Date:Saturday, February 22nd, 2020
Commit:72c1b946 on refactor-and-minor
Hostname:warfa with Racket 7.5
Seed:2020053
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

rewrite10.3m (70.6%)

Algorithm
155×rewrite-expression-head
Calls

466 calls:

5.0s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
494.0ms
(* (/ 1 (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) (+ (* x (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0))) (* x (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182))))))
492.0ms
(/ (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442)))) (+ (+ (* (pow (* x x) 4) (+ 0.0005064034 (* (* x x) 0.0001789971))) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))
491.0ms
(* (* (/ 1 (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) x) (+ (fma (fma x (* x 0.0001789971) 0.0005064034) (pow (* x x) 4) (fma (* 0.1049934947 x) x 1.0)) (* (pow x 4) (+ 0.0424060604 (* (* x x) 0.0072644182)))))
483.0ms
(* (/ 1 (+ (+ (* (* x (* (pow (* x x) 3) (pow x 3))) (+ 0.0008327945 (* (* x x) (* 2.0 0.0001789971)))) (fma (* 0.2909738639 x) (pow x 3) (fma (* 0.7715471019 x) x 1.0))) (* (pow x 6) (+ 0.0694555761 (* (* x x) 0.0140005442))))) x)
Rules
10771×times-frac
9102×*-un-lft-identity
7710×add-sqr-sqrt
6354×add-cube-cbrt
2986×add-exp-log
2099×add-cbrt-cube
1584×prod-diff
1576×pow1
1228×sqrt-prod
1123×distribute-lft-out
1120×prod-exp
1070×associate-*l*
838×associate-*r*
788×div-exp
700×difference-of-squares
693×cbrt-unprod
682×add-log-exp
666×associate-/r/
603×associate-/l*
539×associate-/r*
506×div-inv
473×cbrt-prod
463×log1p-expm1-u expm1-log1p-u
458×pow-prod-down
441×cbrt-undiv
313×flip-+ flip3-+
300×distribute-lft-out--
298×unpow-prod-down
259×flip3-- flip--
256×unswap-sqr
247×fma-neg
238×distribute-rgt-in distribute-lft-in
202×log-pow
200×associate-*r/
195×1-exp
183×associate--l+
182×pow-exp
174×fma-def
165×exp-sum
161×pow1/3
145×associate-*l/
143×log-prod
138×*-commutative sqrt-pow1
126×cube-prod
125×rec-exp
116×swap-sqr
107×associate--r+
102×pow-to-exp
100×sqrt-div
99×sub-neg
91×pow-unpow pow-prod-up
89×frac-2neg frac-times clear-num diff-log
80×associate-/l/ sqr-pow
78×frac-add
71×pow-sqr
70×pow1/2
62×fma-udef
47×distribute-rgt-neg-in
45×distribute-lft-neg-in
38×associate-+l+
36×pow-plus cbrt-div
35×sum-log
33×rem-sqrt-square
30×pow-pow pow2
29×neg-mul-1
28×exp-prod
27×unpow3 pow-flip cube-mult
24×associate-+r+ +-commutative
22×inv-pow
19×associate--l-
17×rem-cube-cbrt
16×hypot-def
12×div-sub
10×difference-of-sqr-1 distribute-rgt-out
9×rem-log-exp
8×frac-sub
7×associate--r- log-div
6×unpow2
5×sqrt-unprod
4×cube-div sin-sum log-rec rem-cbrt-cube
3×pow3 distribute-rgt-neg-out associate-+l-
2×sqrt-pow2 distribute-lft-neg-out distribute-neg-in hypot-udef neg-sub0 neg-log
1×cos-sum distribute-neg-out associate-+r- un-div-inv unsub-neg rem-square-sqrt exp-to-pow

sample1.7m (11.6%)

Algorithm
99×intervals
Results
43.5s11926×body10240exit
19.5s457612×body80valid
11.2s26739×body1280valid
5.2s21061×body640valid
2.6s70349×body80nan
1.7s10678×body320valid
1.7s1550×body1280nan
1.0s9422×body160valid
931.0ms1288×body640nan
887.0ms49536×pre80true
383.0ms1488×body2560valid
314.0ms596×body320nan
153.0ms589×body5120valid
123.0ms341×body160nan

series1.2m (7.9%)

Calls

463 calls:

2.3s
(/ (* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i))))) (/ (fma i 2.0 (+ alpha beta)) (/ (sqrt (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 beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
1.9s
(* (* (/ i (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0))) (/ (+ (+ alpha beta) i) (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)))) (sqrt (fma beta alpha (* i (+ (+ alpha beta) i)))))
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))))
1.2s
(fma (- (* (pow (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 3) (log1p (expm1 (pow (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) (fma (/ 1.0 (+ (* 0.3275911 (fabs x)) 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592) 3))))) (pow (/ 1 (exp (pow (fabs x) 2))) 3) (pow 1.0 3))

prune1.1m (7.3%)

Filtered
18937 candidates to 12297 candidates (64.9%)

simplify13.5s (1.5%)

Algorithm
253×egg-herbie

regimes5.1s (0.6%)

Accuracy

Total 48.3b remaining (34.9%)

Threshold costs 5.7b (4.1%)

9.2b15.4%_divideComplex, real part
8.1b30.4%_divideComplex, imaginary part
7.1b12.4%Octave 3.8, jcobi/2
5.1b13.4%math.sqrt on complex, real part
4.5b17.7%math.sqrt on complex, imaginary part, im greater than 0 branch

localize2.9s (0.3%)

bsearch976.0ms (0.1%)

end1.0ms (0.0%)