Details

simplify5.5m (37.9%)

sample5.1m (35.3%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66924×body1280valid
42.8s17449×body2560valid
26.9s42199×body640valid
14.6s12801×body10240exit
11.4s93801×body80valid
8.5s20601×body320valid
7.1s62840×body80nan
2.9s10865×body160valid
2.3s47582×pre80true
770.0ms649×body1280nan
571.0ms517×body5120valid
485.0ms599×body640nan
221.0ms328×body320nan
51.0ms180×body160nan

prune2.9m (20.0%)

series38.1s (4.4%)

Calls

353 calls:

840.0ms
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (/ (* (tan x) (sin eps)) (cos eps)) (/ (* (tan x) (sin eps)) (cos eps))))) (+ 1 (/ (* (tan x) (sin eps)) (cos eps))) (- (tan x)))
663.0ms
(* (/ (expm1 (* (+ a b) eps)) (expm1 (* eps b))) (/ eps (expm1 (* eps a))))
620.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))
601.0ms
(/ (/ 1 (sqrt (+ (sqrt (+ x 1)) (sqrt x)))) (hypot (sqrt (sqrt (+ x 1))) (sqrt (sqrt x))))
534.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite9.1s (1.1%)

Algorithm
113×rewrite-expression-head
Calls

353 calls:

613.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (tan x) (sin eps)) (cos eps)))) (tan x))
231.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
227.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
216.0ms
(/ (- (sqrt (- (* b_2 b_2) (* a c))) b_2) a)
212.0ms
(* (* -2 (+ (* (sin (* eps 1/2)) (cos x)) (* (cos (* eps 1/2)) (sin x)))) (sin (* eps 1/2)))
Rules
9170×*-un-lft-identity
8311×times-frac
7400×add-sqr-sqrt
6013×add-cube-cbrt
3375×prod-diff
2144×sqrt-prod
1326×pow1
1123×distribute-lft-out
1042×add-exp-log
897×add-cbrt-cube
842×cbrt-prod
552×div-inv
529×add-log-exp
494×associate-+l+
486×difference-of-squares
474×associate-/r*
457×distribute-lft-out--
430×associate-/r/
378×associate-*r*
358×associate-*l*
351×fma-neg
350×associate-/l* log1p-expm1-u pow-prod-up
346×expm1-log1p-u insert-posit16
341×distribute-rgt-neg-in
317×distribute-lft-neg-in
283×flip-+ flip3-+
228×div-exp
218×pow-plus
213×pow-prod-down
208×prod-exp
186×cbrt-unprod
155×cbrt-undiv
153×flip3-- flip--
151×associate-*l/
140×unswap-sqr
127×swap-sqr
123×sqrt-div
120×pow-sqr
117×sqrt-pow1
116×fma-def
97×unpow-prod-down
92×pow1/3
88×neg-mul-1
86×cbrt-div
84×frac-times
83×pow1/2
72×pow2
69×log-prod
68×*-commutative
67×frac-2neg clear-num sub-neg
65×pow-unpow diff-log
62×associate-*r/
59×difference-of-sqr-1
56×distribute-rgt-in log-pow distribute-lft-in
55×associate-/l/
43×exp-prod
42×pow-flip 1-exp rec-exp
41×frac-add
36×rem-sqrt-square
34×tan-quot
33×sum-log sqr-pow
32×fma-udef
28×inv-pow
25×pow3 +-commutative
19×div-sub
18×hypot-def
17×frac-sub
16×pow-div
13×log-div
12×distribute-rgt-out-- associate--l+ distribute-neg-frac
9×sin-mult
8×associate--r+
7×associate--l- cos-mult
6×expm1-udef pow-exp pow-to-exp
5×neg-sub0 neg-log sqrt-unprod pow-pow rem-log-exp
4×expm1-log1p exp-diff sub-div
3×sin-sum associate-+r+ log1p-udef sqr-sin cos-sum
2×sin-cos-mult +.c-commutative un-div-inv tan-sum associate-+l- log1p-def distribute-neg-in
1×diff-atan exp-sum cube-unmult distribute-rgt-neg-out frac-2neg-c hypot-udef rem-exp-log rem-square-sqrt diff-sin sqr-cos rem-cbrt-cube diff-cos expm1-def

regimes5.0s (0.6%)

Accuracy

Total 25.3b remaining (19.3%)

Threshold costs 5.6b (4.3%)

6.1b78%quad2p (problem 3.2.1, positive)
4.2b85.1%quadm (p42, negative)
4.2b85.3%quad2m (problem 3.2.1, negative)
2.8b16.7%expq3 (problem 3.4.2)
2.4b80.3%2nthrt (problem 3.4.6)

localize4.9s (0.6%)

bsearch2.1s (0.2%)

end1.0ms (0.0%)