Details

sample4.9m (48.9%)

Algorithm
56×intervals
16×halfpoints
Results
1.0m66759×body1280valid
37.1s17648×body2560valid
26.7s41715×body640valid
14.0s12438×body10240exit
11.3s94099×body80valid
8.9s20948×body320valid
7.3s63993×body80nan
3.1s10800×body160valid
1.9s47361×pre80true
943.0ms706×body640nan
716.0ms670×body1280nan
674.0ms434×body5120valid
196.0ms366×body320nan
58.0ms220×body160nan

simplify2.6m (25.7%)

prune1.6m (15.7%)

series38.6s (6.4%)

Calls

369 calls:

796.0ms
(* (cbrt (/ 1/2 (sqrt 2))) (* (/ (fma x 2 (fma (pow x 5) 1/60 (* (* (* x x) x) 1/3))) (sqrt 2)) (sin y)))
658.0ms
(/ 1 (+ (hypot (sqrt x) 1) (sqrt x)))
526.0ms
(/ (* (expm1 (* (+ a b) eps)) eps) (* (expm1 (* eps b)) (expm1 (* eps a))))
509.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))
458.0ms
(- (pow (+ x 1) (/ 1 n)) (* (pow (* (cbrt x) (cbrt x)) (/ 1 n)) (pow (cbrt x) (/ 1 n))))

rewrite9.3s (1.5%)

Algorithm
118×rewrite-expression-head
Calls

369 calls:

229.0ms
(+ (- (/ 1 (+ x 1)) (/ 2 x)) (/ 1 (- x 1)))
201.0ms
(cbrt (* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps)))))
190.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (* (sin x) (/ (sin eps) (cos eps))) (cos x)))) (/ (sin x) (cos x)))
157.0ms
(* (- (sqrt (- (* b_2 b_2) (* a c))) b_2) (/ 1 a))
138.0ms
(- (/ (/ (sin x) (cos x)) (- 1 (/ (cbrt (* (* (* (sin x) (sin x)) (sin x)) (* (* (/ (sin eps) (cos eps)) (/ (sin eps) (cos eps))) (/ (sin eps) (cos eps))))) (cos x)))) (/ (sin x) (cos x)))
Rules
14106×times-frac
13339×*-un-lft-identity
12887×add-sqr-sqrt
8956×add-cube-cbrt
5892×prod-diff
2190×sqrt-prod
1747×difference-of-squares
1337×pow1
1228×add-exp-log
1046×add-cbrt-cube
1036×distribute-lft-out
948×distribute-lft-out--
888×associate-*r*
883×div-inv
598×associate-*l*
596×fma-neg
563×cbrt-prod
559×add-log-exp
435×unpow-prod-down
432×associate-/r/
396×associate-/r*
377×associate-/l*
366×log1p-expm1-u
365×expm1-log1p-u
362×insert-posit16
302×pow-prod-down
295×prod-exp
269×associate-+l+
265×div-exp
257×cbrt-unprod
231×pow-prod-up
228×distribute-rgt-neg-in
220×flip3-- flip--
217×flip-+ flip3-+
185×cbrt-undiv
172×unswap-sqr
152×distribute-rgt-out
148×associate-*l/
147×distribute-lft-neg-in
143×sqr-pow
121×swap-sqr
104×log-prod
103×sqrt-div pow-sqr
97×frac-times
81×diff-log
80×sub-neg
78×pow-plus associate-*r/
74×*-commutative
73×fma-def
71×frac-2neg clear-num
67×cbrt-div log-pow
61×pow1/3
58×sqrt-pow1
56×pow2
55×pow1/2
49×neg-mul-1
46×associate-/l/
44×1-exp rec-exp
43×distribute-rgt-in distribute-lft-in exp-prod
39×pow-unpow
37×rem-sqrt-square
34×frac-add
29×tan-quot
25×pow-flip
24×div-sub
23×fma-udef
21×sum-log
20×log-div
18×difference-of-sqr-1
17×sin-mult
16×cube-unmult inv-pow
15×+-commutative
14×frac-sub hypot-def
12×distribute-rgt1-in distribute-lft1-in
10×associate--l- rem-log-exp
neg-sub0
exp-sum associate--l+
neg-log
expm1-udef
expm1-log1p exp-diff cos-mult
log1p-def log1p-expm1 pow-exp log1p-udef pow3 associate--r+ sqr-sin un-div-inv pow-to-exp count-2
sqrt-unprod sub-div pow-pow distribute-rgt-out-- cos-sum
sin-sum sin-cos-mult +.c-commutative tan-sum hypot-udef exp-neg rem-exp-log associate-+l- rem-cbrt-cube
diff-atan frac-2neg.c remove-double-div hypot-1-def rem-square-sqrt diff-sin diff-cos expm1-def

localize4.6s (0.8%)

regimes4.5s (0.7%)

Accuracy

Total 22.9b remaining (16%)

Threshold costs 4.7b (3.3%)

5.0b81.9%quad2p (problem 3.2.1, positive)
4.6b83.4%quadm (p42, negative)
4.6b83.6%quad2m (problem 3.2.1, negative)
2.8b11%expq3 (problem 3.4.2)
1.1b90%2nthrt (problem 3.4.6)

bsearch1.5s (0.3%)

end1.0ms (0.0%)