Details

sample2.1m (57.4%)

Algorithm
56×intervals
16×halfpoints
Results
30.6s66748×body1280valid
19.8s17539×body2560valid
11.5s42086×body640valid
5.2s94022×body80valid
3.8s20773×body320valid
2.9s62834×body80nan
1.3s10734×body160valid
753.0ms47547×pre80true
734.0ms12911×body80overflowed
371.0ms630×body1280nan
276.0ms659×body640nan
209.0ms429×body5120valid
86.0ms338×body320nan
29.0ms175×body160nan

series35.8s (16.5%)

Calls

405 calls:

1.1s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (/ (* (* (tan x) (tan eps)) (* (tan x) (sin eps))) (cos eps)))) (+ 1 (* (tan x) (tan eps)))) (tan x))
905.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
775.0ms
(/ (* eps (- (exp (* (+ a b) eps)) 1.0)) (* (+ (* 1/6 (* (pow a 3) (pow eps 3))) (+ (* 1/2 (* (pow a 2) (pow eps 2))) (* a eps))) (- (exp (* b eps)) 1.0)))
507.0ms
(/ (* 1.0 (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))
504.0ms
(/ (* 1.0 (/ (+ x (- 1.0 x)) (+ (sqrt (+ x 1.0)) (sqrt x)))) (* (sqrt x) (sqrt (+ x 1.0))))

prune33.5s (15.5%)

simplify10.7s (5.0%)

Algorithm
195×egg-herbie

rewrite6.3s (2.9%)

Algorithm
123×rewrite-expression-head
Calls

405 calls:

179.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
118.0ms
(* (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))) (sqrt (/ 1.0 (+ (sqrt (+ x 1.0)) (sqrt x)))))
111.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
100.0ms
(+ (* (/ 1 (pow N 2)) (/ 0.3333333333333333 N)) (- (/ 1.0 N) (/ (/ 0.5 N) N)))
90.0ms
(log (exp (- (pow (+ x 1.0) (/ (/ 1.0 n) 2)) (pow x (/ (/ 1.0 n) 2)))))
Rules
6429×*-un-lft-identity
6023×times-frac
5482×add-sqr-sqrt
3398×add-cube-cbrt
1522×add-exp-log
1402×sqrt-prod
1109×unpow-prod-down
1046×add-cbrt-cube
1000×distribute-lft-out
925×difference-of-squares
828×associate-*r*
826×cbrt-prod
744×pow1 add-log-exp
610×cube-prod
594×distribute-lft-out--
531×associate-/l*
518×associate-*l*
432×sqr-pow
419×prod-exp
405×associate-/r*
369×pow-unpow
359×div-exp
300×unswap-sqr
291×log-prod div-inv
267×flip3-- flip--
227×associate-/r/
204×cbrt-unprod
196×flip-+ flip3-+
194×cbrt-undiv
181×cbrt-div
175×associate-*l/
165×unpow2
137×frac-times
130×exp-prod
122×sub-neg
121×pow-prod-down
116×associate-*r/
115×diff-log
114×log-pow
106×pow-exp
105×pow-to-exp sqrt-div
102×distribute-rgt-neg-in
100×swap-sqr
84×tan-quot
83×unpow3 cube-mult
82×*-commutative
73×exp-sum
70×pow1/3
68×associate-+l+
67×associate-/l/ 1-exp
66×distribute-rgt-in frac-2neg clear-num distribute-lft-in
62×sum-log
54×frac-add
52×rec-exp
50×sqrt-pow1
38×+-commutative
37×pow-pow
36×pow1/2
34×pow-prod-up
32×log-div frac-sub
26×cube-div pow-sqr
25×div-sub
24×rem-sqrt-square difference-of-sqr-1 complex-mul-def
23×associate--l+
21×sum-cubes rem-log-exp
18×exp-to-pow
17×neg-sub0
15×rem-cube-cbrt pow-plus
13×difference-cubes associate-+r+
12×associate--r+
11×associate--l- pow-flip
10×pow2 neg-log
9×exp-diff associate-+l-
8×inv-pow
7×un-div-inv sin-mult
6×associate-+r- cos-mult *.c-commutative
4×rem-exp-log sqrt-unprod distribute-rgt-out-- sub-div +.c-commutative complex-add-def rem-cbrt-cube
3×distribute-lft-neg-in exp-neg
2×cos-sum sub0-neg associate-+l+.c pow-sub associate-*l*.c tan-sum pow-neg sin-sum
1×sin-cos-mult pow3 diff-atan diff-cos unsub-neg rem-square-sqrt neg-mul-1 diff-sin

regimes2.8s (1.3%)

Accuracy

Total 32.6b remaining (14.8%)

Threshold costs 6.2b (2.8%)

5.0b81.7%quadp (p42, positive)
4.9b83%quadm (p42, negative)
3.0b0%expq3 (problem 3.4.2)
2.9b72.1%2cos (problem 3.3.5)
2.8b90.5%quad2m (problem 3.2.1, negative)

localize1.9s (0.9%)

bsearch1.1s (0.5%)

end1.0ms (0.0%)