 0.0001789971 0.0005064034)) (fma (* (* x x) 0.0072644182) (* (* x x) (* x x)) (fma (* (* x x) (* x x)) 0.0424060604 (fma 0.1049934947 (* x x) 1.0)))) (fma (* 2.0 0.0001789971) (* (* (* x x) (* (* x x) (* x x))) (* (* x x) (* (* x x) (* x x)))) (fma (* (* x x) (* (* x x) (* x x))) (+ (* 0.0008327945 (* (* x x) (* x x))) (* (* x x) 0.0140005442)) (fma (* (* x x) (* (* x x) (* x x))) 0.0694555761 (fma 0.2909738639 (* (* x x) (* x x)) (fma (* x x) 0.7715471019 1.0)))))) (sqrt x)) (sqrt x))
Rules
24042×times-frac
20271×*-un-lft-identity
13356×add-sqr-sqrt
11784×add-cube-cbrt
6733×sqrt-prod
4109×distribute-lft-out
3764×add-exp-log
3036×pow1
2686×add-cbrt-cube
1615×associate-*l*
1534×prod-exp
1417×prod-diff
1408×associate-/l*
1195×associate-*r*
1138×pow-prod-up
1039×div-exp
970×cbrt-unprod
746×add-log-exp
637×cbrt-undiv
624×frac-add
622×pow-plus
613×div-inv
554×distribute-rgt-in distribute-lft-in
497×flip-+ flip3-+
478×expm1-log1p-u log1p-expm1-u
474×swap-sqr
470×log-pow
448×pow-prod-down
445×associate-/r*
397×difference-of-squares
371×distribute-lft-out--
366×associate-*l/
356×cbrt-prod
353×associate-/r/
309×unswap-sqr
282×exp-prod
273×pow-exp
263×distribute-rgt-neg-in
256×frac-times
242×associate-*r/
232×sqrt-pow1
211×pow-sqr
207×flip3-- flip--
191×exp-sum
183×pow2
166×associate-/l/
162×fma-def
157×unpow-prod-down
156×*-commutative
152×fma-neg
144×log-prod
133×pow-to-exp
131×sum-log
127×associate-+l+
125×associate--l+
115×sqrt-div
113×1-exp rec-exp
108×cbrt-div
100×associate-+r+
94×pow1/3
90×pow1/2
86×frac-2neg clear-num sub-neg
70×associate--r+
61×sqr-pow
60×fma-udef
56×cube-unmult
50×cube-prod
46×diff-log
30×+-commutative
29×rem-sqrt-square
23×div-sub
22×frac-sub cos-sum
21×pow-unpow
17×hypot-udef distribute-rgt-out
16×pow3 un-div-inv
15×distribute-rgt1-in
11×hypot-def
9×pow-pow rem-log-exp
8×distribute-lft-neg-in
7×pow-flip sin-sum
6×rem-cube-cbrt exp-diff sqrt-unprod rem-square-sqrt cube-div
4×sqrt-undiv unpow3 associate--l- cube-mult inv-pow
3×associate-+r-
2×expm1-log1p expm1-udef neg-mul-1 associate--r-
1×distribute-lft1-in distribute-rgt-out-- neg-sub0 associate-+l- rem-cbrt-cube unsub-neg count-2 log-div

simplify6.0m (22.4%)

sample3.5m (13.0%)

Algorithm
99×intervals
Results
1.1m12082×body10240exit
51.6s447271×body80valid
26.5s26848×body1280valid
11.9s20636×body640valid
8.2s70273×body80nan
4.4s1658×body1280nan
4.1s10752×body320valid
2.7s1329×body640nan
2.5s9427×body160valid
1.8s49536×pre80true
1.2s667×body320nan
896.0ms1463×body2560valid
502.0ms339×body160nan
316.0ms615×body5120valid

prune2.8m (10.6%)

series1.7m (6.3%)

Calls

478 calls:

3.4s
(/ (* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.4s
(/ (* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i)))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))
3.3s
(* (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (+ (* beta alpha) (* i (+ (+ alpha beta) i))) (+ (+ alpha beta) (* 2.0 i))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
1.8s
(pow (* (* (pow -1 1.0) (pow -2.0 1.0)) (pow (- (log u1)) 1.0)) 0.5)
1.7s
(* (pow (* (pow -1 1.0) (pow -2.0 1.0)) 0.5) (pow (pow (- (log u1)) 1.0) 0.5))

regimes12.9s (0.8%)

Accuracy

Total 32.2b remaining (27.9%)

Threshold costs 5.9b (5.1%)

9.5b41%Octave 3.8, jcobi/4
7.6b30.6%_divideComplex, imaginary part
3.3b73%Octave 3.8, jcobi/1
3.0b0%_divideComplex, real part
1.6b0%Jmat.Real.lambertw, newton loop step

localize10.1s (0.6%)

bsearch1.2s (0.1%)

end2.0ms (0.0%)