Date:Wednesday, April 22nd, 2020
Commit:1c116713 on better-rr
Hostname:warfa with Racket 7.5
Seed:2020113
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

prune5.6m (37.4%)

Filtered
248831 candidates to 59385 candidates (23.9%)

simplify2.9m (19.0%)

Algorithm
197×egg-herbie

end2.5m (16.8%)

sample1.8m (12.0%)

Algorithm
56×intervals
16×halfpoints
Results
23.2s67425×body1280valid
17.2s16947×body2560valid
7.9s42070×body640valid
4.1s12926×body10240exit
2.8s92934×body80valid
2.4s20746×body320valid
1.8s63990×body80nan
1.3s2330×body1280nan
810.0ms11008×body160valid
756.0ms1872×body640nan
585.0ms47493×pre80true
228.0ms920×body320nan
119.0ms376×body5120valid
67.0ms474×body160nan

rewrite1.3m (8.9%)

Algorithm
125×rewrite-expression-head
Calls

397 calls:

7.3s
(- (* (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0)))) (* (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0)))))
2.4s
(* (/ (* (cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a))) (cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a)))) (* (cbrt (cbrt a)) (cbrt (cbrt a)))) (/ (cbrt (+ (/ b (* (cbrt a) (cbrt a))) (cbrt a))) (* (cbrt (cbrt a)) b)))
831.0ms
(/ (- (- (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))) (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))))
493.0ms
(/ (- (- (+ (* 1.0 (/ x (pow (cbrt 1.0) 2))) (* 1.0 (/ 1 (pow (cbrt 1.0) 2)))) (* x (pow (cbrt 1.0) 4)))) (* (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (+ (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))))
295.0ms
(- (/ (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))) (/ (* 1.0 x) (fma x 1.0 (- (log 1.0) (* 1/2 (/ (pow x 2) (pow 1.0 2)))))))
Rules
1165819×add-sqr-sqrt
653033×unswap-sqr
323054×cbrt-prod
278254×times-frac
272933×sqrt-prod
254463×associate-*r*
209129×*-un-lft-identity
167757×prod-diff
159064×swap-sqr
128921×add-cube-cbrt
96711×associate-*l*
46805×difference-of-squares
39770×*-commutative
28876×distribute-lft-out
15960×associate-/r*
13500×distribute-rgt-neg-in
13285×distribute-lft-neg-in
11393×associate-/l*
8034×frac-times
7314×frac-add
6776×unpow-prod-down
5238×distribute-lft-out--
5060×frac-sub
3802×div-inv
3357×associate-*r/
3027×sqr-pow
2749×clear-num
2467×frac-2neg
1915×add-cbrt-cube
1696×unpow2
1548×fma-neg
1514×add-exp-log
1258×pow1
1213×associate-/l/
1099×associate-*l/
1012×cbrt-unprod
805×flip-+
803×flip3-+
759×neg-mul-1
717×associate-/r/
660×add-log-exp
600×cbrt-div
552×cbrt-undiv
542×un-div-inv
532×log-pow
412×prod-exp
383×log1p-expm1-u div-exp expm1-log1p-u
274×log-prod
262×sqrt-div
252×associate-+l+ unpow3
247×distribute-rgt-out
227×flip--
225×flip3--
220×pow-prod-down
183×fma-def
162×associate--l+
156×log-div
145×pow-unpow *.c-commutative
143×exp-prod
138×tan-quot associate-*l*.c
113×pow-exp
109×pow-to-exp
107×diff-log
100×distribute-lft-out.c
97×sub-neg
76×pow1/3
64×difference-cubes
56×sqrt-pow1
55×pow1/2
53×1-exp
45×fma-udef
43×rec-exp
42×+-commutative
41×distribute-rgt-in distribute-lft-in
40×pow-prod-up
38×sum-log
37×pow-flip div-sub
36×pow-sqr
32×rem-sqrt-square rem-log-exp
29×log-rec
28×neg-sub0
25×pow-pow associate-+r+ complex-mul-def
22×hypot-def
21×sub-div
20×associate--l-
16×pow-plus
15×neg-log
13×associate-+l-
12×inv-pow pow2 remove-double-div associate--r+
11×exp-sum
10×distribute-rgt-out--
9×distribute-lft1-in
8×rem-cube-cbrt
7×difference-of-sqr-1
6×exp-diff +.c-commutative rem-cbrt-cube
5×distribute-lft-neg-out
4×associate-+l+.c distribute-rgt-out.c complex-add-def distribute-frac-neg cos-sum cos-mult tan-sum distribute-neg-frac sin-sum
3×sin-cos-mult sqrt-unprod expm1-def sin-mult
2×rem-exp-log associate--r- exp-neg expm1-log1p rem-square-sqrt
1×log1p-udef associate-+r- diff-atan log1p-expm1 diff-cos unsub-neg expm1-udef exp-to-pow diff-sin

series46.6s (5.2%)

Calls

397 calls:

2.2s
(/ (- (- (+ (* 1.0 (/ x (pow (cbrt 1.0) 2))) (* 1.0 (/ 1 (pow (cbrt 1.0) 2)))) (* x (pow (cbrt 1.0) 4)))) (* (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (+ (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0))))))
1.5s
(* (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))) (cbrt (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
965.0ms
(* (* (- (sqrt x)) (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (+ (* 1.0 (/ (sqrt (+ x 1.0)) (cbrt 1.0))) (* (sqrt x) (* (cbrt 1.0) (cbrt 1.0)))))
790.0ms
(- (/ (* (+ (tan x) (tan eps)) (fma (tan eps) (tan x) 1)) (- 1 (* (* (tan eps) (tan x)) (* (tan eps) (tan x))))) (tan x))
776.0ms
(fma 1 (pow (+ x 1.0) (/ 1.0 n)) (- (* (* (pow (cbrt (cbrt x)) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))) (pow (cbrt (* (cbrt x) (cbrt x))) (/ 1.0 n)))))

regimes3.4s (0.4%)

Accuracy

Total 33.2b remaining (20.2%)

Threshold costs 7.8b (4.7%)

5.0b82%quad2m (problem 3.2.1, negative)
5.0b82%quadm (p42, negative)
4.6b83.2%quad2p (problem 3.2.1, positive)
4.6b83.3%quadp (p42, positive)
3.3b0%expq3 (problem 3.4.2)

localize2.0s (0.2%)

bsearch1.3s (0.1%)