Date:Wednesday, March 18th, 2020
Commit:7c9a4fcd on better-rr
Hostname:warfa with Racket 7.5
Seed:2020078
Parameters:256 points for 4 iterations
Flags:
setup:simplifyrules:numericsrules:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:better-rrreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
+o rules:numerics

Details

sample1.8m (61.8%)

Algorithm
56×intervals
16×halfpoints
Results
23.4s67912×body1280valid
17.7s17613×body2560valid
7.6s41787×body640valid
4.1s13262×body10240exit
2.8s92422×body80valid
2.4s20365×body320valid
1.8s64376×body80nan
1.4s2241×body1280nan
824.0ms11177×body160valid
779.0ms1849×body640nan
542.0ms47473×pre80true
235.0ms898×body320nan
138.0ms459×body5120valid
67.0ms444×body160nan

series33.6s (18.7%)

Calls

368 calls:

1.3s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
773.0ms
(/ (* (sin x) (/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (fma (pow (cos eps) 2) (sin x) (sin x)))) (fma (cos eps) (sin x) (sin x)))
682.0ms
(* (* (/ 1.0 (sqrt (+ x 1.0))) 1.0) (* (/ 2 (fma (sqrt (+ x 1.0)) (sqrt x) x)) 1/2))
667.0ms
(+ (* (- (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (fma 0.25 (/ (log (/ 1 x)) (* x (pow n 2))) (/ (/ 0.25 n) (pow x 2)))) (* (/ (/ 0.5 n) x) (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
527.0ms
(* (- (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (fma 0.25 (/ (log (/ 1 x)) (* x (pow n 2))) (/ (/ 0.25 n) (pow x 2))))

prune17.1s (9.6%)

Filtered
4503 candidates to 3244 candidates (72.0%)

simplify10.6s (5.9%)

Algorithm
194×egg-herbie

regimes2.2s (1.2%)

Accuracy

Total 17.3b remaining (11.7%)

Threshold costs 8.6b (5.9%)

3.3b0%expq3 (problem 3.4.2)
1.6b84.5%2nthrt (problem 3.4.6)
1.5b84.5%2cos (problem 3.3.5)
1.1b84.2%2tan (problem 3.3.2)
1.1b95.4%quadm (p42, negative)

localize2.0s (1.1%)

rewrite1.8s (1.0%)

Algorithm
122×rewrite-expression-head
Calls

368 calls:

48.0ms
(* (/ (/ 1.0 (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x))))) (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))))
24.0ms
(* (/ 1.0 (+ (pow (sqrt (+ x 1.0)) 3) (pow (sqrt x) 3))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))))
18.0ms
(+ (* (- (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))) (fma 0.25 (/ (log (/ 1 x)) (* x (pow n 2))) (/ (/ 0.25 n) (pow x 2)))) (* (/ (/ 0.5 n) x) (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
16.0ms
(/ (* (sin x) (/ (* (sin x) (- (* (* (sin x) (pow (cos eps) 2)) (pow (cos eps) 2)) (sin x))) (fma (pow (cos eps) 2) (sin x) (sin x)))) (fma (cos eps) (sin x) (sin x)))
14.0ms
(/ (* (sin x) (- (* (* (cos eps) (sin x)) (cos eps)) (sin x))) (fma (cos eps) (sin x) (sin x)))
Rules
1253×sqrt-div
1224×frac-times
899×frac-add
845×flip-+ flip3-+
684×associate-/r/
672×flip-- flip3--
526×associate-*r/
473×associate-/l*
471×associate-*l/
398×*-commutative
367×clear-num
344×frac-2neg
302×associate-/l/
240×div-inv
194×frac-sub
183×exp-neg
181×prod-diff
145×*.c-commutative
138×associate-*l*.c
137×neg-sub0
122×exp-diff
115×sub-neg
114×associate-/r*
109×sqr-pow
100×distribute-lft-out.c
91×fma-neg
90×associate-*r*
86×un-div-inv
68×times-frac
64×associate-*l*
59×tan-quot
57×fma-udef
48×distribute-rgt-in sub-div distribute-neg-frac distribute-lft-in
46×log-div
44×difference-of-squares
36×unpow3
32×unpow2 +-commutative
31×associate-+r+
30×div-sub
29×pow1/2
26×pow-to-exp
25×complex-mul-def exp-prod
24×exp-lft-sqr
23×unpow-prod-down
22×neg-mul-1
20×sum-cubes log-prod unswap-sqr
16×associate--l- cbrt-div
15×distribute-lft-out-- distribute-rgt-out--
13×associate-+l+
12×pow-prod-down associate--l+
11×pow1/3
10×fma-def prod-exp
inv-pow
cbrt-prod pow-exp
associate-+l- pow2
difference-cubes +.c-commutative remove-double-div
pow-prod-up pow-pow pow-sqr
associate-+l+.c distribute-rgt-out.c sin-mult tan-sum cos-sum complex-add-def sin-sum log-rec
sqrt-prod sin-cos-mult swap-sqr cos-mult associate--r+
sqrt-unprod distribute-lft-neg-out rem-square-sqrt
distribute-lft-out pow-unpow associate-+r- diff-atan diff-cos pow-flip distribute-frac-neg rec-exp frac-2neg.c diff-sin diff-log

bsearch1.2s (0.7%)

end1.0ms (0.0%)