Date:Tuesday, February 25th, 2020
Commit:7c13946c on findroot
Hostname:warfa with Racket 7.5
Seed:2020056
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:numericsrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
+o rules:numerics

Details

rewrite10.4m (71.7%)

Algorithm
152×rewrite-expression-head
Calls

447 calls:

7.1s
(* (/ (+ (+ (+ (+ (+ 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)
4.1s
(/ (+ (+ (+ (+ (+ 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)))))
1.0s
(* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
1.0s
(* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
505.0ms
(* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5)))
Rules
9887×times-frac
8569×*-un-lft-identity
7150×add-sqr-sqrt
6058×add-cube-cbrt
2740×add-exp-log
2041×add-cbrt-cube
1536×prod-diff
1506×pow1
1442×associate-*l*
1102×prod-exp
1086×distribute-lft-out
875×associate-*r*
801×sqrt-prod
723×cbrt-unprod
709×associate-/l*
652×add-log-exp
624×div-exp
525×associate-/r/
513×pow-prod-down
449×log1p-expm1-u
446×expm1-log1p-u
398×div-inv
390×associate-/r*
388×flip-+ flip3-+
381×cbrt-undiv
302×cbrt-prod
243×difference-of-squares
241×unswap-sqr
238×associate-*r/
235×distribute-rgt-in distribute-lft-in
234×distribute-lft-out--
228×fma-def
226×unpow-prod-down
217×fma-neg
184×sqrt-div
180×log-pow
175×exp-sum
142×flip3-- flip--
140×associate--l+
128×1-exp
125×*-commutative associate-*l/
120×frac-times
114×cube-prod
113×pow-exp
110×sqr-pow
95×log-prod
94×associate-/l/
91×clear-num frac-2neg
89×sub-neg
83×swap-sqr
76×frac-add
75×sqrt-pow1
74×pow-to-exp
71×pow-unpow diff-log associate--r+
68×cbrt-div pow1/3
66×fma-udef
64×rec-exp
51×pow1/2
43×sum-log
37×pow-prod-up
36×exp-prod
35×unpow3 cube-mult
30×+-commutative
27×distribute-rgt-neg-in distribute-lft-neg-in pow-sqr
25×rem-sqrt-square pow-plus
23×neg-mul-1
22×pow-pow
19×div-sub
18×associate-+l+
17×pow2 hypot-udef
15×pow-flip
14×associate--l-
13×inv-pow
12×associate-+r+ hypot-def
11×rem-cube-cbrt
8×rem-exp-log
6×sqrt-unprod unpow2
5×exp-diff un-div-inv log1p-udef log1p-expm1 rem-cbrt-cube distribute-rgt-neg-out associate-+l- rem-log-exp
4×sqrt-undiv sin-sum distribute-neg-in expm1-log1p frac-sub expm1-udef
2×sqrt-pow2 pow3 rem-square-sqrt neg-sub0 neg-log log-div
1×unpow-prod-up pow-sub unsub-neg cos-sum associate--r-

sample1.7m (11.4%)

Algorithm
98×intervals
Results
44.1s11865×body10240exit
17.1s438149×body80valid
11.2s27353×body1280valid
5.2s21229×body640valid
2.5s69933×body80nan
1.7s1629×body1280nan
1.6s10546×body320valid
994.0ms9479×body160valid
987.0ms1344×body640nan
660.0ms49536×pre80true
354.0ms659×body320nan
325.0ms1394×body2560valid
146.0ms593×body5120valid
116.0ms326×body160nan

series1.1m (7.4%)

Calls

445 calls:

2.0s
(/ (* (* (- (* (+ (+ 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))))
1.4s
(fma (- (* (pow (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x)))))) 3) (log1p (expm1 (pow (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 3))))) (pow (/ 1 (exp (pow (fabs x) 2))) 3) (pow 1.0 3))
1.3s
(- 1.0 (* (* (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))))) (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (sqrt (+ 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 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))))) (exp (- (* (fabs x) (fabs x))))))
1.2s
(fma (- (* (pow (* (/ (sqrt 1.0) (sqrt (+ 1.0 (* 0.3275911 (fabs x))))) (/ (sqrt 1.0) (sqrt (+ 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 (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 3))) (pow (/ 1 (exp (pow (fabs x) 2))) 3) (pow 1.0 3))
1.0s
(- 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 (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429))))))))) (exp (- (* (fabs x) (fabs x))))))

prune1.0m (7.1%)

simplify13.8s (1.6%)

Algorithm
248×egg-herbie

regimes4.9s (0.6%)

Accuracy

Total 39.9b remaining (28.4%)

Threshold costs 6.2b (4.4%)

8.1b33.6%_divideComplex, imaginary part
7.4b33.4%_divideComplex, real part
5.9b9.9%Octave 3.8, jcobi/2
4.1b26.8%math.sqrt on complex, imaginary part, im greater than 0 branch
4.0b38%math.sqrt on complex, real part

localize2.4s (0.3%)

bsearch1.0s (0.1%)

end1.0ms (0.0%)