Date:Tuesday, February 18th, 2020
Commit:5d186d9c on refactor-and-minor
Hostname:warfa with Racket 7.5
Seed:2020049
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

rewrite11.3m (70.3%)

Algorithm
156×rewrite-expression-head
Calls

477 calls:

36.0s
(* (sqrt (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))) (sqrt (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))))
5.4s
(sqrt (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))
5.2s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
5.2s
(sqrt (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))
3.1s
(log (sqrt (exp (+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))))
Rules
29568×times-frac
22855×*-un-lft-identity
16365×add-sqr-sqrt
12773×add-cube-cbrt
4840×fma-def
3647×distribute-lft-out
3344×pow1
2574×add-exp-log
2080×add-cbrt-cube
1908×pow-prod-down
1815×prod-diff
1522×difference-of-squares
1501×distribute-lft-out--
1491×associate-/r/
929×associate-*l*
866×prod-exp
856×sqrt-prod
846×associate-*r*
807×associate-/l*
801×div-inv
776×flip-+ flip3-+
728×add-log-exp
717×associate-/r*
653×cbrt-unprod
643×div-exp
545×sqrt-pow1
479×log1p-expm1-u
476×expm1-log1p-u
451×cbrt-undiv
415×unpow-prod-down
364×exp-sum
351×associate-*r/
346×flip3-- flip--
303×distribute-rgt-in distribute-lft-in
270×cbrt-prod
261×log-prod
256×fma-neg
253×associate-*l/ frac-times
238×frac-add
229×log-pow
218×unswap-sqr
210×cbrt-div
204×cube-prod
184×swap-sqr
176×exp-diff
148×associate--l+
131×pow-prod-up *-commutative
122×associate-/l/
114×sub-neg
111×sqr-pow 1-exp
106×sqrt-div
103×pow-sqr
97×associate--r+
95×diff-log
90×pow1/2 clear-num frac-2neg
82×pow-unpow
77×exp-prod
72×fma-udef
69×rec-exp
68×pow1/3
67×pow-exp
46×unpow3 pow-to-exp cube-mult
43×sum-log
40×pow-flip frac-sub
38×pow-pow
33×distribute-rgt-neg-in distribute-lft-neg-in
31×rem-sqrt-square
25×+-commutative
24×pow-plus neg-mul-1
20×inv-pow
19×pow2
17×rem-cube-cbrt
16×associate-+l+ hypot-udef hypot-def associate--l-
13×div-sub
12×cube-div
10×rem-log-exp
9×rem-exp-log
7×distribute-rgt-out--
6×un-div-inv sum-cubes neg-log
5×distribute-neg-in neg-sub0 distribute-rgt-neg-out associate-+l-
4×log1p-udef exp-neg sin-sum log1p-expm1 unpow2 expm1-log1p associate-+r+ cos-sum expm1-udef log-div
3×sqrt-unprod rem-square-sqrt
2×sqrt-undiv sqrt-pow2 rem-cbrt-cube exp-to-pow
1×difference-cubes pow3 unpow-prod-up pow-sub unsub-neg associate--r-

sample1.7m (10.9%)

Algorithm
99×intervals
Results
44.2s12118×body10240exit
22.8s515538×body80valid
10.9s26859×body1280valid
4.9s21134×body640valid
2.5s69617×body80nan
1.6s1607×body1280nan
1.6s10585×body320valid
974.0ms9448×body160valid
936.0ms1341×body640nan
664.0ms49536×pre80true
351.0ms1459×body2560valid
300.0ms607×body320nan
148.0ms588×body5120valid
114.0ms348×body160nan

prune1.5m (9.3%)

series1.1m (7.0%)

Calls

475 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)))))
2.0s
(* (* (/ 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)))))
2.0s
(/ (* (- (* (+ (+ 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))))
1.9s
(- (pow 1.0 3) (* (sqrt (pow (* (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (fma (- 1.0 (* 0.3275911 (fabs x))) (fma (/ 1.0 (/ (pow (fma 0.3275911 (fabs x) 1.0) 2) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ (* -0.284496736 1.0) (fma 0.3275911 (fabs x) 1.0))) (* 0.254829592 (- 1.0 (* 0.3275911 (fabs x)))))) (exp (- (* (fabs x) (fabs x))))) 3)) (sqrt (pow (* (* (/ 1.0 (- (* 1.0 1.0) (* (* 0.3275911 (fabs x)) (* 0.3275911 (fabs x))))) (fma (- 1.0 (* 0.3275911 (fabs x))) (fma (/ 1.0 (/ (pow (fma 0.3275911 (fabs x) 1.0) 2) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) (fma (/ 1.0 (fma 0.3275911 (fabs x) 1.0)) 1.061405429 -1.453152027) 1.421413741) (/ (* -0.284496736 1.0) (fma 0.3275911 (fabs x) 1.0))) (* 0.254829592 (- 1.0 (* 0.3275911 (fabs x)))))) (exp (- (* (fabs x) (fabs x))))) 3))))

simplify15.2s (1.6%)

Algorithm
254×egg-herbie

regimes5.5s (0.6%)

Accuracy

Total 43.0b remaining (32.3%)

Threshold costs 5.2b (3.9%)

8.6b31.5%_divideComplex, imaginary part
6.9b35.7%_divideComplex, real part
5.7b18.2%Octave 3.8, jcobi/2
4.4b30.6%math.sqrt on complex, real part
4.0b35.6%math.sqrt on complex, imaginary part, im greater than 0 branch

localize2.6s (0.3%)

bsearch1.3s (0.1%)

end1.0ms (0.0%)