Details

simplify5.9m (45.8%)

sample4.4m (34.3%)

Algorithm
56×intervals
16×halfpoints
Results
49.7s66823×body1280valid
33.6s16913×body2560valid
18.4s42623×body640valid
10.4s12526×body10240exit
9.2s93843×body80valid
7.0s20586×body320valid
4.8s63900×body80nan
2.6s10767×body160valid
2.0s47359×pre80true
514.0ms649×body1280nan
329.0ms683×body640nan
268.0ms458×body5120valid
137.0ms348×body320nan
67.0ms192×body160nan

prune1.3m (9.9%)

series48.7s (6.3%)

Calls

370 calls:

2.1s
(fma (pow (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (/ 1.0 n)) (pow (cbrt (+ x 1.0)) (/ 1.0 n)) (- (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)))))
1.1s
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
718.0ms
(cbrt (fma 0.022222222222222223 (pow x 3) (fma 0.0021164021164021165 (pow x 5) (* 0.3333333333333333 x))))
577.0ms
(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))
531.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite17.9s (2.3%)

Algorithm
121×rewrite-expression-head
Calls

370 calls:

932.0ms
(* (/ 1.0 x) (- (/ 1 n) (/ (- (log x)) (pow n 2))))
585.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
509.0ms
(* (/ 1.0 (pow n 2)) (+ (/ (* (- (log x)) -1/3) x) (/ -2/3 (/ x (- (log x))))))
457.0ms
(- (exp (* (+ a b) eps)) 1.0)
429.0ms
(- (/ (+ (/ (sin eps) (cos eps)) (/ (sin x) (cos x))) (- 1 (* (tan x) (tan eps)))) (tan x))
Rules
13274×times-frac
11507×*-un-lft-identity
10890×add-sqr-sqrt
9089×add-cube-cbrt
6024×prod-diff
1921×unpow-prod-down
1407×sqrt-prod
1364×distribute-rgt-in distribute-lft-in
1316×add-exp-log
1182×distribute-rgt-neg-in
1164×distribute-lft-neg-in
1154×pow1
975×add-cbrt-cube
746×div-inv
696×difference-of-squares
685×associate-/l*
654×distribute-lft-out
589×sqr-pow
568×add-log-exp
566×cbrt-prod
563×associate-*l*
556×distribute-lft-out--
522×log-pow
478×associate-*r*
425×fma-neg
398×unpow2
360×associate-/r/ log1p-expm1-u
359×associate-/r*
358×expm1-log1p-u
354×cube-prod
321×div-exp
317×neg-mul-1
316×prod-exp
247×associate-+l+
225×flip-- flip3--
196×cbrt-undiv
191×unswap-sqr
181×cbrt-unprod
157×sqrt-pow1
153×flip-+ flip3-+
127×fma-def
105×pow-unpow
104×pow-prod-down
95×log-prod
93×sub-neg swap-sqr
92×pow1/2
91×pow-exp
87×pow-to-exp
86×diff-log
84×cbrt-div sqrt-div
81×unpow3 cube-mult
79×frac-2neg clear-num
66×*-commutative
63×pow-prod-up associate-*r/
62×associate-/l/
55×associate-*l/
51×pow1/3
48×exp-prod
42×associate--l+
38×fma-udef frac-times
36×tan-quot
35×div-sub
31×pow-sqr
26×rem-sqrt-square
24×rec-exp 1-exp
23×log-div
22×sum-log
21×exp-sum
19×pow-pow
16×cube-div
15×+-commutative neg-sub0
14×frac-add
13×complex-mul-def frac-sub
11×pow-flip rem-log-exp
10×associate--r+
8×sqrt-unprod pow2 pow-plus associate-+l-
7×associate--l-
6×rem-cube-cbrt neg-log
5×un-div-inv inv-pow associate--r-
4×distribute-frac-neg quot-tan *.c-commutative
3×difference-cubes +.c-commutative rem-square-sqrt distribute-rgt-out-- rem-cbrt-cube expm1-udef sin-sum
2×cos-sum exp-diff sin-cos-mult log1p-udef unpow1/3 exp-neg log1p-expm1 expm1-log1p complex-add-def sin-mult tan-sum distribute-neg-frac
1×associate-+l+.c rem-exp-log associate-+r- diff-atan sub-div diff-cos unsub-neg associate-*l*.c hypot-def frac-2neg.c diff-sin

regimes3.9s (0.5%)

Accuracy

Total 23.5b remaining (13.1%)

Threshold costs 7.1b (4%)

4.8b45.8%expq3 (problem 3.4.2)
4.7b83.6%quad2p (problem 3.2.1, positive)
3.1b89.2%quadp (p42, positive)
1.4b83.8%2nthrt (problem 3.4.6)
1.2b95.2%quadm (p42, negative)

localize3.9s (0.5%)

bsearch3.3s (0.4%)

end1.0ms (0.0%)