Details

simplify5.8m (40.4%)

sample4.5m (31.7%)

Algorithm
56×intervals
16×halfpoints
Results
51.2s66935×body1280valid
32.6s17227×body2560valid
19.1s42341×body640valid
10.7s13053×body10240exit
8.7s93690×body80valid
6.5s20770×body320valid
5.4s63040×body80nan
2.2s10808×body160valid
1.6s47470×pre80true
953.0ms641×body640nan
778.0ms492×body5120valid
580.0ms711×body1280nan
151.0ms350×body320nan
33.0ms179×body160nan

prune2.5m (17.6%)

series55.6s (6.5%)

Calls

377 calls:

1.5s
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
922.0ms
(/ (+ 0 (* (* a c) 4.0)) (+ (fma (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c))))) (- b)) (+ (- b) b)))
917.0ms
(fma (pow (cbrt x) (/ 1.0 n)) (- (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))) (pow (cbrt (pow (+ x 1.0) (/ 1.0 n))) 3))
782.0ms
(- (/ (pow 1.0 3) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))) (/ (log1p (expm1 (pow (cos x) 3))) (fma 1.0 1.0 (* (cos x) (+ 1.0 (cos x))))))
521.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite21.9s (2.6%)

Algorithm
122×rewrite-expression-head
Calls

377 calls:

991.0ms
(- (/ (/ 1.0 (sqrt (cbrt x))) (fabs (cbrt x))) (/ (/ 1.0 (sqrt (cbrt (+ x 1.0)))) (fabs (cbrt (+ x 1.0)))))
543.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
467.0ms
(+ (/ (- (exp (+ x x)) (* 2.0 2.0)) (+ (exp x) 2.0)) (exp (- x)))
424.0ms
(* (/ (cbrt 1.0) (cbrt (/ (+ x 1.0) 1.0))) (/ (cbrt 1.0) (cbrt (/ (+ x 1.0) 1.0))))
289.0ms
(- (/ (/ 1.0 (fabs (cbrt x))) (sqrt (cbrt x))) (/ 1.0 (sqrt (+ x 1.0))))
Rules
60451×times-frac
38762×*-un-lft-identity
35597×add-sqr-sqrt
33319×add-cube-cbrt
20125×prod-diff
17482×sqrt-prod
9336×cbrt-prod
2146×distribute-lft-out
2012×div-inv
1798×unpow-prod-down
1221×associate-/r/
1142×add-exp-log
1099×cube-prod
937×sqrt-div
929×difference-of-squares
830×add-cbrt-cube
746×fma-neg
690×cbrt-div
665×associate-/l*
630×sqr-pow
603×pow1
590×distribute-lft-out--
585×add-log-exp
564×flip-+ flip3-+
467×distribute-rgt-neg-in
410×associate-*r*
408×distribute-lft-neg-in
406×associate-*l*
366×log1p-expm1-u
364×expm1-log1p-u
351×associate-/r*
331×unpow3 cube-mult
313×div-exp
249×associate-+l+
235×flip-- flip3--
227×swap-sqr
221×prod-exp
217×pow-unpow
176×log-prod
169×cbrt-undiv
155×unswap-sqr
148×fma-def
143×exp-sum
136×neg-mul-1
117×cbrt-unprod
96×pow1/3
85×diff-log
80×pow-exp
79×clear-num frac-2neg
77×sub-neg
76×associate-/l/ pow-to-exp
68×associate-*l/
63×pow-prod-down
55×1-exp
48×log-pow
42×unpow2
41×*-commutative
39×tan-quot
37×frac-times associate-*r/
31×fma-udef div-sub sqrt-pow1
29×pow1/2 rem-sqrt-square
28×sum-log
27×frac-add
26×rec-exp
25×frac-sub
24×pow-pow
22×log-div
20×+-commutative
18×neg-sub0
14×distribute-rgt-out-- associate--l+
13×pow-prod-up pow-sqr complex-mul-def associate--r+
11×rem-cube-cbrt distribute-rgt-in rem-log-exp distribute-lft-in
10×cube-div associate--l- neg-log
9×associate-+l-
8×pow-flip
7×pow2 pow-plus
6×inv-pow
5×difference-cubes sub-div
4×*.c-commutative
3×exp-diff exp-neg +.c-commutative distribute-frac-neg hypot-def cos-mult rem-cbrt-cube
2×sin-sum cos-sum expm1-log1p complex-add-def sin-mult tan-sum expm1-udef frac-2neg.c
1×rem-exp-log associate-+l+.c sin-cos-mult un-div-inv log1p-udef pow3 diff-atan log1p-expm1 diff-cos associate-+r+ associate-*l*.c exp-prod exp-to-pow diff-sin

regimes5.4s (0.6%)

Accuracy

Total 26.9b remaining (19.8%)

Threshold costs 6.8b (5%)

4.7b83.3%quadp (p42, positive)
4.7b80.7%quad2p (problem 3.2.1, positive)
4.0b85.1%quadm (p42, negative)
3.1b0%expq3 (problem 3.4.2)
1.3b84.7%2nthrt (problem 3.4.6)

localize3.4s (0.4%)

bsearch1.9s (0.2%)

end1.0ms (0.0%)