Details

simplify5.8m (54.3%)

sample2.8m (26.2%)

Algorithm
40×intervals
15×halfpoints
Results
26.7s32615×body1280valid
15.0s7031×body2560valid
10.6s22896×body640valid
4.2s2354×body10240exit
3.7s11411×body320valid
1.9s28524×body80valid
1.2s26309×body80nan
1.1s47408×pre80true
788.0ms5280×body160valid
13.0ms18×body640nan
13.0ms19×body5120valid
8.0ms11×body1280nan
5.0ms13×body320nan
2.0ms8×body160nan

prune54.7s (8.5%)

series49.9s (7.7%)

Calls

351 calls:

2.0s
(- (fma (/ (pow (sin x) 2) (* (pow (cos x) 2) (pow (cos eps) 3))) (/ (pow (sin eps) 3) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (+ (fma (/ (/ (pow (sin eps) 2) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))) (pow (cos eps) 2)) (+ (pow (/ (sin x) (cos x)) 3) (/ (sin x) (cos x))) (/ (sin x) (* (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3)) (cos x)))) (/ (/ (sin eps) (cos eps)) (- 1 (pow (/ (* (sin x) (sin eps)) (* (cos eps) (cos x))) 3))))) (/ (sin x) (cos x)))
1.5s
(fma (/ (+ (tan x) (tan eps)) (- (pow 1 3) (pow (* (tan x) (tan eps)) 3))) (+ (* 1 1) (+ (* (* (tan x) (tan eps)) (* (tan x) (tan eps))) (* 1 (* (tan x) (tan eps))))) (- (tan x)))
856.0ms
(* (cbrt (/ 1 (* (sqrt 2.0) 2.0))) (* (/ (fma 1/3 (pow x 3) (fma 1/60 (pow x 5) (* 2 x))) (sqrt 2.0)) (sin y)))
791.0ms
(/ (/ 1.0 (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))
757.0ms
(/ (/ (- (* (* 1.0 1.0) (+ x 1.0)) (* x (* 1.0 1.0))) (* 1.0 (+ (sqrt x) (sqrt (+ x 1.0))))) (* (sqrt x) (sqrt (+ x 1.0))))

rewrite14.8s (2.3%)

Algorithm
123×rewrite-expression-head
Calls

351 calls:

491.0ms
(+ (- (/ 1.0 (+ x 1.0)) (/ 2.0 x)) (/ 1.0 (- x 1.0)))
341.0ms
(/ (- (* (exp (+ x x)) (exp (+ x x))) (* (* 1.0 1.0) (* 1.0 1.0))) (* (+ 1.0 (exp x)) (fma 1.0 1.0 (exp (* 2 x)))))
254.0ms
(* (cbrt (+ (/ 1 b) (/ 1 a))) (cbrt (+ (/ 1 b) (/ 1 a))))
226.0ms
(- (/ (+ (tan x) (tan eps)) (- 1 (* (tan x) (tan eps)))) (tan x))
208.0ms
(- (+ (pow (exp x) 2) 4.0) (fma 4.0 (exp x) (pow (exp x) -2)))
Rules
8243×*-un-lft-identity
7970×times-frac
7404×add-sqr-sqrt
5970×add-cube-cbrt
3109×prod-diff
1783×sqrt-prod
1121×add-exp-log
928×add-cbrt-cube
699×distribute-lft-out
697×pow1
642×unpow-prod-down
566×difference-of-squares
558×add-log-exp
507×div-inv
497×associate-/l*
495×cbrt-prod
489×associate-*l*
476×distribute-lft-out--
443×pow-unpow
391×fma-neg
362×associate-*r*
360×associate-/r*
340×log1p-expm1-u
339×expm1-log1p-u
328×distribute-rgt-neg-in
312×distribute-lft-neg-in associate-/r/
255×div-exp
247×associate-+l+
244×prod-exp
211×sqr-pow
208×cube-prod
195×flip-- flip3--
189×cbrt-undiv
180×cbrt-unprod
157×flip-+ flip3-+
144×log-prod
129×unswap-sqr
120×fma-def
104×neg-mul-1
103×pow-prod-down
99×sqrt-div
96×associate-*l/
95×sub-neg
91×diff-log
81×log-pow
78×sqrt-pow1
76×swap-sqr
70×frac-2neg associate-*r/ clear-num
66×associate-/l/ tan-quot
60×frac-times
58×exp-sum
57×pow1/2
55×distribute-rgt-in distribute-lft-in
54×cbrt-div
51×unpow2
50×*-commutative pow1/3
48×unpow3 cube-mult
44×associate--l+
42×pow-exp
39×pow-to-exp
31×pow-pow div-sub
30×log-div
28×fma-udef
27×pow-prod-up
25×frac-add 1-exp rec-exp
24×rem-sqrt-square
22×exp-prod
21×sum-log
19×pow-sqr
16×pow-flip
15×+-commutative
13×complex-mul-def
11×rem-cube-cbrt associate--r+
10×pow-plus neg-sub0 rem-log-exp
9×frac-sub
8×associate--l-
7×inv-pow associate-+l- pow2
6×cube-div exp-diff
5×sqrt-unprod distribute-frac-neg neg-log
4×*.c-commutative
3×sin-cos-mult +.c-commutative sin-sum
2×rem-exp-log un-div-inv associate--r- exp-neg complex-add-def rem-square-sqrt cos-sum sin-mult tan-sum rem-cbrt-cube distribute-rgt-neg-out sqrt-undiv exp-to-pow
1×associate-+l+.c difference-cubes sqrt-pow2 log1p-udef diff-atan log1p-expm1 diff-cos expm1-log1p associate-*l*.c expm1-udef frac-2neg.c cube-unmult diff-sin

localize3.3s (0.5%)

regimes2.9s (0.4%)

Accuracy

Total 5.1b remaining (10.4%)

Threshold costs 2.0b (4%)

3.2b0%expq3 (problem 3.4.2)
0.4b0%2cos (problem 3.3.5)
0.4b0%expm1 (example 3.7)
0.3b0%qlog (example 3.10)
0.2b0%2isqrt (example 3.6)

bsearch29.0ms (0.0%)

end0.0ms (0.0%)