Details

prune15.3m (45.2%)

rewrite12.8m (37.8%)

Algorithm
153×rewrite-expression-head
Calls

446 calls:

15.4s
(* (/ (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) x)
9.3s
(/ (sqrt (+ (+ (+ (+ (+ 1.0 (* 0.1049934947 (* x x))) (* 0.0424060604 (* (* x x) (* x x)))) (* 0.0072644182 (* (* (* x x) (* x x)) (* x x)))) (* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0001789971 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x))))) (* (cbrt (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x))))) (cbrt (+ (+ (+ (+ (+ (+ 1.0 (* 0.7715471019 (* x x))) (* 0.2909738639 (* (* x x) (* x x)))) (* 0.0694555761 (* (* (* x x) (* x x)) (* x x)))) (* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))) (* 0.0008327945 (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)))) (* (* 2.0 0.0001789971) (* (* (* (* (* (* x x) (* x x)) (* x x)) (* x x)) (* x x)) (* x x)))))))
9.1s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
9.1s
(cbrt (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))
8.9s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
Rules
129854×times-frac
82324×*-un-lft-identity
58354×add-sqr-sqrt
45506×add-cube-cbrt
17422×distribute-lft-out
6465×difference-of-squares
4764×sqrt-prod
3458×div-inv
2990×distribute-lft-out--
2776×add-exp-log
2555×associate-/r/
2062×add-cbrt-cube
1808×prod-diff
1518×pow1
1246×associate-/l*
1025×prod-exp
931×associate-*l*
859×unpow-prod-down
745×cube-prod
716×div-exp
699×flip3-- flip--
686×cbrt-unprod
678×associate-*r*
640×add-log-exp
558×associate-/r*
480×pow-prod-down
455×flip-+ flip3-+
444×log1p-expm1-u
443×expm1-log1p-u
441×cbrt-undiv
409×cbrt-prod
235×fma-neg
229×log-pow
211×unswap-sqr
191×associate-*r/
184×associate--l+
178×exp-sum
173×distribute-rgt-in distribute-lft-in
153×sqrt-div
150×1-exp
145×sqr-pow
137×fma-def
132×cube-mult
129×cbrt-div
125×sqrt-pow1
122×log-prod
120×*-commutative
108×associate-*l/
106×pow1/3
104×associate-/l/
103×swap-sqr
98×frac-2neg clear-num
92×frac-times
88×sub-neg
86×pow-exp
84×unpow3
83×rec-exp
82×diff-log
73×pow1/2 pow-unpow
59×distribute-rgt-neg-in pow-to-exp
57×distribute-lft-neg-in
50×fma-udef
48×sum-cubes
47×pow-prod-up
38×exp-prod
35×pow-sqr
33×neg-mul-1
30×cube-div sum-log
29×rem-sqrt-square
23×pow-pow
22×pow-plus div-sub
20×+-commutative
19×associate--l-
18×pow2
16×pow-flip hypot-def
15×rem-cube-cbrt
14×inv-pow
un-div-inv
log-div
frac-sub associate--r+ rem-log-exp
exp-diff
rem-exp-log associate-+l+ sqrt-unprod sin-sum cos-sum unpow2
associate-+l-
frac-add expm1-log1p associate-+r+ rem-square-sqrt neg-sub0 neg-log distribute-rgt-neg-out expm1-udef
sqrt-undiv difference-cubes sqrt-pow2 log1p-udef pow3 log1p-expm1 hypot-udef rem-cbrt-cube

sample2.2m (6.6%)

Algorithm
99×intervals
Results
48.7s12168×body10240exit
38.5s488902×body80valid
13.4s27440×body1280valid
6.2s21142×body640valid
3.3s70021×body80nan
2.5s1615×body1280nan
2.0s10504×body320valid
1.7s9271×body160valid
1.4s1299×body640nan
720.0ms49536×pre80true
515.0ms647×body320nan
441.0ms1466×body2560valid
175.0ms554×body5120valid
165.0ms307×body160nan

end1.2m (3.6%)

series1.1m (3.2%)

Calls

443 calls:

2.0s
(/ (/ i (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
1.7s
(/ (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
1.7s
(/ (* (* (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (fma i 2.0 (+ alpha beta))) (fma i 2.0 (+ alpha beta))) (fma beta alpha (* i (+ (+ alpha beta) i))))
1.3s
(fma (- (* (pow (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 3) (* (sqrt (pow (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (cbrt (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))) (* (cbrt (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))) (cbrt (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))) 1.421413741) -0.284496736) 0.254829592) 3)) (sqrt (pow (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (cbrt (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))) (* (cbrt (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))) (cbrt (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))) 1.421413741) -0.284496736) 0.254829592) 3))))) (pow (/ 1 (exp (pow (fabs x) 2))) 3) (pow 1.0 3))
1.3s
(fma (- (* (pow (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 3) (pow (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (cbrt (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))) (* (cbrt (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))) (cbrt (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (+ -1.453152027 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))) 1.421413741) -0.284496736) 0.254829592) 3))) (pow (/ 1 (exp (pow (fabs x) 2))) 3) (pow 1.0 3))

bsearch27.7s (1.4%)

simplify26.7s (1.3%)

Algorithm
251×egg-herbie

regimes16.2s (0.8%)

Accuracy

Total 53.3b remaining (49.3%)

Threshold costs 5.7b (5.2%)

9.0b43.7%Octave 3.8, jcobi/4
8.7b31.8%_divideComplex, imaginary part
7.4b7.3%Octave 3.8, jcobi/2
7.3b37.1%_divideComplex, real part
5.9b3.5%math.sqrt on complex, real part

localize2.7s (0.1%)