Details

sample2.0m (58.4%)

Algorithm
56×intervals
16×halfpoints
Results
28.7s67679×body1280valid
17.3s17819×body2560valid
9.6s42071×body640valid
4.9s12904×body10240exit
3.2s2217×body1280nan
3.1s20341×body320valid
3.0s92644×body80valid
1.9s64089×body80nan
1.7s1823×body640nan
962.0ms10532×body160valid
561.0ms47497×pre80true
461.0ms906×body320nan
143.0ms460×body160nan
132.0ms435×body5120valid

series35.0s (16.9%)

Calls

385 calls:

1.6s
(- (/ 1 (/ (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)) (* (+ (* (* (tan x) (tan eps)) (+ (* (tan x) (tan eps)) 1)) 1) (+ (tan x) (tan eps))))) (tan x))
695.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))
585.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))
583.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))
579.0ms
(- (pow (+ x 1.0) (/ 1.0 n)) (pow (pow x (/ (* (cbrt 1.0) (cbrt 1.0)) (* (cbrt n) (cbrt n)))) (/ (cbrt 1.0) (cbrt n))))

prune29.7s (14.3%)

simplify9.7s (4.7%)

Algorithm
191×egg-herbie

rewrite6.0s (2.9%)

Algorithm
119×rewrite-expression-head
Calls

385 calls:

423.0ms
(- (/ 1 (/ (- (pow 1 3) (pow (* (tan x) (tan eps)) 3)) (* (+ (* (* (tan x) (tan eps)) (+ (* (tan x) (tan eps)) 1)) 1) (+ (tan x) (tan eps))))) (tan x))
189.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
162.0ms
(/ (+ (- (pow b 2) (pow b 2)) (* 4.0 (* a c))) (* 2.0 a))
82.0ms
(* (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))) (cbrt (+ (pow x 2) (+ (* 1/360 (pow x 6)) (* 1/12 (pow x 4))))))
81.0ms
(- (/ 1 (/ (- 1 (* (tan x) (tan eps))) (+ (tan x) (tan eps)))) (tan x))
Rules
3880×add-sqr-sqrt
3715×*-un-lft-identity
3135×times-frac
2211×add-cube-cbrt
1240×add-exp-log
901×add-cbrt-cube
699×add-log-exp
695×pow1
647×unpow-prod-down
621×difference-of-squares
620×associate-*r*
514×associate-*l*
511×sqrt-prod
428×distribute-lft-out--
368×cbrt-prod
335×associate-/l*
331×distribute-lft-out
314×flip3-- flip--
312×associate-*l/
304×associate-/r*
300×prod-exp
267×sqr-pow
265×div-exp
237×unswap-sqr
233×flip-+ flip3-+
219×associate-/r/
195×log-prod
170×cbrt-unprod
149×cbrt-undiv div-inv
145×frac-times
144×cube-prod
133×cbrt-div
126×sub-neg
117×sqrt-div unpow2
114×associate-/l/ associate-*r/
111×diff-log
104×frac-add sqrt-pow1
93×pow-prod-down
81×pow1/3
80×swap-sqr
76×pow-exp
75×*-commutative
74×pow1/2
68×pow-to-exp
63×log-pow
61×frac-2neg clear-num
56×sum-log
49×1-exp rec-exp
48×pow-unpow
44×distribute-rgt-in distribute-lft-in
43×tan-quot frac-sub
36×rem-sqrt-square log-div
35×associate-+l+ exp-prod
31×pow-prod-up cos-mult
30×+-commutative
27×associate-+r+
25×distribute-rgt-neg-in
24×complex-mul-def
23×pow-sqr
19×associate--l+
18×pow-pow div-sub rem-log-exp
17×pow-flip
16×cube-mult neg-sub0 associate-+l- associate--r+
14×unpow3
13×inv-pow exp-to-pow
12×rem-cube-cbrt
11×cube-div
10×distribute-rgt-out-- neg-log
9×associate--l- pow2 pow-plus exp-sum
8×difference-cubes
7×rem-exp-log
6×exp-diff sqrt-unprod *.c-commutative sin-mult
5×associate-+r-
4×+.c-commutative complex-add-def
3×un-div-inv unsub-neg rem-square-sqrt log-rec rem-cbrt-cube
2×cos-sum sin-cos-mult associate-+l+.c associate--r- exp-neg pow-sub difference-of-sqr-1 associate-*l*.c tan-sum exp-lft-cube pow-neg sin-sum
1×diff-atan sub-div diff-cos frac-2neg.c +-inverses diff-sin

regimes2.6s (1.2%)

Accuracy

Total 24.5b remaining (11.7%)

Threshold costs 6.1b (2.9%)

4.7b-46.9%expq3 (problem 3.4.2)
4.4b83.1%quadm (p42, negative)
2.8b90.2%quad2p (problem 3.2.1, positive)
1.7b84%2nthrt (problem 3.4.6)
1.4b86.1%2cos (problem 3.3.5)

localize1.9s (0.9%)

bsearch1.2s (0.6%)

end1.0ms (0.0%)