Details

sample4.5m (41.4%)

Algorithm
56×intervals
16×halfpoints
Results
52.1s67398×body1280valid
32.0s17079×body2560valid
18.8s42063×body640valid
10.0s12817×body10240exit
8.2s93914×body80valid
8.1s20796×body320valid
6.1s62743×body80nan
2.1s10416×body160valid
1.1s47460×pre80true
539.0ms670×body1280nan
394.0ms709×body640nan
235.0ms469×body5120valid
128.0ms386×body320nan
45.0ms184×body160nan

simplify3.8m (35.7%)

prune1.1m (10.0%)

series53.7s (8.3%)

Calls

384 calls:

2.0s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (pow (* eps b) 3) (fma 1/2 (* (pow eps 2) (pow b 2)) (* b eps)))))
2.0s
(- (fma (/ (pow (sin eps) 3) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin x) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3)))) (+ (fma (/ (pow (sin eps) 2) (* (pow (cos eps) 2) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (+ (/ (sin x) (cos x)) (/ (pow (sin x) 3) (pow (cos x) 3))) (/ (/ (sin x) (cos x)) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))) (/ (sin eps) (* (cos eps) (- 1 (/ (pow (* (sin x) (sin eps)) 3) (pow (* (cos x) (cos eps)) 3))))))) (/ (sin x) (cos x)))
1.4s
(fma (/ (+ (tan x) (tan eps)) (- 1 (pow (* (tan x) (tan eps)) 3))) (fma (* (tan x) (tan eps)) (fma (tan x) (tan eps) 1) 1) (- (tan x)))
1.2s
(- (/ 1.0 (- x 1.0)) (- (/ 2.0 x) (log1p (expm1 (/ 1.0 (+ x 1.0))))))
794.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))

rewrite20.1s (3.1%)

Algorithm
121×rewrite-expression-head
Calls

384 calls:

1.2s
(- (+ (/ 2.0 (pow x 3)) (/ 2.0 (pow x 5))) (/ 2.220446049250313e-16 (pow x 6)))
725.0ms
(* x (+ (* (* (* a a) (+ (* (* x 1/6) a) 1/2)) x) a))
588.0ms
(- (+ (* (/ 1 x) (/ 2.0 (* x x))) (/ 2.0 (pow x 5))) (/ 2.220446049250313e-16 (pow x 6)))
457.0ms
(* (sqrt (/ 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt (/ (* (cbrt 1.0) (cbrt 1.0)) (sqrt (+ (sqrt x) (sqrt (+ x 1.0)))))) (sqrt (/ (cbrt 1.0) (sqrt (+ (sqrt x) (sqrt (+ x 1.0))))))))
372.0ms
(+ (/ (- (pow (exp x) 3) (pow 2.0 3)) (fma (+ 2.0 (exp x)) 2.0 (exp (+ x x)))) (exp (- x)))
Rules
9660×*-un-lft-identity
9034×add-sqr-sqrt
8169×times-frac
6744×add-cube-cbrt
4589×prod-diff
3140×sqrt-prod
1395×unpow-prod-down
1218×add-exp-log
967×add-cbrt-cube
950×difference-of-squares
849×distribute-lft-out
743×cbrt-prod
721×associate-*l*
700×pow1
648×distribute-lft-out--
630×add-log-exp
611×cube-prod
547×fma-neg
504×div-inv
498×sqr-pow
491×associate-/l*
426×associate-*r*
393×associate-/r*
373×log1p-expm1-u
372×expm1-log1p-u
342×associate-/r/
285×associate--r+
282×distribute-rgt-neg-in
281×log-prod
273×div-exp
272×prod-exp
253×log-pow
240×distribute-lft-neg-in
221×fma-def
212×flip-- flip3--
209×exp-prod
188×unswap-sqr
184×cbrt-undiv
180×cbrt-unprod
151×flip-+ flip3-+
149×sqrt-div
125×pow-unpow
119×exp-sum
118×unpow3 cube-mult
111×diff-log
107×associate-+l+
105×pow-prod-down
100×sub-neg
80×neg-mul-1
76×clear-num frac-2neg
74×sqrt-pow1
73×unpow2
72×associate-/l/
70×pow-exp
64×pow1/2
62×pow-to-exp
57×associate-*l/
56×associate-*r/
53×*-commutative
48×swap-sqr
41×distribute-rgt-in distribute-lft-in
39×tan-quot
36×rem-sqrt-square
35×div-sub pow1/3
33×log-div
30×pow-pow
27×frac-times
25×fma-udef 1-exp rec-exp
24×sum-log
23×frac-sub
21×pow-flip
20×frac-add
18×neg-sub0 associate--l+
17×cbrt-div rem-log-exp
15×exp-diff rem-cube-cbrt +-commutative
13×complex-mul-def
12×cube-div difference-cubes
11×associate--l-
10×pow-div
neg-log
sqrt-unprod inv-pow pow-prod-up
hypot-def associate-+l-
log1p-udef exp-neg pow-sqr
rem-exp-log *.c-commutative expm1-log1p expm1-udef distribute-frac-neg
log1p-expm1 +.c-commutative cos-mult sin-sum
sin-cos-mult associate--r- pow2 complex-add-def pow-plus cos-sum sin-mult tan-sum frac-2neg.c
associate-+l+.c rem-cbrt-cube un-div-inv diff-atan diff-cos rem-square-sqrt associate-*l*.c exp-to-pow diff-sin

regimes3.9s (0.6%)

Accuracy

Total 25.3b remaining (19.9%)

Threshold costs 6.5b (5.1%)

4.6b84.1%quadm (p42, negative)
4.2b85.1%quad2p (problem 3.2.1, positive)
3.1b0%expq3 (problem 3.4.2)
2.8b82.4%2nthrt (problem 3.4.6)
1.5b93.8%quad2m (problem 3.2.1, negative)

localize3.7s (0.6%)

bsearch2.2s (0.3%)

end1.0ms (0.0%)