Details

sample4.6m (43.9%)

Algorithm
56×intervals
16×halfpoints
Results
51.4s67033×body1280valid
33.1s17171×body2560valid
20.5s41921×body640valid
11.6s12497×body10240exit
8.3s93883×body80valid
6.6s20731×body320valid
4.4s64322×body80nan
3.0s10736×body160valid
1.8s47439×pre80true
601.0ms712×body1280nan
456.0ms704×body640nan
308.0ms414×body5120valid
142.0ms396×body320nan
35.0ms177×body160nan

simplify3.3m (31.3%)

prune1.1m (10.6%)

series55.0s (8.8%)

Calls

405 calls:

1.9s
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (tan x) (tan eps)) (* (tan x) (tan eps)))) (+ 1 (* (tan x) (tan eps))))) (tan x))
1.5s
(- (/ (+ (tan x) (tan eps)) (/ (- 1 (* (* (* (tan x) (tan eps)) (tan x)) (tan eps))) (+ 1 (* (tan x) (tan eps))))) (tan x))
1.0s
(/ (+ 0 (* 4.0 (* a c))) (- (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))) b))
843.0ms
(pow (/ (+ 1.0 0) (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (+ (cbrt x) (cbrt (+ x 1.0)))))) 3)
813.0ms
(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (/ 0.5 (* x n)) (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (- (log x)) (* x (pow n 2)))))))

rewrite22.4s (3.6%)

Algorithm
123×rewrite-expression-head
Calls

405 calls:

557.0ms
(/ (- (+ (* 1.0 x) (log 1.0)) (* 1/2 (/ (pow x 2) (pow 1.0 2)))) (- (log 1.0) (+ (* 1.0 x) (* 1/2 (/ (pow x 2) (pow 1.0 2))))))
552.0ms
(/ (/ (/ 1.0 (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))) (sqrt (+ (sqrt (+ x 1.0)) (sqrt x))))
390.0ms
(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (/ 0.5 (* x n)) (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (- (log x)) (exp (log (* x (pow n 2)))))))))
337.0ms
(* (+ (sqrt (pow (+ x 1.0) (/ 1.0 n))) (pow x (/ (/ 1.0 n) 2))) (- (/ 0.5 (* x n)) (* 0.25 (+ (/ 1 (* (pow x 2) n)) (/ (- (log x)) (* x (pow n 2)))))))
297.0ms
(/ (- (* (/ 1.0 (sqrt x)) (/ 1.0 (sqrt x))) (* (/ 1.0 (sqrt (+ x 1.0))) (/ 1.0 (sqrt (+ x 1.0))))) (+ (/ 1.0 (sqrt x)) (/ 1.0 (sqrt (+ x 1.0)))))
Rules
23369×sqrt-prod
21245×*-un-lft-identity
20986×times-frac
10856×add-sqr-sqrt
8828×add-cube-cbrt
6471×distribute-lft-out
1666×add-exp-log
1148×associate-/l*
1146×add-cbrt-cube
789×difference-of-squares
740×pow1
701×sqrt-div
671×add-log-exp
652×associate-*l*
622×associate-/r/
554×unpow-prod-down associate-*r*
528×distribute-lft-out--
494×prod-exp
466×log-prod
463×associate-/r*
419×flip-+ flip3-+
417×div-inv
363×div-exp
333×cbrt-prod
323×associate-*r/
322×cube-prod
293×unswap-sqr
272×sqr-pow
241×cbrt-unprod
232×cbrt-undiv
227×flip-- flip3--
223×distribute-rgt-neg-in
192×distribute-lft-neg-in
151×frac-times
136×cbrt-div
132×log-pow
128×pow-unpow
116×associate-*l/
110×pow-exp
107×sub-neg
106×pow-prod-down
102×tan-quot
101×swap-sqr diff-log
99×pow-to-exp
90×*-commutative
82×associate-/l/
79×frac-add
75×frac-sub
74×unpow2
73×clear-num frac-2neg sqrt-pow1
68×exp-prod
66×distribute-rgt-in distribute-lft-in
64×neg-mul-1
51×pow1/2
44×rec-exp sum-log 1-exp
42×pow1/3
39×rem-log-exp
34×log-div
31×rem-sqrt-square
29×unpow3 cube-mult
28×associate--l+
27×div-sub
26×+-commutative
23×associate--r+
21×pow-pow
19×pow-prod-up
15×cube-div rem-cube-cbrt pow-sqr
13×complex-mul-def
12×difference-cubes
9×associate-+l+
8×pow-flip neg-sub0
7×associate--l- pow-plus
6×exp-diff inv-pow associate-+r+ exp-sum pow2
5×neg-log rem-cbrt-cube sin-sum
4×*.c-commutative
3×distribute-rgt-out-- +.c-commutative associate-+l- exp-to-pow
2×un-div-inv rem-exp-log cos-sum exp-neg sin-cos-mult complex-add-def sin-mult tan-sum frac-2neg.c
1×unpow1/3 associate-+l+.c associate-+r- associate--r- diff-atan diff-cos rem-square-sqrt associate-*l*.c quot-tan sub-div sqrt-unprod diff-sin

regimes4.4s (0.7%)

Accuracy

Total 32.2b remaining (17.1%)

Threshold costs 7.9b (4.2%)

5.1b43.2%expq3 (problem 3.4.2)
4.5b83.5%quadm (p42, negative)
4.3b84.9%quad2p (problem 3.2.1, positive)
4.0b85%quad2m (problem 3.2.1, negative)
3.8b86.3%quadp (p42, positive)

localize3.9s (0.6%)

bsearch3.6s (0.6%)

end1.0ms (0.0%)