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: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

sample1.9m (42.3%)

Algorithm
100×intervals
Results
47.8s15984×body10240exit
19.0s452097×body80valid
14.5s30706×body1280valid
6.8s23639×body640valid
2.9s3056×body1280nan
2.9s69417×body80nan
2.3s12077×body320valid
1.8s2583×body640nan
1.2s10075×body160valid
680.0ms49536×pre80true
668.0ms1301×body320nan
357.0ms1539×body2560valid
212.0ms660×body160nan
136.0ms568×body5120valid

prune1.1m (24.6%)

series59.8s (22.2%)

Calls

448 calls:

1.9s
(/ (* (- (* (+ (+ 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))))
1.9s
(/ (* (* (- (* (+ (+ 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))))
1.0s
(* 6.0 (pow (/ 1 (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0)))) 0.5))
1.0s
(/ 1 (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0))))
962.0ms
(/ 1.0 (* 6.0 (pow (/ 1 (* (pow -1 1.0) (* (pow -2.0 1.0) (pow (log (/ 1 u1)) 1.0)))) 0.5)))

simplify13.9s (5.1%)

Algorithm
253×egg-herbie

rewrite6.4s (2.4%)

Algorithm
153×rewrite-expression-head
Calls

448 calls:

444.0ms
(* (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (* (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0)))) (/ (/ (/ 1 (+ (+ alpha beta) (* 2.0 1.0))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (cbrt (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))))
366.0ms
(* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
180.0ms
(* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
157.0ms
(* (* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 0.5))) (exp (- (+ (+ (- z 1.0) 7.0) 0.5)))) (+ (+ (+ (+ (+ (+ (+ (+ 0.9999999999998099 (/ 676.5203681218851 (* 1 z))) (/ -1259.1392167224028 (+ (- z 1.0) 2.0))) (/ 771.3234287776531 (+ (- z 1.0) 3.0))) (/ -176.6150291621406 (+ (- z 1.0) 4.0))) (/ 12.507343278686905 (+ (- z 1.0) 5.0))) (/ -0.13857109526572012 (+ (- z 1.0) 6.0))) (/ 9.984369578019572e-06 (+ (- z 1.0) 7.0))) (/ 1.5056327351493116e-07 (+ (- z 1.0) 8.0))))
135.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* (+ (fma 1.875 (pow (fabs x) (- 6)) (* 0.75 (/ 1 (pow (fabs x) 4)))) 1) 1.0) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
Rules
8073×times-frac
7708×*-un-lft-identity
7261×add-sqr-sqrt
5446×add-cube-cbrt
3946×add-exp-log
2031×add-cbrt-cube
1866×prod-exp
1721×associate-*r*
1520×pow1
1519×sqrt-prod
1442×prod-diff
1202×associate-*l*
1050×div-exp
1011×distribute-lft-out
737×unpow-prod-down
728×cbrt-unprod
707×cbrt-prod
684×add-log-exp
620×pow-exp
522×pow-prod-down
519×unswap-sqr
500×associate-/r*
494×associate-/l*
449×log1p-expm1-u
448×expm1-log1p-u
432×frac-add
427×associate-/r/
415×flip-+ flip3-+
409×cbrt-undiv
388×div-inv
369×distribute-rgt-in distribute-lft-in
344×pow-to-exp
318×associate-*r/
273×1-exp
241×frac-times
219×fma-neg
214×rec-exp
207×difference-of-squares
192×log-pow
186×associate-*l/
177×sqr-pow
169×distribute-lft-out--
165×cube-prod
149×sqrt-pow1
146×sqrt-div log-prod
145×cbrt-div
140×*-commutative associate--l+ flip3-- flip--
134×fma-def
133×exp-sum
88×frac-2neg clear-num
85×pow1/3
84×sub-neg
82×diff-log
81×swap-sqr
78×pow1/2
75×associate-/l/
69×associate--r+
62×pow-unpow
57×fma-udef associate-+l-
56×exp-prod
53×exp-neg pow-sub
52×sum-log
43×exp-diff
42×distribute-rgt-neg-in distribute-lft-neg-in
37×neg-sub0
34×pow-prod-up
31×rem-sqrt-square
28×pow-sqr frac-sub
27×unpow3 cube-mult
22×+-commutative
21×un-div-inv pow-flip
20×neg-mul-1
18×associate-+l+
17×pow-pow
16×div-sub hypot-def
15×rem-exp-log rem-log-exp
14×inv-pow
13×associate--l- pow2 pow-plus log-div
10×rem-cube-cbrt unpow2
9×cube-div
8×neg-log
6×distribute-neg-in
5×sqrt-unprod hypot-udef
4×pow-div sin-sum associate-+r+
3×unpow-prod-up distribute-rgt-neg-out
2×expm1-log1p expm1-udef
1×sqrt-undiv sqrt-pow2 e-exp-1 distribute-lft-neg-out log1p-udef log1p-expm1 unsub-neg rem-square-sqrt distribute-frac-neg cos-sum associate--r- rem-cbrt-cube

regimes5.0s (1.9%)

Accuracy

Total 45.5b remaining (41.1%)

Threshold costs 5.0b (4.5%)

9.9b16.4%_divideComplex, imaginary part
7.4b36.9%_divideComplex, real part
5.5b15.6%Octave 3.8, jcobi/2
4.4b24.6%math.sqrt on complex, imaginary part, im greater than 0 branch
4.1b30.2%math.sqrt on complex, real part

localize2.8s (1.0%)

bsearch1.3s (0.5%)

end1.0ms (0.0%)