Date:Wednesday, February 26th, 2020
Commit:2c6cda94 on refactor-and-minor
Hostname:warfa with Racket 7.5
Seed:2020057
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

series10.9m (44.4%)

Calls

492 calls:

20.0s
(- (pow 1.0 3) (/ (pow (* (* (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (- (* 0.254829592 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))))))) (* (/ 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) (pow (- 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)))))))) 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))
2.7s
(* (sqrt (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (* (sqrt (/ (/ (* 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)))))
2.7s
(/ (* (sqrt (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i)))) (* (sqrt (/ (/ (* 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))))) (* (sqrt (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))))
2.4s
(* (/ (/ (* 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))))

rewrite10.5m (42.6%)

Algorithm
162×rewrite-expression-head
Calls

496 calls:

6.8s
(* (/ (+ (+ (+ (+ (+ 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)
3.9s
(/ (+ (+ (+ (+ (+ 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)))))
1.4s
(/ (* (+ (+ (/ (* (+ (* 3.0 (* (fabs x) (fabs x))) (* 4.0 (* (* 1.0 1.0) (/ 15.0 8.0)))) (pow 1.0 3)) (* (* (* (pow (fabs x) 4) (fabs x)) (pow (fabs x) 2)) 4.0)) (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3)))) (/ 1.0 (fabs x))) 1.0) (/ (sqrt PI) (exp (* (fabs x) (fabs x)))))
799.0ms
(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (+ (* (* x x) (+ 0.7715471019 (* 0.2909738639 (* x x)))) 1.0)) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (+ 1.0 (* 0.1049934947 (* x x)))) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))
592.0ms
(* (sqrt (/ (/ (* i (+ (+ alpha beta) i)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (* (sqrt (/ (/ (* 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)))))
Rules
15300×times-frac
10747×*-un-lft-identity
9433×add-sqr-sqrt
7395×add-cube-cbrt
3052×add-exp-log
2789×pow1
2509×sqrt-prod
2192×add-cbrt-cube
1884×distribute-rgt-neg-in distribute-lft-neg-in
1454×distribute-lft-out
1365×log-pow
1361×associate-*r*
1272×prod-exp
966×associate-/l*
898×flip-+ flip3-+
863×associate-*l*
798×add-log-exp
770×cbrt-unprod
758×difference-of-squares
709×associate-/r/
643×unpow-prod-down
632×associate-*r/
621×frac-times
617×associate-/r*
612×div-exp
608×pow-prod-down
526×div-inv
477×cube-prod
400×sqr-pow
372×cbrt-undiv
354×associate-*l/
345×cbrt-prod
329×distribute-lft-out--
314×neg-mul-1
294×sqrt-pow1
279×sqrt-div
278×cbrt-div
257×pow1/2
244×unswap-sqr
216×frac-add
213×pow1/3
178×flip3-- flip--
155×swap-sqr pow-exp
148×*-commutative
136×associate-/l/
125×distribute-lft1-in distribute-rgt-out
122×distribute-rgt-in distribute-lft-in
118×pow-prod-up
111×sub-neg
109×pow-to-exp
100×clear-num frac-2neg
99×diff-log
88×log-prod
79×pow-sqr
72×pow-plus
65×sum-log
57×exp-prod
55×distribute-neg-frac
53×rem-sqrt-square
52×associate--l+
50×distribute-rgt1-in count-2 1-exp
48×rec-exp
45×+-commutative div-sub
43×pow-unpow
39×exp-diff pow2
38×log-div
34×unpow3 cube-mult
32×pow-pow
29×exp-neg
27×neg-sub0
26×cube-div
20×rem-cube-cbrt associate-+l+
17×unpow2
16×associate--l-
14×exp-sum associate--r+
13×difference-cubes associate-+r+
11×un-div-inv inv-pow pow-flip
8×rem-exp-log frac-sub
6×pow3 sum-cubes
5×distribute-neg-in rem-log-exp
4×neg-log sin-sum cos-sum
3×distribute-frac-neg associate-+l-
2×distribute-rgt-neg-out exp-to-pow
1×unpow1/3 associate-+r- distribute-rgt-out-- unpow-prod-up pow-sub associate--r-

sample1.7m (6.9%)

Algorithm
98×intervals
Results
43.2s11974×body10240exit
21.3s490521×body80valid
11.2s27113×body1280valid
5.0s20737×body640valid
2.5s69825×body80nan
1.7s1594×body1280nan
1.6s10710×body320valid
947.0ms1325×body640nan
656.0ms49536×pre80true
591.0ms5710×body160valid
380.0ms1532×body2560valid
332.0ms648×body320nan
126.0ms540×body5120valid
115.0ms342×body160nan

prune1.0m (4.2%)

Filtered
20516 candidates to 12397 candidates (60.4%)

simplify15.3s (1.0%)

Algorithm
258×egg-herbie

regimes7.2s (0.5%)

Accuracy

Total 102.2b remaining (38.2%)

Threshold costs 3.8b (1.4%)

17.6b48.3%math.sqrt on complex, imaginary part, im greater than 0 branch
12.5b52.8%math.sqrt on complex, real part
10.7b56.6%math.log/2 on complex, real part
10.7b56%math.log10 on complex, real part
10.5b55.2%math.abs on complex

localize2.9s (0.2%)

bsearch2.2s (0.1%)

end1.0ms (0.0%)