Date:Wednesday, March 4th, 2020
Commit:29625745 on findroot
Hostname:warfa with Racket 7.5
Seed:2020064
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

series3.6m (45.0%)

Calls

489 calls:

2.4m
(- (pow (pow 1.0 3) 3) (pow (* (sqrt (pow (* (* (/ 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))))) 3)) (sqrt (pow (* (* (/ 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))))) 3))) 3))
3.3s
(- (pow 1.0 3) (* (sqrt (pow (* (* (/ 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))))) 3)) (sqrt (pow (* (* (/ 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))))) 3))))
3.2s
(- (pow 1.0 3) (pow (* (* (/ 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))))) 3))
2.2s
(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))))
2.2s
(* (/ (/ (* 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))))

sample1.9m (23.5%)

Algorithm
100×intervals
Results
47.7s15984×body10240exit
18.8s452097×body80valid
14.1s30706×body1280valid
6.8s23639×body640valid
2.8s3056×body1280nan
2.5s69417×body80nan
2.3s12077×body320valid
1.7s2583×body640nan
1.1s10075×body160valid
653.0ms49536×pre80true
631.0ms1301×body320nan
348.0ms1539×body2560valid
210.0ms660×body160nan
137.0ms568×body5120valid

prune1.7m (21.0%)

simplify19.5s (4.1%)

Algorithm
261×egg-herbie

rewrite18.6s (3.9%)

Algorithm
161×rewrite-expression-head
Calls

489 calls:

9.3s
(* (/ (/ i (/ (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (/ (sqrt (+ (* beta alpha) (* i (+ (+ alpha beta) i)))) (+ (+ alpha beta) (* 2.0 i))))))
746.0ms
(* (/ (/ (* (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))) (/ (/ (/ (cbrt (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
274.0ms
(* (/ (/ (* 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))))
178.0ms
(* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
176.0ms
(* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
Rules
48198×times-frac
28531×add-sqr-sqrt
27214×*-un-lft-identity
19307×add-cube-cbrt
11701×sqrt-prod
5425×associate-*r*
3634×difference-of-squares
3438×add-exp-log
2519×add-cbrt-cube
2096×distribute-lft-out
1909×distribute-lft-out--
1863×pow1
1853×associate-*l*
1641×associate-/r/
1565×cbrt-prod
1375×div-inv
1358×prod-exp
1201×flip-+ flip3-+
939×cbrt-unprod
849×div-exp
778×add-log-exp
730×associate-/l*
683×associate-/r*
635×unswap-sqr
624×pow-prod-down
576×unpow-prod-down frac-times
562×cbrt-undiv
478×frac-add
470×associate-*r/
354×associate-*l/
332×swap-sqr
291×sqrt-div
261×pow-exp
246×cbrt-div
228×log-pow
189×sqr-pow
168×flip3-- flip--
163×*-commutative
137×exp-neg
134×pow-to-exp
127×pow1/3
118×sqrt-pow1
115×cube-div pow-unpow
114×cube-prod
111×log-prod
109×neg-sub0
108×exp-diff
103×associate-/l/
102×pow1/2
101×1-exp
89×diff-log
81×clear-num frac-2neg
76×sum-log
71×sub-neg
69×distribute-rgt-in distribute-lft-in
65×rec-exp
64×rem-sqrt-square
59×associate-+l-
54×pow-prod-up
53×pow-sub
44×pow-sqr
43×pow-pow
42×pow-plus
41×un-div-inv
40×distribute-neg-frac
36×+-commutative exp-prod
34×pow2 associate--l+
30×rem-cube-cbrt
23×unpow3 cube-mult
21×distribute-rgt-neg-in distribute-lft-neg-in
15×unpow2
14×div-sub
13×associate--l-
12×associate-+l+
11×rem-exp-log rem-log-exp
10×associate-+r+
8×inv-pow pow-flip neg-log
6×sin-sum distribute-neg-in associate--r+
5×neg-mul-1 log-div
4×frac-sub
3×cos-sum difference-cubes sqrt-pow2 unpow-prod-up exp-sum
2×pow3 associate-+r- distribute-rgt-neg-out
1×e-exp-1 sqrt-unprod associate--r- rem-cbrt-cube

regimes7.5s (1.6%)

Accuracy

Total 95.9b remaining (36.8%)

Threshold costs 4.2b (1.6%)

17.0b50.9%math.sqrt on complex, imaginary part, im greater than 0 branch
10.3b57.4%math.log/2 on complex, real part
10.1b58.7%math.log10 on complex, real part
10.0b59.1%math.log/1 on complex, real part
9.8b58.5%math.abs on complex

localize2.8s (0.6%)

bsearch1.8s (0.4%)

end1.0ms (0.0%)