Details

simplify3.9m (50.4%)

sample1.9m (24.5%)

Algorithm
56×intervals
16×halfpoints
Results
23.9s66479×body1280valid
17.3s17648×body2560valid
8.3s41957×body640valid
3.7s12572×body10240exit
2.9s94057×body80valid
2.5s20613×body320valid
1.6s63188×body80nan
868.0ms10858×body160valid
572.0ms47437×pre80true
299.0ms653×body1280nan
223.0ms694×body640nan
117.0ms460×body5120valid
65.0ms360×body320nan
22.0ms203×body160nan

prune52.6s (11.5%)

series38.1s (8.3%)

Calls

371 calls:

1.5s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma (* 1/6 (pow b 3)) (pow eps 3) (* b (+ eps (* (* 1/2 (pow eps 2)) b))))))
1.3s
(- (fma (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin eps) 3) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (+ (fma (/ (/ (pow (sin eps) 2) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (pow (cos eps) 2)) (+ (pow (/ (sin x) (cos x)) 3) (/ (sin x) (cos x))) (/ (sin x) (* (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3)) (cos x)))) (/ (/ (sin eps) (cos eps)) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))))) (/ (sin x) (cos x)))
954.0ms
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
806.0ms
(expm1 (log1p (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))))
606.0ms
(fma (cbrt (fma 2.0 (+ (exp x) 2.0) (exp (+ x x)))) (cbrt (fma 2.0 (+ (exp x) 2.0) (exp (+ x x)))) (* (* (* (cbrt (- (pow (exp x) 3) (pow 2.0 3))) (cbrt (- (exp x) 2.0))) (cbrt (- (pow (exp x) 3) (pow 2.0 3)))) (exp x)))

rewrite19.4s (4.2%)

Algorithm
122×rewrite-expression-head
Calls

371 calls:

5.2s
(+ (+ (- (pow (/ (cbrt 1.0) (cbrt (+ x 1.0))) 3) (/ 2.0 x)) 0) (/ 1.0 (- x 1.0)))
1.5s
(* (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))) (cbrt (+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))))
524.0ms
(/ (- (/ (/ 1 b) b) (/ (/ 1 a) a)) (- (/ 1 b) (/ 1 a)))
471.0ms
(* (cbrt (/ (- 1.0) (/ (+ x 1.0) 1.0))) (cbrt (/ (- 1.0) (/ (+ x 1.0) 1.0))))
362.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
Rules
20681×times-frac
16487×*-un-lft-identity
16360×add-sqr-sqrt
11233×add-cube-cbrt
6204×prod-diff
2279×cbrt-prod
1923×difference-of-squares
1517×sqrt-prod
1437×div-inv
1370×add-exp-log
1150×distribute-lft-out--
1136×distribute-lft-out
960×add-cbrt-cube
956×associate-+l+
695×unpow-prod-down pow1
658×distribute-rgt-neg-in
606×distribute-lft-neg-in
602×associate-*l*
593×add-log-exp
541×associate-/l*
536×associate-*r*
504×fma-neg
476×associate-/r/
420×cube-prod
378×prod-exp
362×expm1-log1p-u
359×log1p-expm1-u
351×log-pow
341×swap-sqr
321×exp-prod div-exp
317×associate-/r*
314×flip-- flip3--
313×pow-unpow
253×log-prod
243×sqr-pow
209×cbrt-div
202×neg-mul-1
194×cbrt-unprod
191×cbrt-undiv
182×flip-+ flip3-+
146×unswap-sqr
130×frac-times
108×frac-add
102×associate-*l/
98×sub-neg
97×sqrt-div
96×fma-def
95×diff-log pow-prod-down
88×associate-*r/
69×associate-/l/
67×frac-2neg clear-num
65×tan-quot
64×sqrt-pow1
59×pow1/2 rec-exp 1-exp
58×distribute-rgt-in pow1/3 distribute-lft-in
51×*-commutative exp-sum
46×unpow3 cube-mult
40×pow-exp
37×pow-to-exp div-sub unpow2
35×rem-sqrt-square
34×exp-diff
33×fma-udef
31×neg-sub0
28×exp-neg
27×frac-sub
26×sum-log
23×pow-pow log-div
22×pow-prod-up
21×pow-flip rem-log-exp
18×pow-sqr
16×+-commutative associate--l+
13×difference-cubes complex-mul-def
11×rem-cube-cbrt inv-pow
cube-div
pow-plus
pow2 associate-+l-
associate--r+
associate--l- sqrt-unprod hypot-def
pow-div un-div-inv rem-exp-log log1p-udef log1p-expm1 *.c-commutative
+.c-commutative distribute-rgt-out-- sin-sum
cos-sum sin-cos-mult expm1-log1p expm1-udef complex-add-def rem-square-sqrt distribute-frac-neg quot-tan neg-log sin-mult tan-sum rem-cbrt-cube
associate-+l+.c pow3 diff-atan sub-div diff-cos associate-*l*.c frac-2neg.c diff-sin log-rec

regimes2.4s (0.5%)

Accuracy

Total 24.4b remaining (18.9%)

Threshold costs 6.5b (5.1%)

4.9b82.7%quadp (p42, positive)
4.9b82.9%quad2p (problem 3.2.1, positive)
3.2b0%expq3 (problem 3.4.2)
1.4b84.4%2nthrt (problem 3.4.6)
1.4b91%2tan (problem 3.3.2)

localize1.9s (0.4%)

bsearch1.2s (0.3%)

end1.0ms (0.0%)