Details

sample1.8m (49.9%)

Algorithm
56×intervals
16×halfpoints
Results
23.7s66709×body1280valid
16.8s17663×body2560valid
8.0s41712×body640valid
3.7s12814×body10240exit
2.8s94023×body80valid
2.4s20595×body320valid
1.6s62230×body80nan
876.0ms10950×body160valid
523.0ms47613×pre80true
287.0ms654×body1280nan
213.0ms677×body640nan
117.0ms429×body5120valid
73.0ms377×body320nan
22.0ms206×body160nan

prune43.4s (19.8%)

series38.1s (17.4%)

Calls

400 calls:

1.5s
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (- (exp (* a eps)) 1.0) (fma 1/6 (* (pow eps 3) (pow b 3)) (fma 1/2 (* (pow eps 2) (pow b 2)) (* eps b)))))
923.0ms
(fma (fma (fma (tan x) (tan eps) 1) (* (tan x) (tan eps)) 1) (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (- (tan x)))
479.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
479.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
460.0ms
(log (cbrt (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n))))))

simplify11.5s (5.2%)

rewrite10.1s (4.6%)

Algorithm
123×rewrite-expression-head
Calls

400 calls:

334.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
210.0ms
(* (cbrt (/ 1.0 (/ (+ x 1.0) (- 0 1.0)))) (cbrt (/ 1.0 (/ (+ x 1.0) (- 0 1.0)))))
182.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
149.0ms
(* (/ (* (cbrt (+ (exp x) (exp (- x)))) (cbrt (+ (exp x) (exp (- x))))) 1) (* (/ (cbrt (+ (exp x) (exp (- x)))) 2.0) (cos y)))
137.0ms
(/ (/ (+ 1.0 0) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
Rules
13023×times-frac
12550×*-un-lft-identity
10234×add-sqr-sqrt
7968×add-cube-cbrt
3694×prod-diff
2393×sqrt-prod
1359×distribute-lft-out
1168×cbrt-prod
1039×add-exp-log
997×difference-of-squares
978×distribute-lft-out--
847×add-cbrt-cube
793×associate-/l*
778×unpow-prod-down
713×pow1
707×log-prod
639×add-log-exp
545×div-inv
479×associate-/r/
419×fma-neg associate-*l*
384×log1p-expm1-u expm1-log1p-u
330×associate-+l+
312×flip-- flip3--
301×associate-*r*
275×distribute-rgt-neg-in
271×associate-/r*
259×sqr-pow
220×exp-sum
219×div-exp
217×cube-prod
189×prod-exp
184×sqrt-div
183×flip-+ flip3-+
177×swap-sqr
162×log-pow
160×cbrt-undiv
132×fma-def cbrt-unprod
123×unswap-sqr
122×associate-+r+
118×associate-*l/
103×sub-neg
102×distribute-lft-neg-in
100×diff-log
94×pow-unpow
91×cbrt-div
83×pow1/3
74×sqrt-pow1
71×pow-prod-down
69×log-div
66×associate-/l/
65×exp-prod
63×frac-times
62×clear-num frac-2neg
56×associate-*r/
50×pow1/2
46×*-commutative
39×tan-quot
37×distribute-rgt-in distribute-lft-in rem-log-exp
35×rem-sqrt-square sum-log
34×unpow3 cube-mult neg-mul-1
31×fma-udef
29×pow-exp
28×pow-to-exp
26×+-commutative
24×complex-mul-def
21×1-exp
19×pow-prod-up
18×div-sub
16×pow-pow
15×rec-exp sum-cubes associate-+l-
14×neg-sub0
13×pow-sqr hypot-def distribute-rgt-out-- frac-sub
12×pow-plus associate--l+
11×exp-diff
10×associate--l- frac-add unpow2
associate-+r-
pow2 neg-log
rem-cube-cbrt rem-exp-log *.c-commutative
cube-div pow-flip
difference-of-sqr-1 +.c-commutative complex-add-def sin-mult cos-mult associate--r+
difference-cubes sqrt-unprod inv-pow sub-div
cos-sum associate-+l+.c expm1-def un-div-inv exp-neg pow-sub associate-*l*.c sqr-cos tan-sum frac-2neg.c pow-neg exp-to-pow rem-cbrt-cube sin-sum
sin-cos-mult pow3 diff-atan diff-cos expm1-log1p expm1-udef distribute-rgt-out diff-sin

regimes3.5s (1.6%)

Accuracy

Total 32.2b remaining (12.1%)

Threshold costs 4.8b (1.8%)

7.3b72.8%quad2p (problem 3.2.1, positive)
5.3b81.3%quad2m (problem 3.2.1, negative)
3.6b86.6%quadp (p42, positive)
3.3b0%expq3 (problem 3.4.2)
3.3b88.5%quadm (p42, negative)

localize2.1s (0.9%)

bsearch1.2s (0.6%)

end1.0ms (0.0%)