Details

simplify12.5m (54.9%)

sample4.9m (21.6%)

Algorithm
56×intervals
16×halfpoints
Results
58.6s66750×body1280valid
33.7s16915×body2560valid
25.0s42952×body640valid
13.4s12723×body10240exit
10.8s93370×body80valid
8.5s20720×body320valid
6.2s63553×body80nan
2.9s10923×body160valid
2.1s47339×pre80true
562.0ms622×body1280nan
443.0ms655×body640nan
428.0ms520×body5120valid
206.0ms358×body320nan
44.0ms187×body160nan

prune2.8m (12.3%)

series1.3m (5.7%)

Calls

402 calls:

6.0s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma eps b (fma (* 1/2 (* eps eps)) (* b b) (* (* (* eps (* eps eps)) 1/6) (* (* b b) b))))))
2.1s
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan x)) (* (tan eps) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
2.1s
(fma (/ (+ (tan x) (tan eps)) (- (* 1 1) (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps))) (- (tan x)))
1.8s
(fma (- (pow (cbrt x) (/ 1.0 n))) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))
1.8s
(fma (- (pow (cbrt x) (/ 1.0 n))) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n)) (* (pow (cbrt x) (/ 1.0 n)) (pow (* (cbrt x) (cbrt x)) (/ 1.0 n))))

rewrite39.9s (2.9%)

Algorithm
123×rewrite-expression-head
Calls

402 calls:

1.0s
(* (* (* eps (* eps eps)) 1/6) (* (* b b) b))
955.0ms
(+ 1 (log (exp (- (/ (/ (sin x) x) (cos x)) (fma (/ (/ (sin x) x) x) (/ (sin x) (cos x)) (/ (sin x) x))))))
896.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
887.0ms
(* (/ (fma 0.3333333333333333 (* 0.3333333333333333 0.3333333333333333) (* (* x (* x 0.022222222222222223)) (* (* x (* x 0.022222222222222223)) (* x (* x 0.022222222222222223))))) 1) (/ x (+ (* (* x (* x 0.022222222222222223)) (* x (* x 0.022222222222222223))) (- (* 0.3333333333333333 0.3333333333333333) (* (* x (* x 0.022222222222222223)) 0.3333333333333333)))))
496.0ms
(/ 1.0 (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
Rules
9398×*-un-lft-identity
7957×times-frac
7877×add-sqr-sqrt
6139×add-cube-cbrt
3887×prod-diff
3162×sqrt-prod
2186×pow1
1645×add-exp-log
1401×add-cbrt-cube
1240×distribute-lft-out
647×add-log-exp
632×difference-of-squares
574×pow-prod-down
569×prod-exp
557×associate-*r*
526×div-inv
517×fma-neg
502×associate-+r+
497×associate-*l*
491×pow-prod-up
485×distribute-lft-out--
483×associate-/r/
473×cbrt-unprod
393×log1p-expm1-u
392×expm1-log1p-u
390×insert-posit16
371×log-prod
357×sqrt-div
346×associate-/l*
340×cbrt-prod
316×flip-+ flip3-+
314×div-exp
295×exp-sum
286×pow-plus
282×associate-+l+
264×associate-/r*
253×associate-*r/
235×associate-*l/
229×flip3-- flip--
228×cbrt-undiv
219×pow-sqr
194×frac-times
191×unpow-prod-down
162×swap-sqr
161×sqrt-pow1
156×unswap-sqr
150×exp-prod
146×distribute-rgt-neg-in
126×fma-def
125×distribute-lft-neg-in
111×pow2 sub-neg
105×tan-quot
104×diff-log
101×log-pow
82×pow1/2 associate-/l/
80×*-commutative
66×frac-2neg clear-num
65×pow-unpow
62×distribute-rgt-in distribute-lft-in
61×sqr-pow
48×frac-add
46×cbrt-div
45×fma-udef
43×neg-mul-1
41×pow1/3
37×rem-sqrt-square
34×div-sub
32×1-exp pow3
30×rec-exp
28×sum-log frac-sub log-div
23×associate--r+
19×+-commutative
17×neg-sub0
15×exp-diff complex-mul-def
14×associate--l+
13×rem-log-exp
12×hypot-def
11×pow-exp pow-to-exp
10×associate-+l-
associate--l-
pow-flip exp-neg
cube-unmult neg-log sqrt-unprod pow-pow rem-square-sqrt
expm1-log1p expm1-udef log1p-expm1 difference-cubes rem-exp-log log1p-udef
cos-mult *.c-commutative sqr-cos un-div-inv
sin-sum associate-+r- distribute-frac-neg sin-mult +.c-commutative inv-pow cos-sum associate--r-
associate-*l*.c complex-def-add tan-sum +-inverses exp-to-pow distribute-rgt-out-- complex-add-def
distribute-lft-neg-out diff-atan frac-2neg.c sin-cos-mult distribute-lft-in.c distribute-rgt-in.c diff-sin associate-+l+.c diff-cos rem-cbrt-cube

localize19.9s (1.5%)

regimes13.3s (1.0%)

Accuracy

Total 27.4b remaining (21%)

Threshold costs 6.7b (5.1%)

4.1b85.8%quadp (p42, positive)
4.1b85.9%quad2p (problem 3.2.1, positive)
3.3b0%expq3 (problem 3.4.2)
3.0b90%quad2m (problem 3.2.1, negative)
3.0b90%quadm (p42, negative)

bsearch2.0s (0.1%)

end1.0ms (0.0%)