Details

sample4.9m (40.8%)

Algorithm
56×intervals
16×halfpoints
Results
1.1m66947×body1280valid
38.8s17832×body2560valid
26.4s41632×body640valid
13.7s12720×body10240exit
10.6s93671×body80valid
10.0s20637×body320valid
6.3s64013×body80nan
3.5s11214×body160valid
2.2s47341×pre80true
810.0ms471×body5120valid
729.0ms696×body1280nan
437.0ms625×body640nan
178.0ms344×body320nan
85.0ms193×body160nan

prune3.1m (26.0%)

simplify3.1m (25.7%)

series35.2s (4.8%)

Calls

344 calls:

Slowest
716.0ms
(- (/ 1 (sqrt x)) (/ 1 (hypot (sqrt x) 1)))
596.0ms
(/ (* (expm1 (* (+ a b) eps)) (/ eps (expm1 (* eps b)))) (expm1 (* eps a)))
552.0ms
(fma (/ (/ (sin x) (cos x)) (- (* 1 1) (* (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))) (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))))) (+ 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps)))) (- (/ (sin x) (cos x))))
544.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
378.0ms
(/ (- (* x (* x x)) (* (tan x) (* (tan x) (tan x)))) (fma (tan x) (+ x (tan x)) (* x x)))

rewrite9.0s (1.2%)

Algorithm
112×rewrite-expression-head
Calls

344 calls:

Slowest
375.0ms
(* (* 1/3 (* x x)) x)
362.0ms
(/ (* x (fma 1/91125 (* (* x (* x x)) (* x (* x x))) 1/27)) (+ (* 1/3 1/3) (- (* (* 1/45 (* x x)) (* 1/45 (* x x))) (* 1/3 (* 1/45 (* x x))))))
211.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
201.0ms
(* (exp (cos (/ (+ x (+ eps x)) 2))) (exp (cos (/ (+ x (+ eps x)) 2))))
170.0ms
(* (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))) (sqrt (/ 1 (+ (sqrt (+ x 1)) (sqrt x)))))
Rules
9099×times-frac
8908×*-un-lft-identity
7976×add-sqr-sqrt
6610×add-cube-cbrt
3794×prod-diff
3490×sqrt-prod
2014×pow1
1321×add-exp-log
1171×add-cbrt-cube
871×distribute-lft-out
780×associate-*l*
617×div-inv
593×cbrt-prod
533×pow-prod-up
511×add-log-exp
411×associate-*r*
395×difference-of-squares
393×pow-prod-down
382×fma-neg
381×prod-exp
372×associate-/l*
342×cbrt-unprod
341×log1p-expm1-u
338×expm1-log1p-u
336×insert-posit16
325×unpow-prod-down
300×associate-/r/
274×div-exp
265×associate-/r*
264×distribute-lft-out--
252×pow-sqr
248×associate-+l+
227×pow-plus
216×cbrt-undiv
186×unswap-sqr
165×flip-+ flip3-+
158×pow2
157×log-prod
153×swap-sqr
139×sqrt-div
137×distribute-rgt-neg-in
128×flip3-- flip--
114×sqr-pow
106×distribute-lft-neg-in
102×sqrt-pow1
97×fma-def
88×associate-*l/
83×exp-prod
81×exp-sum
79×log-pow
74×pow1/2
71×*-commutative
68×pow-unpow
66×pow-flip frac-2neg clear-num diff-log
64×sub-neg
56×frac-times
45×associate-*r/
43×associate-/l/
39×rem-sqrt-square
38×pow1/3
35×neg-mul-1
34×1-exp rec-exp
33×inv-pow
32×tan-quot
29×cbrt-div distribute-rgt-in distribute-lft-in
27×sum-log
26×pow-div fma-udef
23×difference-of-sqr-1
21×div-sub
18×hypot-def
17×+-commutative pow-pow
12×cube-unmult
11×frac-sub
10×neg-sub0 frac-add
9×pow-exp associate--r+ rem-log-exp log-div
7×expm1-log1p expm1-udef neg-log pow-to-exp
6×associate--l-
5×exp-diff log1p-udef pow3 associate-+l- difference-cubes
4×distribute-neg-frac sin-mult
3×log1p-expm1 sqr-sin
2×sin-sum associate-+r+ log1p-def associate--l+ sqrt-unprod +.c-commutative un-div-inv tan-sum frac-2neg-c rem-square-sqrt cos-sum exp-neg rem-cbrt-cube expm1-def
1×quot-tan distribute-lft-neg-out diff-atan sin-cos-mult hypot-udef rem-exp-log diff-sin unpow1/3 diff-cos

regimes4.6s (0.6%)

Accuracy

Total 26.2b remaining (18.4%)

Threshold costs 4.6b (3.2%)

4.3b84.7%quad2p (problem 3.2.1, positive)
4.3b84.8%quadp (p42, positive)
4.2b85.1%quad2m (problem 3.2.1, negative)
4.2b85.1%quadm (p42, negative)
3.1b0%expq3 (problem 3.4.2)

localize3.9s (0.5%)

bsearch1.8s (0.2%)

end1.0ms (0.0%)