Details

sample1.8m (46.3%)

Algorithm
56×intervals
16×halfpoints
Results
23.6s67247×body1280valid
16.8s17368×body2560valid
8.0s42325×body640valid
3.8s12816×body10240exit
3.1s94008×body80valid
2.4s20324×body320valid
1.6s63505×body80nan
823.0ms10560×body160valid
525.0ms47432×pre80true
510.0ms658×body1280nan
220.0ms684×body640nan
112.0ms411×body5120valid
66.0ms363×body320nan
18.0ms173×body160nan

prune56.2s (23.6%)

series39.3s (16.5%)

Calls

401 calls:

1.1s
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (/ (* (sin x) (tan eps)) (cos x))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
948.0ms
(- (* (/ (+ (tan x) (tan eps)) (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps))))) (+ 1 (* (tan x) (tan eps)))) (tan x))
614.0ms
(* (cbrt (+ (pow x 2) (* 1/360 (pow x 6)))) (cbrt (+ (pow x 2) (* 1/360 (pow x 6)))))
582.0ms
(cbrt (+ (pow x 2) (* 1/360 (pow x 6))))
566.0ms
(cbrt (+ (pow x 2) (* 1/360 (pow x 6))))

rewrite14.5s (6.1%)

Algorithm
122×rewrite-expression-head
Calls

401 calls:

632.0ms
(- (+ (- 1.0 (+ (* 1.0 (log (/ 1 n))) (* 0.16666666666666669 (/ 1 (pow n 2))))) (/ 0.5 n)) 1.0)
360.0ms
(/ (/ (/ a (/ (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2)) c)) (sqrt (- (sqrt (- (* b_2 b_2) (* a c))) b_2))) a)
344.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ (- 1.0) (- (- x 1.0))))
342.0ms
(* (/ (+ 0 (* 1 (* 4.0 (* a c)))) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b)) (/ 1 (* 2.0 a)))
274.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
Rules
35590×times-frac
22167×add-sqr-sqrt
21037×*-un-lft-identity
14579×add-cube-cbrt
9622×sqrt-prod
3630×difference-of-squares
3122×cbrt-prod
2573×distribute-lft-out--
2213×associate-/l*
1649×add-exp-log
1109×add-cbrt-cube
766×add-log-exp
712×pow1
711×distribute-lft-out
704×associate-*l*
674×distribute-rgt-neg-in
592×associate-*r*
531×div-inv
527×unpow-prod-down
511×div-exp
435×associate-/r*
417×prod-exp
365×log-prod
300×associate-/r/
294×flip3-- flip--
260×sqr-pow
251×cbrt-undiv
214×cbrt-unprod
193×unswap-sqr
180×associate-*l/
169×flip-+ flip3-+
150×cube-prod
140×sqrt-div diff-log
137×sub-neg
112×distribute-lft-neg-in frac-times
102×1-exp associate-*r/
97×pow-prod-down
92×log-pow
89×cbrt-div unpow2
87×associate-/l/
81×tan-quot
77×swap-sqr
76×clear-num frac-2neg
70×rec-exp
68×*-commutative
62×sqrt-pow1
57×pow1/3
56×sum-log
52×pow-unpow
51×pow-exp
49×pow1/2 pow-to-exp
46×exp-prod
44×frac-add
34×distribute-rgt-in distribute-lft-in
30×neg-mul-1
29×rem-sqrt-square +-commutative
28×frac-sub
27×log-div
24×complex-mul-def associate--l+
23×pow-flip div-sub
22×difference-cubes
21×rem-log-exp pow-pow
18×associate-+l+
17×neg-sub0
15×associate--l- associate--r+
14×unpow3 cube-mult
13×pow-sqr pow-prod-up
12×cube-div exp-to-pow
11×neg-log
10×pow-div
9×inv-pow difference-of-sqr-1 exp-sum
8×rem-cube-cbrt associate-+l-
7×un-div-inv associate-+r+ pow-plus sin-mult
6×exp-diff pow2 *.c-commutative cos-mult
5×rem-exp-log exp-lft-cube
4×unpow-prod-up +.c-commutative complex-add-def distribute-neg-frac
3×sqrt-unprod associate-+r- distribute-rgt-out-- distribute-frac-neg rem-cbrt-cube
2×cos-sum sin-sum associate-+l+.c exp-neg sub-div pow-sub tan-sum associate-*l*.c
1×sin-cos-mult sqrt-pow2 e-exp-1 diff-atan diff-cos unsub-neg frac-2neg.c diff-sin

simplify11.6s (4.9%)

Algorithm
194×egg-herbie

regimes2.8s (1.2%)

Accuracy

Total 22.5b remaining (8.3%)

Threshold costs 6.4b (2.3%)

5.1b52%expq3 (problem 3.4.2)
3.3b87.7%quad2m (problem 3.2.1, negative)
1.5b93.8%quad2p (problem 3.2.1, positive)
1.3b86.5%2cos (problem 3.3.5)
1.3b84.8%2nthrt (problem 3.4.6)

localize1.9s (0.8%)

bsearch1.7s (0.7%)

end1.0ms (0.0%)