Details

simplify5.0m (50.5%)

sample2.5m (25.8%)

Algorithm
39×intervals
15×halfpoints
Results
21.0s29169×body1280valid
11.0s4454×body2560valid
8.8s21862×body640valid
2.7s11037×body320valid
2.3s28073×body80valid
1.5s26309×body80nan
937.0ms37419×pre80true
822.0ms5159×body160valid
261.0ms368×body10240exit
11.0ms18×body640nan
11.0ms19×body5120valid
7.0ms11×body1280nan
3.0ms13×body320nan
1.0ms8×body160nan

prune56.0s (9.5%)

series50.6s (8.6%)

Calls

375 calls:

844.0ms
(cbrt (+ (* 0.022222222222222223 (pow x 3)) (+ (* 0.0021164021164021165 (pow x 5)) (* 0.3333333333333333 x))))
761.0ms
(/ (+ 0 (* (* 4.0 a) c)) (- (sqrt (- (* b b) (* 4.0 (* a c)))) b))
636.0ms
(- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))
621.0ms
(/ (* (cos x) (- (/ (+ (* (sin x) (cos eps)) (* (cos x) (sin eps))) (- 1 (* (tan x) (tan eps)))) (* (sin x) (cos eps)))) (* (* (cos x) (cos eps)) (cos x)))
612.0ms
(- (* (+ (tan x) (tan eps)) (/ 1 (- 1 (* (tan x) (tan eps))))) (tan x))

rewrite26.4s (4.5%)

Algorithm
123×rewrite-expression-head
Calls

375 calls:

3.2s
(- (+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0)) 1.0)
667.0ms
(+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (- (* (log n) 1.0) 1.0))
597.0ms
(+ (- (+ (/ 0.5 n) 1.0) (/ 0.16666666666666669 (* n n))) (* (log n) 1.0))
481.0ms
(/ (- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0))) (* (+ (exp x) 1.0) (+ (exp (+ x x)) (* 1.0 1.0))))
465.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
Rules
24354×sqrt-prod
21073×times-frac
20773×*-un-lft-identity
10538×add-sqr-sqrt
8951×add-cube-cbrt
6211×distribute-lft-out
1421×add-exp-log
1101×add-cbrt-cube
1033×associate-/l*
877×associate-*r*
743×pow1
701×sqrt-div
684×associate-*l*
664×add-log-exp
566×unpow-prod-down
557×associate-/r/
555×difference-of-squares
471×distribute-lft-out--
446×associate-/r*
437×div-inv
428×pow-unpow
409×cbrt-prod
384×flip-+ flip3-+
374×prod-exp
316×div-exp
247×cbrt-unprod
237×flip3-- flip--
236×unswap-sqr
220×sqr-pow
212×cbrt-undiv
202×associate-*l/
150×cube-prod
142×pow-prod-down
133×associate-*r/
128×cbrt-div
114×log-prod
108×unpow2
101×associate-/l/
100×diff-log
92×sub-neg
90×frac-times
86×distribute-rgt-neg-in
84×*-commutative
81×frac-2neg clear-num
78×distribute-lft-neg-in neg-mul-1
72×pow-exp
71×frac-add
70×pow-to-exp
66×sum-log
64×log-pow pow1/3 swap-sqr
48×sqrt-pow1
45×distribute-rgt-in distribute-lft-in
39×tan-quot frac-sub
36×pow1/2
35×div-sub
33×+-commutative
30×log-div
26×1-exp rec-exp
25×unpow3 cube-mult associate--l+
24×pow-flip
19×pow-pow rem-sqrt-square exp-prod
17×associate-+l+
14×pow-prod-up pow-sqr exp-sum associate--r+
13×complex-mul-def
12×distribute-frac-neg
10×pow-div rem-log-exp
9×associate--l-
8×inv-pow neg-sub0
7×cube-div pow-plus
6×exp-diff rem-cube-cbrt associate-+r+ associate-+l- pow2
5×sin-cos-mult
4×*.c-commutative
3×sub0-neg un-div-inv rem-exp-log sqrt-unprod +.c-commutative rem-cbrt-cube sin-sum
2×cos-sum difference-cubes associate-+r- pow3 associate--r- exp-neg complex-add-def neg-log sin-mult cos-mult tan-sum exp-to-pow
1×associate-+l+.c diff-atan distribute-rgt-out-- diff-cos associate-*l*.c distribute-rgt-neg-out frac-2neg.c sqrt-undiv diff-sin

localize3.5s (0.6%)

regimes2.5s (0.4%)

Accuracy

Total 2.0b remaining (4.3%)

Threshold costs 2.0b (4.3%)

0.4b0%2cos (problem 3.3.5)
0.4b0%expm1 (example 3.7)
0.3b0%qlog (example 3.10)
0.3b0%2isqrt (example 3.6)
0.2b0%invcot (example 3.9)

bsearch25.0ms (0.0%)

end0.0ms (0.0%)