Details

simplify9.2m (42.7%)

prune8.1m (37.9%)

rewrite1.9m (9.0%)

Algorithm
97×rewrite-expression-head
Calls

272 calls:

8.2s
(/ (/ 1 (/ (+ b a) 1)) (/ (- b a) (/ (/ PI 2.0) (/ (/ 1 1.0) (- b a)))))
5.1s
(* (/ (/ (/ PI 2.0) (/ (/ (+ b a) 1.0) (- b a))) (- b a)) (/ (/ 1.0 b) a))
3.2s
(+ (+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0))) (/ x (* 2.0 y)))
3.1s
(+ (+ (* 333.75 (pow y 6.0)) (* (* x x) (- (- (- (* (* (* (* 11.0 x) x) y) y) (pow y 6.0)) (* 121.0 (pow y 4.0))) 2.0))) (* 5.5 (pow y 8.0)))
1.6s
(- (+ (exp (* x (- eps 1.0))) (/ (exp (* x (- eps 1.0))) eps)) (/ (exp (- (* x (+ eps 1.0)))) eps))
Rules
1782106×times-frac
874513×*-un-lft-identity
785748×add-sqr-sqrt
579501×add-cube-cbrt
102873×difference-of-squares
102787×distribute-lft-out--
62545×div-inv
44758×distribute-lft-out
12747×associate-/r/
6009×associate-*l*
5953×associate-/r*
4103×flip-- flip3--
4093×prod-diff
2407×add-exp-log
1587×associate-/l*
1573×add-cbrt-cube
1256×div-exp
755×unpow-prod-down
750×pow1
640×associate-*r*
588×associate-*r/
563×cbrt-undiv
513×add-log-exp
477×prod-exp
463×sqrt-prod
435×distribute-rgt-in distribute-lft-in
374×cbrt-unprod
351×frac-times
323×cbrt-div
280×sqr-pow
277×log1p-expm1-u
274×expm1-log1p-u
272×associate-+l+
250×cube-prod
234×cbrt-prod
225×associate-*l/
212×pow-prod-down
206×flip-+ flip3-+
181×fma-neg
159×distribute-rgt-neg-in
152×1-exp
150×frac-add
129×distribute-lft-neg-in
127×unswap-sqr
112×exp-sum
107×sum-log
92×rec-exp
89×frac-sub
85×fma-def
82×unpow3 cube-mult
77×exp-neg
67×*-commutative
65×neg-sub0 frac-2neg clear-num associate-/l/
61×sub-neg
58×exp-diff
47×swap-sqr
44×sqrt-pow1
41×neg-mul-1
40×fma-udef diff-log
38×pow1/3
36×pow-prod-up
32×log-prod
28×pow-sqr
26×distribute-neg-in
25×sqrt-div
24×pow1/2
21×+-commutative
20×un-div-inv
18×pow-plus log-pow
16×associate-+r+ rem-sqrt-square
13×div-sub
12×distribute-neg-frac
11×pow2
8×hypot-udef
7×pow-flip associate--l+ neg-log
6×expm1-log1p expm1-udef associate--l- associate--r+ exp-prod log-div
5×inv-pow
4×pow-exp log1p-expm1 pow-to-exp log1p-udef
3×distribute-lft-neg-out pow-unpow distribute-rgt-neg-out rem-log-exp
2×pow-div rem-exp-log associate-+l- associate--r-
1×distribute-rgt-out-- pow3 sqrt-unprod sub-div pow-pow rem-square-sqrt rem-cbrt-cube

sample1.2m (5.7%)

Algorithm
72×intervals
Results
23.7s276905×body80valid
9.6s25107×body160valid
9.2s13861×body1280valid
5.7s3831×body2560valid
4.2s9354×body640valid
4.1s2227×body10240exit
2.9s100605×pre80true
1.7s19460×body80nan
1.6s6845×body320valid
224.0ms253×body5120valid
4.0ms100×pre80false

series48.4s (3.8%)

Calls

272 calls:

3.5s
(cbrt (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))))
3.2s
(cbrt (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))))
3.0s
(cbrt (- (fma n (log 1.0) (* i (+ (* i 0.5) 1.0))) (* (* (* i i) 0.5) (log 1.0))))
1.7s
(fma (sqrt (pow x 4.0)) (sqrt (pow x 4.0)) (- (pow y 4.0)))
1.3s
(+ (* (fma (/ (* (cbrt (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1)) (cbrt (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1))) 1) (/ (cbrt (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1)) (+ (* x1 x1) 1.0)) (- (* (cbrt 3.0) (* (cbrt 3.0) (cbrt 3.0))))) (* (* 2.0 x1) (/ (- (+ (* (* 3.0 x1) x1) (* 2.0 x2)) x1) (+ (* x1 x1) 1.0)))) (fma (+ (- 3.0) 3.0) (* (/ (fma (* 3.0 x1) x1 (fma 2.0 x2 (- x1))) (fma x1 x1 1.0)) (* x1 2.0)) (* (* (fma 4.0 (/ (fma (* 3.0 x1) x1 (fma 2.0 x2 (- x1))) (fma x1 x1 1.0)) (- 6.0)) x1) x1)))

regimes5.5s (0.4%)

Accuracy

Total 37.0b remaining (15.5%)

Threshold costs 2.3b (1%)

10.5b53.9%Compound Interest
7.4b34.8%Complex division, real part
7.2b36.4%Complex division, imag part
4.3b84%The quadratic formula (r1)
4.1b85.7%The quadratic formula (r2)

localize4.6s (0.4%)

bsearch1.2s (0.1%)

end1.0ms (0.0%)