Details

simplify4.8m (39.2%)

sample4.4m (36.4%)

Algorithm
56×intervals
16×halfpoints
Results
49.0s66906×body1280valid
32.6s17504×body2560valid
20.6s42466×body640valid
10.5s12824×body10240exit
8.2s93701×body80valid
6.1s20408×body320valid
4.3s62864×body80nan
2.1s10800×body160valid
1.9s47484×pre80true
657.0ms719×body1280nan
358.0ms661×body640nan
306.0ms490×body5120valid
118.0ms359×body320nan
86.0ms193×body160nan

prune1.7m (14.1%)

series48.1s (6.6%)

Calls

387 calls:

1.3s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma (* a a) (* 1/2 (* eps eps)) (fma (* eps (* eps eps)) (* 1/6 (* a (* a a))) (* eps a))) (- (exp (* b eps)) 1.0)))
605.0ms
(- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))
585.0ms
(/ 1.0 (* (* (sqrt x) (sqrt (+ x 1.0))) (+ (* 1.0 (sqrt (+ x 1.0))) (* (sqrt x) 1.0))))
574.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))
524.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))

rewrite14.0s (1.9%)

Algorithm
123×rewrite-expression-head
Calls

387 calls:

631.0ms
(* (* x (* (* x a) (* x a))) (* a 1/6))
446.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
231.0ms
(* (/ (cos y) (sqrt (sqrt (exp x)))) (/ (/ 1 (sqrt (exp x))) (sqrt (sqrt (exp x)))))
208.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (/ (* (sin x) (tan eps)) (cos x)))) (tan x))
204.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
Rules
9582×*-un-lft-identity
9139×add-sqr-sqrt
9135×times-frac
7304×add-cube-cbrt
4740×prod-diff
3144×sqrt-prod
1195×add-exp-log
1093×add-cbrt-cube
1062×pow1
926×unpow-prod-down
645×add-log-exp
638×difference-of-squares
613×distribute-lft-out
571×associate-*r*
561×div-inv
549×fma-neg
519×distribute-lft-out--
461×associate-*l*
449×cbrt-prod
420×associate-/l*
381×associate-/r/
376×expm1-log1p-u log1p-expm1-u
334×prod-exp
329×sqr-pow
304×cbrt-unprod
285×associate-/r*
280×log-prod
271×associate-+l+ flip3-- flip--
269×pow-prod-down
261×distribute-rgt-neg-in
243×distribute-lft-neg-in
212×unswap-sqr
201×cube-prod
200×flip-+ flip3-+
185×div-exp
166×associate-*l/
156×cbrt-undiv
126×log-pow
124×sqrt-div
112×sub-neg
110×diff-log
99×associate-*r/
88×exp-prod
84×sqrt-pow1
81×exp-sum
80×*-commutative
79×swap-sqr associate-/l/
76×frac-times fma-def
74×neg-mul-1
71×pow-unpow distribute-rgt-in distribute-lft-in
66×pow1/3
65×frac-2neg clear-num
62×pow-prod-up
55×pow1/2
51×unpow3 cube-mult
48×cbrt-div
44×frac-add
40×pow-sqr
39×pow-plus
38×log-div
30×tan-quot associate--l+ div-sub rem-sqrt-square
26×fma-udef
25×sum-log
21×pow2
20×rem-log-exp
19×+-commutative
17×associate-+r+
16×pow-flip
15×1-exp rec-exp
14×frac-sub complex-mul-def
13×neg-sub0 associate--l- pow3 difference-cubes
12×exp-diff
11×pow-div
10×cube-unmult
9×pow-exp associate--r+ pow-to-exp
8×distribute-neg-frac rem-exp-log
7×pow-pow exp-to-pow
6×distribute-frac-neg neg-log
5×cos-mult hypot-def sin-mult
4×sin-cos-mult sqrt-unprod inv-pow un-div-inv
3×distribute-rgt-out-- *.c-commutative sqr-cos +.c-commutative
2×associate-*l*.c sin-sum associate-+r- sub-div exp-neg associate-+l- cos-sum tan-sum distribute-neg-in associate--r- complex-add-def
1×quot-tan diff-atan rem-cube-cbrt distribute-rgt-neg-out frac-2neg.c rem-square-sqrt diff-sin associate-+l+.c diff-cos

regimes6.2s (0.8%)

Accuracy

Total 28.7b remaining (18.1%)

Threshold costs 6.7b (4.2%)

4.2b87.8%quad2p (problem 3.2.1, positive)
4.1b87.9%quadp (p42, positive)
3.7b87.1%quadm (p42, negative)
3.7b87.2%quad2m (problem 3.2.1, negative)
3.4b0%expq3 (problem 3.4.2)

localize5.0s (0.7%)

bsearch1.6s (0.2%)

end1.0ms (0.0%)