Details

sample5.2m (42.7%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66923×body1280valid
40.1s17483×body2560valid
27.8s41576×body640valid
14.1s12622×body10240exit
11.0s94031×body80valid
10.3s20441×body320valid
7.7s62674×body80nan
3.8s11017×body160valid
1.9s47397×pre80true
930.0ms442×body5120valid
770.0ms660×body1280nan
596.0ms699×body640nan
212.0ms401×body320nan
56.0ms182×body160nan

simplify3.4m (27.9%)

prune2.5m (20.2%)

series38.4s (5.3%)

Calls

366 calls:

Slowest
1.7s
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (+ (* b (* (* 1/6 eps) (* (* eps b) (* eps b)))) (* eps b)) (* (* (* eps b) (* eps b)) 1/2))))
629.0ms
(* (cbrt x) (cbrt x))
579.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (sin eps)) (* (cos x) (cos eps))))) (tan x))
520.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
483.0ms
(/ (- (* (- (/ 1 (+ x 1)) (/ 2 x)) (- (/ 1 (+ x 1)) (/ 2 x))) (* (/ 1 (- x 1)) (/ 1 (- x 1)))) (- (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1))))

rewrite16.0s (2.2%)

Algorithm
116×rewrite-expression-head
Calls

366 calls:

Slowest
964.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1)) (* (- (exp (* a eps)) 1) (+ (+ (* b (* (* 1/6 eps) (* (* eps b) (* eps b)))) (* eps b)) (* (* (* eps b) (* eps b)) 1/2))))
523.0ms
(* (* (* x (sqrt (+ (* 1/3 (* x x)) 2))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2)))) (sqrt (sqrt (+ (* 1/3 (* x x)) 2))))
487.0ms
(sqrt (- (* b_2 b_2) (* a c)))
463.0ms
(+ (+ (log (/ (* (cbrt (+ N 1)) (cbrt (+ N 1))) (sqrt N))) (log (/ 1 (* (cbrt (sqrt N)) (cbrt (sqrt N)))))) (log (/ (cbrt (+ N 1)) (cbrt (sqrt N)))))
415.0ms
(* (* (* (* a x) (* a x)) (* a x)) 1/6)
Rules
4360×add-sqr-sqrt
4264×*-un-lft-identity
3151×times-frac
1951×add-cube-cbrt
1313×add-exp-log
1282×pow1
1139×add-cbrt-cube
1083×sqrt-prod
916×cbrt-prod
837×difference-of-squares
630×add-log-exp
594×associate-*r*
592×distribute-lft-out--
574×associate-*l*
538×frac-times
475×distribute-lft-out
453×swap-sqr
445×flip-+ flip3-+
415×prod-exp
377×associate-*l/
372×pow-prod-down
366×cbrt-unprod
359×insert-posit16
358×cbrt-div
318×div-inv
314×flip3-- flip--
284×log-prod associate-*r/
257×associate-/r*
248×frac-sub
240×associate-/l*
216×sqrt-div
194×unswap-sqr div-exp
142×cbrt-undiv
141×associate-/r/
139×associate-/l/
134×pow-prod-up
115×associate-+r+
113×sub-neg
104×*-commutative
102×sqrt-pow1 diff-log
101×pow-unpow
77×pow1/3 pow1/2
76×pow-sqr
73×unpow-prod-down
59×frac-add
57×frac-2neg clear-num
53×difference-of-sqr-1
52×pow-plus log-pow
51×distribute-rgt-in distribute-lft-in
47×distribute-rgt-neg-in
41×pow-flip log-div
40×un-div-inv
36×sum-log sqr-pow
34×1-exp rec-exp exp-prod
32×pow2
27×associate--l+
24×+-commutative rem-sqrt-square
22×tan-quot
21×inv-pow
20×associate-+l+ div-sub
17×rem-log-exp
16×pow-exp sin-mult
15×pow-to-exp
14×associate--l-
13×associate--r+ pow-pow exp-to-pow
12×neg-sub0
9×distribute-lft-neg-in sin-sum
8×cos-mult neg-log associate-+l-
5×distribute-rgt-out distribute-rgt1-in
4×sqrt-unprod
3×associate-+r- sin-cos-mult pow3 sqr-sin neg-mul-1 cos-sum
2×exp-diff distribute-rgt-out-- log-rec sub-div tan-sum exp-neg +.c-commutative rem-square-sqrt associate--r-
1×diff-atan distribute-lft1-in distribute-frac-neg frac-2neg-c rem-exp-log diff-sin diff-cos rem-cbrt-cube unsub-neg pow-sub pow-neg

localize6.2s (0.8%)

regimes5.7s (0.8%)

Accuracy

Total 30.6b remaining (22.1%)

Threshold costs 6.6b (4.8%)

5.1b82.3%quad2m (problem 3.2.1, negative)
5.0b82.5%quadm (p42, negative)
4.8b82.5%quad2p (problem 3.2.1, positive)
4.6b83.2%quadp (p42, positive)
3.3b0%expq3 (problem 3.4.2)

bsearch1.1s (0.2%)

end2.0ms (0.0%)