Details

sample5.0m (36.1%)

Algorithm
56×intervals
16×halfpoints
Results
1.0m67181×body1280valid
39.8s17537×body2560valid
27.7s41629×body640valid
14.3s12987×body10240exit
10.7s94232×body80valid
8.6s20503×body320valid
7.5s62935×body80nan
2.7s10734×body160valid
2.4s47453×pre80true
809.0ms649×body1280nan
547.0ms690×body640nan
512.0ms464×body5120valid
169.0ms367×body320nan
53.0ms179×body160nan

prune4.7m (33.9%)

simplify3.2m (23.4%)

series34.1s (4.1%)

Calls

329 calls:

Slowest
778.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (* (/ (sin x) (cos x)) (/ (sin eps) (cos eps))))) (/ (sin x) (cos x)))
657.0ms
(/ (expm1 (* (+ a b) eps)) (* (expm1 (* eps b)) (expm1 (* eps a))))
604.0ms
(* (/ (expm1 (* (+ a b) eps)) (* (expm1 (* eps b)) (expm1 (* eps a)))) eps)
603.0ms
(- (pow (+ x 1) (/ 1 n)) (pow x (/ 1 n)))
565.0ms
(* (sqrt 2) (/ a (/ (- (- b) (sqrt (fma (* -4 a) c (* b b)))) (sqrt 2))))

rewrite9.9s (1.2%)

Algorithm
108×rewrite-expression-head
Calls

329 calls:

Slowest
362.0ms
(/ (+ (exp (+ x (+ x x))) 1) (fma (exp x) (exp x) (- 1 (exp x))))
300.0ms
(/ (- (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
282.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (sin x) (/ (* (cos eps) (cos x)) (sin eps))))) (/ (sin x) (cos x)))
205.0ms
(* (- (* (cos (* eps 1/2)) (cos x)) (* (sin (* eps 1/2)) (sin x))) (sin (* 1/2 eps)))
199.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
Rules
23510×times-frac
17051×add-sqr-sqrt
16884×*-un-lft-identity
13816×add-cube-cbrt
8320×prod-diff
3266×sqrt-prod
1573×pow1
1438×difference-of-squares
1394×div-inv
1072×add-exp-log
941×add-cbrt-cube
713×distribute-lft-out--
681×distribute-lft-out
607×fma-neg
601×unpow-prod-down
569×sqrt-div
522×add-log-exp
507×associate-/l*
470×associate-/r*
445×pow-prod-up
440×associate-*r*
336×cbrt-div
332×cbrt-prod
329×associate-/r/
319×expm1-log1p-u
318×log1p-expm1-u
317×insert-posit16 flip-+ flip3-+
313×associate-*l*
296×pow-prod-down
287×distribute-rgt-neg-in
263×div-exp
248×associate-+l+
219×frac-times
217×prod-exp
212×sqr-pow
201×cbrt-undiv
199×cbrt-unprod
192×pow-sqr
174×distribute-lft-neg-in
168×flip3-- flip--
165×pow-plus
119×pow2
114×cube-prod
111×associate-*r/
110×unswap-sqr
107×sqrt-pow1 fma-def
99×associate-*l/
79×frac-2neg clear-num
75×swap-sqr diff-log
73×pow1/2
72×log-prod
70×frac-add
65×sub-neg
60×neg-mul-1
55×pow-unpow *-commutative
52×pow1/3
51×associate-/l/
46×tan-quot
44×associate-+r+
36×sum-log rem-sqrt-square
28×pow-flip 1-exp rec-exp
26×unpow3 cube-mult
25×div-sub
21×log-pow
20×fma-udef
18×exp-prod
17×+-commutative
16×inv-pow
15×frac-sub
13×complex-mul-def
12×neg-sub0 pow-exp neg-log pow-to-exp hypot-def
10×distribute-rgt-out-- log-div
9×difference-of-sqr-1 associate--l-
8×sin-mult
7×exp-sum log1p-udef associate--r+ associate-+l- distribute-rgt-out
6×sqrt-unprod rem-log-exp
5×quot-tan cos-mult sub-div pow-pow
4×exp-diff associate-+r-
3×expm1-udef cube-unmult log1p-expm1 distribute-rgt-in +.c-commutative sqr-sin rem-exp-log *.c-commutative cos-sum distribute-lft-in difference-cubes
2×expm1-log1p associate-*l*.c sin-sum associate--l+ un-div-inv tan-sum frac-2neg-c exp-neg complex-add-def log1p-def rem-square-sqrt pow-div
1×diff-atan distribute-rgt1-in rem-cube-cbrt sin-cos-mult distribute-lft1-in associate-+l+.c diff-sin diff-cos unsub-neg expm1-def difference-of-sqr--1

regimes4.1s (0.5%)

Accuracy

Total 23.5b remaining (16.3%)

Threshold costs 5.1b (3.5%)

4.6b83%quad2p (problem 3.2.1, positive)
4.5b83.5%quadm (p42, negative)
4.3b84%quad2m (problem 3.2.1, negative)
3.6b0%expq3 (problem 3.4.2)
1.4b88.1%2nthrt (problem 3.4.6)

localize4.0s (0.5%)

bsearch2.6s (0.3%)

end1.0ms (0.0%)