Date:Saturday, February 29th, 2020
Commit:c75aaa3c on more-ival-tests
Hostname:warfa with Racket 7.5
Seed:2020060
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

series10.9m (73.3%)

Calls

467 calls:

22.1s
(- (pow 1.0 3) (/ (pow (* (* 1.0 (- (* 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)))))))) (fma 0.3275911 (fabs x) 1.0)) 3)))
3.3s
(- (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))
2.3s
(/ (/ i (* (/ (+ (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) 1) (/ (- (+ (+ alpha beta) (* 2.0 i)) (sqrt 1.0)) (+ (+ alpha beta) i)))) (/ (fma i 2.0 (+ alpha beta)) (/ (fma beta alpha (* i (+ (+ alpha beta) i))) (fma i 2.0 (+ alpha beta)))))
2.1s
(/ (* (- (* (+ (+ 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))))

sample1.9m (12.7%)

Algorithm
99×intervals
Results
48.8s16237×body10240exit
18.4s446225×body80valid
14.2s30560×body1280valid
6.6s23723×body640valid
3.0s3102×body1280nan
2.5s69403×body80nan
2.2s12140×body320valid
1.9s2710×body640nan
762.0ms6326×body160valid
655.0ms49536×pre80true
649.0ms1319×body320nan
359.0ms1478×body2560valid
213.0ms650×body160nan
134.0ms568×body5120valid

prune1.5m (9.8%)

simplify19.9s (2.2%)

Algorithm
256×egg-herbie

rewrite8.7s (1.0%)

Algorithm
158×rewrite-expression-head
Calls

471 calls:

271.0ms
(- (pow (pow 1.0 3) 3) (pow (/ (pow (* (* 1.0 (- (* 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)))))))) (fma 0.3275911 (fabs x) 1.0)) 3)) 3))
194.0ms
(* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
190.0ms
(* 0.0140005442 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
190.0ms
(* 0.0005064034 (* (* (* (* x x) (* x x)) (* x x)) (* x x)))
153.0ms
(* (* (sqrt (* PI 2.0)) (pow (+ (+ (- z 1.0) 7.0) 0.5) (+ (- z 1.0) 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))) (exp (+ (+ (- z 1.0) 7.0) 0.5))))
Rules
37231×times-frac
25881×*-un-lft-identity
19857×add-sqr-sqrt
17582×add-cube-cbrt
8365×prod-diff
6684×unpow-prod-down
6487×cube-prod
4250×distribute-lft-out
2962×add-exp-log
2390×sqrt-prod
2339×add-cbrt-cube
2023×sqr-pow
1888×pow1
1770×unpow3 cube-mult
1420×associate-/r/
1269×div-inv
1240×difference-of-squares
1189×prod-exp
935×associate-/l*
888×cbrt-unprod
798×associate-*l*
786×fma-neg
764×associate-*r*
722×pow-prod-down
718×add-log-exp
667×flip-+ flip3-+
648×div-exp
607×associate-/r*
523×fma-def
472×expm1-log1p-u
471×log1p-expm1-u
436×cbrt-undiv
427×cbrt-prod
398×distribute-lft-out--
354×associate-*l/
347×associate-*r/
333×frac-times
294×frac-add
251×distribute-rgt-in distribute-lft-in
214×log-pow unswap-sqr
208×exp-sum
199×flip3-- flip--
174×cube-div associate--l+
161×log-prod
134×sqrt-div
129×associate-/l/
128×*-commutative
120×1-exp
112×pow-exp
107×clear-num frac-2neg
105×sub-neg
99×associate--r+
98×diff-log
90×pow-to-exp
85×pow-unpow
68×rec-exp swap-sqr
67×fma-udef pow1/3
63×sqrt-pow1
53×associate-+l-
51×pow1/2
48×pow-prod-up
40×pow-sqr pow-sub
39×cbrt-div
36×pow-pow sum-log
30×exp-prod
28×pow-plus
23×pow-flip +-commutative
22×rem-sqrt-square
21×distribute-lft-neg-in neg-mul-1 distribute-rgt-neg-in
20×rem-cube-cbrt
19×pow2 div-sub associate--l-
18×inv-pow
16×associate-+l+ hypot-def rem-log-exp
14×exp-diff
11×rem-exp-log
8×neg-sub0
7×difference-cubes associate-+r+ exp-neg
5×un-div-inv exp-to-pow log-div
4×sqrt-undiv sin-sum unpow-prod-up frac-sub rem-cbrt-cube unpow2
3×sqrt-pow2 distribute-rgt-neg-out
2×distribute-lft-neg-out neg-log
1×log1p-udef sqrt-unprod pow3 log1p-expm1 expm1-log1p hypot-udef rem-square-sqrt distribute-frac-neg log-rec cos-sum associate--r- expm1-udef mul-1-neg

regimes5.1s (0.6%)

Accuracy

Total 47.2b remaining (52.8%)

Threshold costs 6.4b (7.1%)

9.0b44.8%Octave 3.8, jcobi/4
7.4b35.1%_divideComplex, real part
6.4b0%Octave 3.8, jcobi/2
4.9b15.8%math.sqrt on complex, real part
4.1b30.4%math.sqrt on complex, imaginary part, im greater than 0 branch

localize2.7s (0.3%)

bsearch1.2s (0.1%)

end1.0ms (0.0%)