Date:Friday, February 28th, 2020
Commit:6d7f8a61 on more-ival-tests
Hostname:warfa with Racket 7.5
Seed:2020059
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

prune2.4m (29.1%)

rewrite2.3m (28.2%)

Algorithm
150×rewrite-expression-head
Calls

437 calls:

2.2m
(* (/ (/ 1 (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1)) (sqrt (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))) (/ (/ i (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))) (sqrt (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))))
154.0ms
(* (* (* (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 (- z 0))) (/ -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))))
149.0ms
(/ (/ i (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i))) (sqrt (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta))))))
134.0ms
(* (+ (/ 1.0 (/ 2.0 (pow (/ 1.0 (fabs x)) 3))) (/ (* 1.0 (+ (/ (* (/ 1.0 (pow (fabs x) 6)) 15.0) 8.0) (fma (/ 3.0 4.0) (pow (/ 1.0 (fabs x)) 4) 1))) (fabs x))) (* (/ 1.0 (sqrt PI)) (pow (exp (fabs x)) (/ (fabs x) 2))))
116.0ms
(/ (/ i (/ (- (* (+ (+ alpha beta) (* 2.0 i)) (+ (+ alpha beta) (* 2.0 i))) 1.0) (+ (+ alpha beta) i))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
Rules
81967×times-frac
48960×*-un-lft-identity
40661×add-sqr-sqrt
30443×add-cube-cbrt
15875×sqrt-prod
8648×distribute-lft-out
6033×associate-*r*
3762×difference-of-squares
3426×associate-*l*
3184×add-exp-log
2634×div-inv
2167×cbrt-prod
2033×associate-/r/
1839×add-cbrt-cube
1654×distribute-lft-out--
1420×prod-diff
1228×pow1
1171×prod-exp
964×div-exp
883×flip-+ flip3-+
698×unswap-sqr
663×unpow-prod-down
635×associate-/l*
603×add-log-exp
527×cbrt-unprod
508×associate-/r*
470×frac-add
439×expm1-log1p-u
437×log1p-expm1-u
421×cbrt-undiv
335×associate-*r/
282×pow-prod-down
263×distribute-rgt-in distribute-lft-in
262×1-exp
259×log-pow
207×frac-times
202×fma-neg
185×pow-exp
174×rec-exp
155×sqr-pow
143×exp-sum
139×associate--l+
133×log-prod
127×*-commutative
124×sqrt-div
123×associate-*l/
119×flip3-- flip--
105×associate--r+
104×fma-def
97×sqrt-pow1
91×pow1/3
87×pow-to-exp cube-prod
82×clear-num frac-2neg
78×sub-neg
72×associate-/l/
71×diff-log
69×fma-udef
64×exp-prod
63×associate-+l-
62×pow1/2
61×cbrt-div
59×pow-unpow pow-sub
57×exp-neg swap-sqr
51×rem-log-exp
49×exp-diff rem-sqrt-square
39×neg-sub0
37×pow-flip
34×inv-pow
24×sum-log
23×un-div-inv log-div
22×distribute-rgt-neg-in distribute-lft-neg-in
21×unpow3 cube-mult
19×pow-pow
18×hypot-def div-sub
17×pow-prod-up pow-sqr
15×associate-+l+
13×+-commutative associate--l-
12×neg-mul-1
11×rem-cube-cbrt unpow2
10×pow2 pow-plus
rem-exp-log
associate--r-
cube-div
sin-sum hypot-udef frac-sub
log-rec
log1p-udef sqrt-unprod log1p-expm1 distribute-neg-in unpow-prod-up expm1-log1p expm1-udef distribute-frac-neg rem-cbrt-cube distribute-rgt-neg-out
sqrt-pow2 cos-sum

sample1.9m (22.7%)

Algorithm
100×intervals
Results
46.5s15580×body10240exit
19.5s459502×body80valid
14.5s30673×body1280valid
6.6s23385×body640valid
3.0s3119×body1280nan
2.5s69681×body80nan
2.2s11651×body320valid
1.7s2493×body640nan
1.2s10054×body160valid
670.0ms49536×pre80true
584.0ms1175×body320nan
374.0ms1544×body2560valid
208.0ms661×body160nan
165.0ms629×body5120valid

series1.2m (13.9%)

Calls

437 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))))
1.3s
(fma (/ (* (sqrt (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592)) (sqrt (log (* (pow (exp (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736)) (exp 0.254829592))))) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)
1.1s
(fma (/ (* (sqrt (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592)) (sqrt (log (* (pow (exp (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736)) (exp 0.254829592))))) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)
1.1s
(exp (log (fma (/ (* (sqrt (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) (fma (/ 1.0 (+ 1.0 (* 0.3275911 (fabs x)))) 1.061405429 -1.453152027) 1.421413741) -0.284496736) 0.254829592)) (sqrt (log (* (pow (exp (/ 1.0 (fma (fabs x) 0.3275911 1.0))) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) (fma (/ 1.0 (fma (fabs x) 0.3275911 1.0)) 1.061405429 -1.453152027) 1.421413741) -0.284496736)) (exp 0.254829592))))) (exp (* (fabs x) (fabs x)))) (/ (- 1.0) (fma (fabs x) 0.3275911 1.0)) 1.0)))

simplify21.5s (4.3%)

Algorithm
250×egg-herbie

regimes5.3s (1.1%)

Accuracy

Total 47.7b remaining (34.2%)

Threshold costs 6.2b (4.4%)

10.0b18.3%_divideComplex, imaginary part
8.7b-4%Octave 3.8, jcobi/2
7.1b36.5%_divideComplex, real part
5.0b13%math.sqrt on complex, imaginary part, im greater than 0 branch
4.0b27.3%math.sqrt on complex, real part

localize2.6s (0.5%)

bsearch1.1s (0.2%)

end1.0ms (0.0%)