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:arithmeticrules:polynomialsrules:fractionsrules:exponentsrules:trigonometryrules:hyperbolicrules:complexrules:specialrules:boolsrules:branchesgenerate:rrgenerate:taylorgenerate:simplifygenerate:better-rrreduce:regimesreduce:avg-errorreduce:binary-searchreduce:branch-expressionsprecision:doubleprecision:fallback
default

Details

prune7.8m (59.2%)

Filtered
75973 candidates to 73348 candidates (96.5%)

simplify2.5m (19.0%)

Algorithm
196×egg-herbie

sample1.8m (13.7%)

Algorithm
55×intervals
16×halfpoints
Results
22.1s64584×body1280valid
17.2s16978×body2560valid
7.3s39962×body640valid
4.3s13262×body10240exit
2.8s91326×body80valid
2.3s19596×body320valid
1.9s64376×body80nan
1.3s2241×body1280nan
811.0ms10830×body160valid
727.0ms1849×body640nan
573.0ms47473×pre80true
222.0ms898×body320nan
141.0ms459×body5120valid
63.0ms444×body160nan

series34.5s (4.4%)

Calls

401 calls:

1.5s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan eps) (tan x)) 3))) (+ (* 1 1) (+ (* (* (tan eps) (tan x)) (* (tan eps) (tan x))) (* 1 (* (tan eps) (tan x)))))) (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)))
509.0ms
(/ (* 1.0 (/ (+ 1.0 0) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
497.0ms
(/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (+ (pow (* 1.0 x) 3) (pow (log 1.0) 3)) 1.0) (* (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) (* 1/2 (/ (pow x 2) 1.0)))))

rewrite23.9s (3.0%)

Algorithm
125×rewrite-expression-head
Calls

401 calls:

5.9s
(- (+ (+ (/ (* (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)))
133.0ms
(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (- (+ (* 0.5 (/ 1 (* x n))) (* 0.25 (/ (log x) (* x (pow n 2))))) (* 0.25 (/ 1 (* (pow x 2) n)))))
103.0ms
(* (+ (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2))) (+ (- (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (log (/ 1 x)) (* x (pow n 2)))))) (/ (/ 0.5 n) x)))
54.0ms
(* (/ (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))) (- (* (+ (pow (* 1.0 x) 3) (pow (log 1.0) 3)) 1.0) (* (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) (* 1/2 (/ (pow x 2) 1.0))))) (* (+ (* (* 1.0 x) (* 1.0 x)) (- (* (log 1.0) (log 1.0)) (* (* 1.0 x) (log 1.0)))) 1.0))
36.0ms
(* (/ (/ 1.0 (+ (* (sqrt x) (- (sqrt x) (sqrt (+ x 1.0)))) (+ x 1.0))) (+ (sqrt (+ x 1.0)) (sqrt x))) (+ (* (sqrt (+ x 1.0)) (sqrt (+ x 1.0))) (- (* (sqrt x) (sqrt x)) (* (sqrt (+ x 1.0)) (sqrt x)))))
Rules
201389×frac-add
104139×associate-/r*
77694×clear-num
77054×frac-2neg
70047×frac-sub
61607×frac-times
60179×associate-/l*
56796×sqr-pow
43274×associate-*r*
32572×*-commutative
25295×unpow2
24296×unpow3
15254×associate-*l*
13470×associate-*r/
7180×unswap-sqr
4487×flip-+ flip3-+
3038×associate-*l/
1642×distribute-neg-frac
1092×un-div-inv
973×associate-/l/
509×sqrt-div
491×flip-- flip3--
469×associate-/r/
405×div-inv
205×inv-pow
196×log-pow
183×exp-neg
145×*.c-commutative
141×sub-neg
140×neg-sub0
138×associate-*l*.c
122×exp-diff
121×times-frac
103×+-commutative
100×distribute-lft-out.c
88×tan-quot
85×difference-of-squares
78×distribute-rgt-in distribute-lft-in
49×sub-div
42×associate-+l+
40×div-sub
38×log-div
36×pow1/2
34×associate--l+
32×associate-+r+
31×sum-cubes
30×neg-mul-1
25×complex-mul-def
22×pow-to-exp
20×distribute-lft-out--
19×exp-prod
18×log-prod
17×associate--l-
16×cbrt-prod
14×distribute-rgt-out--
12×difference-cubes distribute-neg-in cbrt-div associate--r+
11×pow1/3
10×pow-prod-down
9×associate-+l-
8×remove-double-div exp-sum pow-exp pow2
7×sin-mult cos-mult prod-exp
6×+.c-commutative
5×pow-pow sqrt-unprod distribute-frac-neg
4×unpow-prod-down sin-sum complex-add-def associate-+l+.c distribute-rgt-out.c swap-sqr tan-sum cos-sum log-rec
3×sqrt-prod pow-prod-up sin-cos-mult associate-+r- pow-sqr distribute-lft-neg-out exp-lft-cube
2×rem-square-sqrt distribute-rgt-neg-out
1×diff-log distribute-lft-out sub0-neg pow-unpow diff-atan diff-cos pow-flip frac-2neg.c diff-sin

regimes2.4s (0.3%)

Accuracy

Total 17.2b remaining (13.6%)

Threshold costs 8.0b (6.3%)

3.1b0%expq3 (problem 3.4.2)
1.7b83.8%2nthrt (problem 3.4.6)
1.6b93.7%quadp (p42, positive)
1.5b93.9%quadm (p42, negative)
1.3b93.9%expax (section 3.5)

localize2.2s (0.3%)

bsearch1.2s (0.2%)

end1.0ms (0.0%)