Date:Tuesday, February 18th, 2020
Commit:3b7244d2 on master
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

rewrite11.2m (70.2%)

Algorithm
156×rewrite-expression-head
Calls

479 calls:

33.3s
(* (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)))))
5.0s
(sqrt (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))
4.8s
(* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)))
4.8s
(sqrt (* (/ 1.0 21.0) (* (* (* (* (* (* (fabs x) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x)) (fabs x))))
2.9s
(log (sqrt (exp (+ (/ (/ 1 (/ (/ (fma i 2.0 (+ alpha beta)) (+ alpha beta)) (- beta alpha))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0))))
Rules
28564×times-frac
21838×*-un-lft-identity
15978×add-sqr-sqrt
12388×add-cube-cbrt
4836×fma-def
3282×distribute-lft-out
3275×pow1
2520×add-exp-log
2033×add-cbrt-cube
1873×pow-prod-down
1823×prod-diff
1524×difference-of-squares
1499×distribute-lft-out--
1359×associate-/r/
838×prod-exp
836×sqrt-prod
814×associate-*l*
779×associate-*r*
769×div-inv
737×flip-+ flip3-+
720×associate-/r*
718×add-log-exp
714×associate-/l*
627×div-exp
622×cbrt-unprod
503×sqrt-pow1
481×log1p-expm1-u
478×expm1-log1p-u
433×cbrt-undiv
391×unpow-prod-down
370×exp-sum
305×associate-*r/
293×flip3-- flip--
287×distribute-rgt-in distribute-lft-in
260×fma-neg
249×log-prod
248×cbrt-prod
224×log-pow
213×unswap-sqr
206×associate-*l/
180×cube-prod
170×swap-sqr
149×frac-times associate--l+
136×frac-add
126×*-commutative
122×associate-/l/ sqrt-div
117×pow-prod-up
114×sqr-pow sub-neg
112×1-exp
97×associate--r+
95×pow-sqr diff-log
90×clear-num frac-2neg
86×pow1/2
85×pow-unpow
75×fma-udef exp-prod
73×pow-exp
69×pow1/3
68×rec-exp
58×cbrt-div
49×pow-to-exp
46×unpow3 cube-mult
40×exp-diff pow-pow frac-sub
36×sum-log
35×rem-sqrt-square
33×distribute-rgt-neg-in distribute-lft-neg-in
24×neg-mul-1
23×pow-plus +-commutative
20×hypot-def
18×pow2
17×rem-cube-cbrt
16×hypot-udef associate--l-
15×associate-+l+
14×pow-flip
13×div-sub
12×cube-div inv-pow
10×rem-exp-log rem-log-exp
6×un-div-inv neg-log distribute-rgt-out--
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-undiv
2×sqrt-pow2 sqrt-unprod rem-square-sqrt rem-cbrt-cube exp-to-pow
1×difference-cubes pow3 unpow-prod-up pow-sub unsub-neg associate--r-

sample1.8m (11.1%)

Algorithm
99×intervals
Results
44.4s12118×body10240exit
23.7s515538×body80valid
11.1s26859×body1280valid
5.2s21134×body640valid
2.5s69617×body80nan
1.7s1607×body1280nan
1.6s10585×body320valid
1.0s9448×body160valid
947.0ms1341×body640nan
662.0ms49536×pre80true
352.0ms1459×body2560valid
308.0ms607×body320nan
144.0ms588×body5120valid
129.0ms348×body160nan

prune1.5m (9.2%)

series1.1m (6.8%)

Calls

477 calls:

2.2s
(/ (* (* (/ 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
(- (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))))
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 beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))
1.9s
(- (pow 1.0 3) (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))

simplify15.3s (1.6%)

Algorithm
254×egg-herbie

regimes5.6s (0.6%)

Accuracy

Total 43.1b remaining (32.4%)

Threshold costs 5.2b (3.9%)

8.6b31.5%_divideComplex, imaginary part
7.0b35.5%_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%)