Date:Wednesday, March 18th, 2020
Commit:1a959946 on master
Hostname:warfa with Racket 7.5
Seed:2020078
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 (52.4%)

Algorithm
56×intervals
16×halfpoints
Results
23.6s67912×body1280valid
17.8s17613×body2560valid
8.0s41787×body640valid
4.2s13262×body10240exit
2.9s92422×body80valid
2.4s20365×body320valid
1.8s64376×body80nan
1.3s2241×body1280nan
876.0ms11177×body160valid
758.0ms1849×body640nan
556.0ms47473×pre80true
227.0ms898×body320nan
131.0ms459×body5120valid
66.0ms444×body160nan

series47.0s (22.1%)

Calls

413 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))
1.3s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* 1/6 (* (pow eps 3) (pow b 3))) (+ (* 1/2 (* (pow eps 2) (pow b 2))) (* eps b)))))
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)))
1.1s
(* (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))) (cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
941.0ms
(cbrt (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x)))

prune33.8s (15.9%)

Filtered
12327 candidates to 8120 candidates (65.9%)

simplify10.5s (4.9%)

Algorithm
196×egg-herbie

rewrite3.8s (1.8%)

Algorithm
124×rewrite-expression-head
Calls

413 calls:

65.0ms
(- (/ (pow (* (cos x) (cos eps)) 3) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (+ (/ (pow (* (sin x) (sin eps)) 3) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x)))
36.0ms
(- (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0))))
36.0ms
(- (/ (- (pow (* (cos x) (cos eps)) 3) (pow (* (sin x) (sin eps)) 3)) (+ (* (* (sin x) (sin eps)) (+ (* (sin x) (sin eps)) (* (cos x) (cos eps)))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps))))) (cos x))
35.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
35.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
Rules
4687×*-un-lft-identity
4631×add-sqr-sqrt
4019×times-frac
2660×add-cube-cbrt
1372×add-exp-log
1030×add-cbrt-cube
970×sqrt-prod
875×pow1
798×add-log-exp
785×difference-of-squares
676×associate-*l*
559×associate-*r*
555×distribute-lft-out
549×unpow-prod-down
504×distribute-lft-out--
451×associate-/l*
430×cbrt-prod
421×log-prod
390×prod-exp
304×sqr-pow
301×associate-/r*
293×cube-prod
282×unswap-sqr
247×flip-- flip3--
227×div-exp
224×cbrt-unprod
221×flip-+ flip3-+
219×associate-*l/
216×associate-/r/
168×pow-prod-down
166×div-inv
160×cbrt-undiv
141×cbrt-div
133×diff-log
132×sub-neg
119×frac-times
108×associate-*r/
98×pow-exp
93×pow-to-exp log-pow
89×swap-sqr
87×*-commutative
79×frac-add
78×associate-/l/
75×pow-unpow sum-log
74×associate-+r+
70×unpow2
64×sqrt-div
62×frac-2neg clear-num
61×sqrt-pow1
60×pow1/3
59×tan-quot
55×distribute-rgt-neg-in
53×exp-prod
51×pow1/2
45×associate-+l+
44×log-div
41×pow-prod-up distribute-rgt-in distribute-lft-in
39×+-commutative
34×rem-log-exp
33×pow-pow frac-sub
31×difference-cubes rec-exp pow-sqr unpow3 cube-mult 1-exp
29×rem-sqrt-square
26×associate--l+
25×div-sub
24×complex-mul-def exp-sum
18×associate--r+ neg-sub0
17×rem-cube-cbrt cos-mult
15×pow-plus distribute-neg-frac
14×cube-div exp-to-pow
13×associate-+l-
12×distribute-lft-neg-in
11×pow2 neg-log
10×exp-diff associate--l- distribute-rgt-out-- neg-mul-1
pow-flip
sqrt-unprod inv-pow exp-lft-cube sin-mult *.c-commutative cube-unmult
unpow-1
un-div-inv unpow-prod-up pow-sub +.c-commutative complex-add-def
rem-exp-log associate-+r-
cos-sum pow-neg associate-+l+.c exp-neg difference-of-sqr-1 rem-square-sqrt distribute-frac-neg distribute-rgt-out tan-sum associate-*l*.c rem-cbrt-cube sin-sum
sin-cos-mult sqrt-pow2 e-exp-1 distribute-lft1-in distribute-lft-neg-out distribute-rgt1-in diff-atan sub-div sqr-sin diff-cos count-2 sqrt-undiv +-inverses distribute-rgt-neg-out frac-2neg.c diff-sin

regimes3.0s (1.4%)

Accuracy

Total 22.2b remaining (10.7%)

Threshold costs 8.0b (3.9%)

3.4b0%expq3 (problem 3.4.2)
3.2b89%quadp (p42, positive)
2.7b89.9%quad2m (problem 3.2.1, negative)
2.0b79.6%2cos (problem 3.3.5)
1.8b83.3%2nthrt (problem 3.4.6)

localize2.1s (1.0%)

bsearch1.1s (0.5%)

end1.0ms (0.0%)