Details

simplify10.5m (55.3%)

sample4.4m (23.2%)

Algorithm
56×intervals
16×halfpoints
Results
49.0s66642×body1280valid
33.4s17576×body2560valid
18.9s42571×body640valid
10.5s13021×body10240exit
8.4s93739×body80valid
6.1s20711×body320valid
5.1s63589×body80nan
1.8s10639×body160valid
1.6s47423×pre80true
553.0ms640×body1280nan
444.0ms646×body640nan
381.0ms172×body160nan
378.0ms478×body5120valid
110.0ms366×body320nan

prune1.9m (10.2%)

series1.1m (5.9%)

Calls

391 calls:

6.1s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (+ (* (* 1/6 (* b (* b b))) (* eps (* eps eps))) (+ (* eps b) (* (* (* b eps) (* b eps)) 1/2)))))
3.6s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
3.1s
(- (* (/ (+ (tan x) (tan eps)) (- (* 1 1) (/ (* (* (sin x) (sin eps)) (* (sin x) (sin eps))) (* (* (cos x) (cos eps)) (* (cos x) (cos eps)))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
1.1s
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
713.0ms
(- (cbrt (* (* (posit16->real (real->posit16 (+ (+ 1 (/ 1.0 (* n x))) (* 1.0 (/ (log x) n))))) (pow (+ x 1.0) (/ 1.0 n))) (pow (+ x 1.0) (/ 1.0 n)))) (pow x (/ 1.0 n)))

rewrite37.4s (3.3%)

Algorithm
122×rewrite-expression-head
Calls

391 calls:

4.2s
(- (+ (+ 1.0 (- (/ 0.5 n) (/ 0.16666666666666669 (* n n)))) (* 1.0 (log n))) 1.0)
1.4s
(* (- (exp (* a eps)) 1.0) (+ (* (* 1/6 (* b (* b b))) (* eps (* eps eps))) (+ (* eps b) (* (* (* b eps) (* b eps)) 1/2))))
1.3s
(* (/ (+ (* x (* (+ x 1.0) 1.0)) (* (- x 1.0) (- (* 1.0 x) (* (+ x 1.0) 2.0)))) (* (* (- x 1.0) (* (+ x 1.0) (- x 1.0))) x)) (- x 1.0))
1.3s
(* (/ 2.0 (* (* (- x 1.0) (* (+ x 1.0) (- x 1.0))) x)) (- x 1.0))
755.0ms
(+ (+ 1.0 (- (/ 0.5 n) (/ 0.16666666666666669 (* n n)))) (* 1.0 (log n)))
Rules
3820×*-un-lft-identity
3510×add-sqr-sqrt
2851×times-frac
2044×add-cube-cbrt
1717×pow1
1461×add-exp-log
1372×add-cbrt-cube
1213×sqrt-prod
689×add-log-exp
583×associate-*l*
580×associate-*r*
570×pow-prod-down
537×prod-exp
530×difference-of-squares
497×cbrt-unprod
487×distribute-lft-out--
447×distribute-lft-out
379×insert-posit16
354×flip3-- flip--
337×associate-*l/
325×associate-/l*
275×frac-times
261×cbrt-prod
250×log-prod
236×associate-/r/
224×associate-/r*
222×associate-*r/
213×flip-+ flip3-+
193×pow-prod-up
175×div-exp
169×unswap-sqr
152×cbrt-undiv
151×div-inv
124×swap-sqr sub-neg
119×*-commutative
113×pow-sqr
106×diff-log
104×pow-unpow
103×sqrt-pow1
97×sqrt-div
87×distribute-rgt-neg-in
86×pow-plus log-pow
77×exp-prod associate-/l/ unpow-prod-down
73×distribute-lft-neg-in
71×distribute-rgt-in distribute-lft-in
69×pow1/2
64×tan-quot
61×frac-2neg clear-num
60×cube-unmult frac-add
51×sum-log
49×pow2
42×pow1/3
36×associate-+l+
35×div-sub
33×sqr-pow
31×rem-sqrt-square
29×pow3 log-div
26×frac-sub sum-cubes
25×+-commutative
24×neg-mul-1
23×associate-+r+ associate--l+ difference-cubes
21×rem-log-exp
16×pow-exp pow-to-exp
14×exp-to-pow complex-mul-def
13×sin-mult
11×1-exp rec-exp
10×associate--l- associate--r+
9×neg-sub0 cos-mult
8×pow-pow
6×cbrt-div neg-log sqrt-unprod rem-exp-log associate-+l- exp-lft-cube
5×associate-+r-
4×distribute-frac-neg un-div-inv distribute-neg-frac
3×sin-sum sin-cos-mult *.c-commutative difference-of-sqr-1 sub-div sqr-sin +.c-commutative cos-sum
2×associate-*l*.c frac-2neg.c rem-square-sqrt tan-sum distribute-neg-in complex-add-def
1×pow-flip remove-posit16 diff-atan unsub-neg distribute-rgt-neg-out inv-pow +-inverses distribute-rgt-out-- diff-sin associate-+l+.c rem-cbrt-cube diff-cos distribute-rgt-out

regimes13.2s (1.2%)

Accuracy

Total 38.9b remaining (26.3%)

Threshold costs 6.3b (4.3%)

14.6b30.4%expax (section 3.5)
4.7b83.9%quad2p (problem 3.2.1, positive)
4.7b83.9%quadp (p42, positive)
3.6b86.5%quad2m (problem 3.2.1, negative)
1.8b92.9%quadm (p42, negative)

localize9.2s (0.8%)

bsearch1.9s (0.2%)

end1.0ms (0.0%)