Date:Monday, June 29th, 2020
Commit:6b86a4bc on ival-find-range
Hostname:warfa with Racket 7.5
Seed:2020181
Parameters:256 points for 4 iterations
Flags:
setup:simplifysetup:searchrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

rewrite2.4min (40.0%)

Algorithm
158×rewrite-expression-head
Calls

474 calls:

1.4s
(/ (+ 0.9999999999998099 (+ (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))))))) (exp (+ (neg z) (+ 7.0 0.5))))
194.0ms
(/ (/ (/ (/ (+ alpha (+ beta (+ (* alpha beta) 1.0))) (sqrt (+ alpha (+ beta (* 1.0 2.0))))) (sqrt (+ (+ alpha beta) (* 2.0 1.0)))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
170.0ms
(* (sqrt (* PI 2.0)) (* (* (/ (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))))) (exp (- (+ 7.0 0.5) z))) (pow (- (+ 7.0 0.5) z) (+ (neg z) 0.5))) (/ PI (sin (* PI z)))))
163.0ms
(/ (+ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (/ -176.6150291621406 (+ (neg z) 4.0))) (+ (+ (/ 676.5203681218851 (- 1.0 z)) (/ -1259.1392167224028 (+ 2.0 (neg z)))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (/ 1.5056327351493116e-07 (+ (neg z) 8.0))) 0.9999999999998099))))) (exp (- (+ 7.0 0.5) z)))
138.0ms
(* (sqrt (* PI 2.0)) (* PI (* (/ (+ (/ 771.3234287776531 (+ (neg z) 3.0)) (+ (/ -176.6150291621406 (+ (neg z) 4.0)) (+ (/ 676.5203681218851 (- 1.0 z)) (+ (/ -1259.1392167224028 (+ 2.0 (neg z))) (+ (/ 12.507343278686905 (+ (neg z) 5.0)) (+ (/ -0.13857109526572012 (+ (neg z) 6.0)) (+ (/ 9.984369578019572e-06 (+ (neg z) 7.0)) (+ (/ 1.5056327351493116e-07 (+ (neg z) 8.0)) 0.9999999999998099)))))))) (exp (+ 7.0 (- 0.5 z)))) (pow (+ 7.0 (- 0.5 z)) (+ (neg z) 0.5)))))
Rules
22427×times-frac
20800×*-un-lft-identity
10777×add-sqr-sqrt
9816×add-cube-cbrt
6630×sqrt-prod
6382×distribute-lft-out
2370×add-exp-log
1824×add-cbrt-cube
1637×associate-/l*
1589×pow1
1136×associate-*r*
849×associate-*l*
802×prod-exp
792×flip-+ flip3-+
743×associate-/r/
739×add-log-exp
594×sqrt-div
569×cbrt-unprod
547×div-exp
543×cbrt-prod
414×associate-*r/
408×div-inv
383×pow-prod-down
370×associate-/r*
333×cbrt-undiv unpow-prod-down
321×frac-add
270×unswap-sqr
248×log-pow
246×frac-times
208×associate-*l/
196×sqrt-pow1
163×flip-- flip3--
160×cbrt-div
147×*-commutative
141×difference-of-squares
138×associate-/l/ swap-sqr
137×cube-prod
130×pow-exp
120×sum-log
111×pow-unpow
110×log-prod
108×pow1/2
107×pow1/3
93×pow-prod-up
92×sqr-pow
91×clear-num frac-2neg
90×sub-neg
89×distribute-lft-out--
85×exp-sum
82×distribute-rgt-in distribute-lft-in
80×pow-to-exp
72×exp-prod
67×pow-sqr
65×1-exp rec-exp
51×rem-sqrt-square
48×+-commutative pow-pow
47×associate--l+
41×diff-log
36×frac-sub pow-plus
31×pow2
24×cube-mult unpow3 rem-cube-cbrt
20×distribute-rgt-neg-in
18×cube-div log-div
16×associate-+r+ div-sub distribute-neg-frac
12×associate-+l-
11×rem-log-exp
10×exp-diff
8×neg-sub0 associate--r+
6×associate-+l+ unpow2 pow-sub
5×distribute-neg-in
4×inv-pow unpow1/3 sin-sum neg-log un-div-inv pow-flip
3×cos-sum rem-square-sqrt sqrt-unprod
2×associate--l- rem-cbrt-cube rem-exp-log
1×difference-cubes associate--r-

prune1.5min (25.1%)

Filtered
20650 candidates to 11331 candidates (45.1%)

sample55.2s (15.1%)

Algorithm
98×intervals
Results
19.0s352066×body80valid
7.4s16020×body1280valid
5.3s11108×body1280invalid
3.3s12351×body640valid
2.8s8557×body640invalid
2.5s4165×body5120exit
1.4s7511×body160valid
1.2s74907×pre80true
1.1s6646×body320valid
884.0ms17810×body80invalid
835.0ms3924×body320invalid
401.0ms1413×body2560valid
259.0ms1898×body160invalid
209.0ms2441×body80nan
185.0ms538×body5120valid
98.0ms59×body2560invalid
0.0ms3×body80overflowed

analyze23.6s (6.4%)

Algorithm
98×search
Search
TrueOtherFalseIter
0%87.9%12.1%0
2.3%85.6%12.1%1
9.2%76.3%14.4%2
22.1%63%14.9%3
27.1%56.2%16.8%4
36.4%46.2%17.4%5
39.8%41.1%19%6
44.4%33.8%21.8%7
47.9%29.6%22.5%8
51%25.4%23.6%9
53.5%21.8%24.7%10
55.6%18.9%25.5%11
57.6%16.4%26%12
59.5%13.6%26.9%13
60.6%12.2%27.2%14

series16.2s (4.4%)

Calls

474 calls:

1.6s
(* (+ d1 (sqrt (* d1 (+ d2 (- d4 d3))))) (- (sqrt (* d1 (+ d2 (- d4 d3)))) d1))
844.0ms
(- (pow 1.0 3) (* (sqrt (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 (pow (fabs x) 2)))) 3)) (sqrt (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 (pow (fabs x) 2)))) 3))))
828.0ms
(- (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 (pow (fabs x) 2)))) 3))
404.0ms
(- 1.0 (* (/ 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 1.0) (* 0.3275911 (* 0.3275911 (pow (fabs x) 2))))) (- 1.0 (* 0.3275911 (fabs x)))) 1.061405429)))))))) (pow (exp (fabs x)) (fabs x)))))
381.0ms
(* (/ (+ 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 (pow (fabs x) 2))) (+ 1.0 (* (/ 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 (pow (fabs x) 2))))))

simplify13.6s (3.7%)

Algorithm
254×egg-herbie

regimes11.6s (3.2%)

Accuracy

Total 95.4b remaining (34.4%)

Threshold costs 3.6b (1.3%)

10.8b56.7%math.log10 on complex, real part
10.6b57.4%math.log/1 on complex, real part
10.6b45.2%math.sqrt on complex, imaginary part, im greater than 0 branch
10.3b58.6%math.log/2 on complex, real part
10.1b52.4%math.sqrt on complex, real part

bsearch5.1s (1.4%)

localize2.5s (0.7%)

end2.0ms (0.0%)

Profiling

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