Date:Friday, May 8th, 2020
Commit:4abb449a on separate-biginterval
Hostname:warfa with Racket 7.5
Seed:2020129
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifyreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

sample1.9m (56.2%)

Algorithm
56×intervals
16×halfpoints
Results
25.4s67802×body1280valid
18.3s17372×body2560valid
8.8s42252×body640valid
3.6s91651×body80valid
2.8s20808×body320valid
2.4s64851×body80nan
1.4s1082×body1280nan
1.1s15998×body80overflowed
975.0ms10888×body160valid
676.0ms47367×pre80true
674.0ms946×body640nan
180.0ms415×body320nan
162.0ms437×body5120valid
51.0ms225×body160nan

series39.0s (19.4%)

Calls

404 calls:

1.5s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps)))))) (tan x))
1.2s
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))
768.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (pow (* eps a) 3)) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
664.0ms
(pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 3)
504.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

prune28.2s (14.0%)

Filtered
12737 candidates to 8222 candidates (64.6%)

simplify10.5s (5.2%)

Algorithm
196×egg-herbie

rewrite3.7s (1.9%)

Algorithm
124×rewrite-expression-head
Calls

404 calls:

68.0ms
(- (/ (/ 1.0 n) x) (- (/ (/ 0.5 n) (pow x 2)) (/ (* (log x) 1.0) (* x (pow n 2)))))
54.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (cbrt (pow (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) 3)))
39.0ms
(cbrt (pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3))
39.0ms
(- (+ (+ (/ (* (pow (sin x) 2) (pow (sin eps) 3)) (* (pow (cos x) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 3)))) (* (/ (pow (sin eps) 2) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (pow (cos eps) 2))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))))) (/ (sin x) (* (- 1 (/ (* (pow (sin x) 3) (pow (sin eps) 3)) (* (pow (cos x) 3) (pow (cos eps) 3)))) (cos x)))) (/ (sin x) (cos x)))
38.0ms
(pow (+ (/ 1.0 N) (/ (- (/ 0.3333333333333333 N) 0.5) (pow N 2))) 3)
Rules
5356×*-un-lft-identity
5106×add-sqr-sqrt
4730×times-frac
2971×add-cube-cbrt
1398×add-exp-log
1343×sqrt-prod
1040×add-cbrt-cube
807×pow1
806×difference-of-squares
729×add-log-exp
666×distribute-lft-out-- associate-*l*
611×associate-*r*
579×distribute-lft-out
538×unpow-prod-down
481×associate-/l*
404×associate-/r*
383×cbrt-prod
371×prod-exp
323×log-prod
292×unswap-sqr
286×flip-- flip3--
280×div-exp
224×associate-/r/
221×sqr-pow
214×cube-prod
210×cbrt-unprod
200×div-inv
194×flip-+ flip3-+
189×associate-*l/
183×cbrt-undiv
137×sub-neg
132×diff-log
127×pow-prod-down
126×distribute-rgt-neg-in
122×frac-times
111×associate-*r/
109×log-pow
106×cbrt-div
100×sqrt-div
99×associate-/l/ swap-sqr
88×*-commutative
86×sqrt-pow1
84×unpow2
78×pow-exp
77×pow-to-exp
73×frac-2neg clear-num
70×pow1/2 associate-+l+
68×frac-add
59×tan-quot
57×exp-prod
56×pow1/3
50×pow-unpow
49×sum-log
47×associate--l+ 1-exp
46×distribute-rgt-in distribute-lft-in
44×rec-exp
40×associate-+r+
39×log-div
38×frac-sub
36×pow-prod-up
33×rem-sqrt-square
31×exp-sum
30×+-commutative
28×pow-sqr
26×div-sub
24×complex-mul-def unpow3
22×rem-log-exp
21×cube-div
19×cube-mult
16×neg-sub0
15×associate--l-
14×pow-flip associate--r+
13×pow-pow
12×neg-log pow-plus
10×inv-pow pow2
9×exp-diff rem-cube-cbrt sin-mult
8×cos-mult associate-+l-
7×associate-+r-
6×un-div-inv sqrt-unprod *.c-commutative
5×distribute-rgt-out-- difference-of-sqr-1
4×associate--r- +.c-commutative complex-add-def rem-cbrt-cube
3×difference-cubes rem-exp-log rem-square-sqrt
2×distribute-lft-neg-in associate-+l+.c exp-neg associate-*l*.c cos-sum neg-mul-1 tan-sum distribute-neg-frac sin-sum
1×sin-cos-mult sqrt-pow2 diff-atan sub-div diff-cos sqr-cos diff-sin exp-to-pow log-rec

regimes3.0s (1.5%)

Accuracy

Total 26.2b remaining (12.4%)

Threshold costs 5.9b (2.8%)

3.4b87.7%quadp (p42, positive)
3.3b88.8%quadm (p42, negative)
3.1b0%expq3 (problem 3.4.2)
2.9b90%quad2m (problem 3.2.1, negative)
2.7b90%quad2p (problem 3.2.1, positive)

localize2.0s (1.0%)

bsearch1.6s (0.8%)

end1.0ms (0.0%)

Profiling

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