Details

sample2.0m (53.8%)

Algorithm
56×intervals
16×halfpoints
Results
26.8s67246×body1280valid
17.6s17146×body2560valid
9.6s42329×body640valid
5.2s94223×body80valid
4.6s12595×body10240exit
3.2s20800×body320valid
3.1s63403×body80nan
1.1s10247×body160valid
743.0ms39136×pre80overflowed
346.0ms661×body1280nan
256.0ms654×body640nan
150.0ms448×body5120valid
114.0ms8256×pre80true
90.0ms358×body320nan
27.0ms174×body160nan

prune41.1s (18.8%)

series36.9s (16.8%)

Calls

382 calls:

1.1s
(pow (exp (* (cbrt (log (fma 1/6 (pow x 3) x))) (cbrt (log (fma 1/6 (pow x 3) x))))) (cbrt (log (fma 1/6 (pow x 3) x))))
879.0ms
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
770.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (fma 1/6 (* (pow a 3) (pow eps 3)) (fma 1/2 (* (pow a 2) (pow eps 2)) (* a eps))) (- (exp (* b eps)) 1.0)))
532.0ms
(* (cbrt (/ (/ 1 2.0) (sqrt 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
516.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

simplify11.5s (5.3%)

Algorithm
194×egg-herbie

rewrite5.9s (2.7%)

Algorithm
122×rewrite-expression-head
Calls

382 calls:

247.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
152.0ms
(* (sqrt (sqrt (/ (+ (exp x) (exp (- x))) 2.0))) (* (sqrt (sqrt (/ (+ (exp x) (exp (- x))) 2.0))) (* (sqrt (/ (+ (exp x) (exp (- x))) 2.0)) (cos y))))
121.0ms
(log (exp (- (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2)))))
102.0ms
(log (exp (- (pow (+ x 1.0) (/ 1.0 n)) (pow x (/ 1.0 n)))))
85.0ms
(- (/ (- b_2) a) (/ (sqrt (- (* b_2 b_2) (* a c))) a))
Rules
9808×*-un-lft-identity
9138×add-sqr-sqrt
8494×times-frac
7248×add-cube-cbrt
5284×prod-diff
2312×sqrt-prod
1560×unpow-prod-down
1233×add-exp-log
912×add-cbrt-cube
826×cbrt-prod
802×cube-prod
758×pow1
738×difference-of-squares
709×distribute-lft-out
697×associate-*r*
637×add-log-exp
598×distribute-rgt-neg-in
589×distribute-lft-out--
545×sqr-pow
523×fma-neg
522×distribute-lft-neg-in
501×div-inv
437×associate-*l*
429×associate-/l*
366×associate-/r* log1p-expm1-u expm1-log1p-u
365×associate-/r/
299×div-exp
289×prod-exp
276×log-prod
270×associate-+l+
230×flip-- flip3--
221×unswap-sqr
210×log-pow
184×pow-unpow
177×cbrt-undiv
174×neg-mul-1
165×flip-+ flip3-+ exp-sum
160×cbrt-unprod unpow3 cube-mult
140×exp-prod
136×unpow2
133×sqrt-div
131×associate-*l/
118×distribute-rgt-in distribute-lft-in
114×diff-log
113×sub-neg
110×sqrt-pow1
109×pow-exp
106×pow-to-exp
99×pow-prod-down
86×fma-def
78×pow1/2
74×associate-*r/
71×frac-2neg clear-num
67×associate-/l/ tan-quot
60×frac-times
55×pow1/3
53×swap-sqr
49×*-commutative
47×pow-prod-up
42×cbrt-div
41×rem-sqrt-square
31×log-div
30×fma-udef
28×div-sub
24×complex-mul-def sum-log
23×pow-pow
21×pow-sqr
20×associate--l- neg-sub0
19×1-exp
18×sum-cubes
17×+-commutative rem-log-exp
16×associate-+r+ rec-exp
15×neg-log
13×associate--l+
12×frac-add frac-sub
11×associate--r+
9×rem-cube-cbrt pow-flip
8×exp-diff
7×difference-cubes pow-plus distribute-rgt-out--
6×sqrt-unprod inv-pow pow2 *.c-commutative associate-+l-
5×rem-exp-log
4×pow-div +.c-commutative complex-add-def sin-mult
3×cube-div sin-cos-mult associate-+r- sub-div difference-of-sqr-1 cos-mult exp-to-pow
2×associate-+l+.c expm1-def associate--r- exp-neg associate-*l*.c tan-sum cos-sum frac-2neg.c sin-sum
1×un-div-inv diff-atan diff-cos rem-square-sqrt diff-sin

regimes2.6s (1.2%)

Accuracy

Total 30.9b remaining (14.2%)

Threshold costs 5.6b (2.6%)

6.7b74.6%quad2p (problem 3.2.1, positive)
4.5b84.5%quad2m (problem 3.2.1, negative)
4.4b84.7%quadm (p42, negative)
3.4b0%expq3 (problem 3.4.2)
2.3b76.9%2cos (problem 3.3.5)

localize1.9s (0.9%)

bsearch1.3s (0.6%)

end1.0ms (0.0%)