Details

simplify6.5m (43.2%)

sample5.1m (33.6%)

Algorithm
78×intervals
Results
1.9m21677×body10240exit
1.3m44002×body1280valid
28.6s30671×body640valid
20.1s202829×body80valid
14.4s152220×body80nan
13.4s27697×body320valid
8.9s35848×body160valid
8.5s159048×pre80true
1.7s2961×body2560valid
1.0s7872×body160nan
773.0ms4103×pre10240exit
606.0ms230×body5120valid
298.0ms8220×pre80false

prune1.3m (8.3%)

series1.1m (7.4%)

Calls

473 calls:

1.2s
(expm1 (log1p (log (/ (sqrt (+ 1.0 x)) (- 1.0 x)))))
1.1s
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (fma (sin phi1) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (cos delta)))
814.0ms
(* (cbrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))) (cbrt (+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))))
790.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
716.0ms
(log1p (log (/ (sqrt (+ 1.0 x)) (- 1.0 x))))

rewrite26.1s (2.9%)

Algorithm
145×rewrite-expression-head
Calls

473 calls:

1.1s
(* (+ (- (* (+ (sqrt 1.0) (sqrt m)) (/ m (/ v (- (sqrt 1.0) (sqrt m))))) 1.0) (+ (- 1.0) 1.0)) m)
970.0ms
(cbrt (pow (- (log 2) (+ (- (/ 0.09375 (pow x 4)) (log x)) (/ 0.25 (* x x)))) 3))
802.0ms
(pow (- (log 2) (+ (- (/ 0.09375 (pow x 4)) (log x)) (/ 0.25 (* x x)))) 3)
751.0ms
(- (log 2) (- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x)))
542.0ms
(- (pow (/ x (+ x 1.0)) 3) (pow (/ (+ x 1.0) (- x 1.0)) 3))
Rules
13088×*-un-lft-identity
10923×times-frac
10259×add-sqr-sqrt
7551×add-cube-cbrt
5473×prod-diff
2567×add-exp-log
2541×unpow-prod-down
2366×cube-prod
1630×add-cbrt-cube
1627×distribute-lft-out
1614×sqrt-prod
1213×difference-of-squares
1195×distribute-lft-out--
1031×pow1
974×associate-/r/
849×prod-exp
753×div-exp
690×add-log-exp
670×div-inv
642×associate-*r*
631×associate-/l*
590×cbrt-prod
565×fma-neg
503×associate-/r*
475×expm1-log1p-u
473×log1p-expm1-u
390×associate-*l*
389×flip-- cbrt-unprod
388×flip3--
355×cbrt-undiv pow-exp
330×flip-+
329×flip3-+
285×distribute-rgt-neg-in
255×pow-to-exp
226×distribute-rgt-in distribute-lft-in
219×fma-def
218×pow-prod-down
206×log-prod
193×sqr-pow
157×distribute-lft-neg-in
147×log-pow
133×sqrt-div
130×unpow3 cube-mult
126×unswap-sqr
117×clear-num frac-2neg
97×*-commutative
96×sub-neg
95×associate-+l+ associate-*r/
92×associate-/l/
79×associate-*l/
74×diff-log
70×swap-sqr
66×exp-prod
64×cbrt-div
63×cos-sum
58×pow1/3
52×associate-+r+ neg-mul-1
47×frac-times
45×pow-unpow
44×sin-sum
42×div-sub
40×sum-log
36×frac-add
35×fma-udef
34×log-div
30×+-commutative
29×1-exp rec-exp
28×pow1/2 sqrt-pow1
27×sin-mult associate--r+
26×exp-sum rem-log-exp
24×rem-sqrt-square
21×cos-mult
20×pow-pow
19×cube-div
17×unpow2 tan-quot sin-diff
16×rem-cube-cbrt
15×associate--l+
14×neg-sub0
13×pow-prod-up pow-sqr
11×cos-diff
10×distribute-lft-neg-out associate-+l- distribute-rgt-out acos-asin neg-log distribute-rgt-neg-out
9×pow2 pow-plus
8×sin-cos-mult associate--l- pow-flip
7×inv-pow rem-cbrt-cube
6×associate--r-
5×unsub-neg frac-sub
4×exp-diff acos-neg sin-neg un-div-inv distribute-frac-neg asin-acos rem-exp-log
3×expm1-udef
2×log1p-udef log1p-expm1 sum-cubes expm1-log1p hypot-udef hypot-def sub-div distribute-neg-frac
1×distribute-neg-out difference-cubes associate-+r- sqrt-unprod sqr-sin tanh-undef sqr-cos distribute-rgt-out-- tanh-def

bsearch25.7s (2.8%)

regimes12.3s (1.4%)

Accuracy

Total 34.7b remaining (26.2%)

Threshold costs 7.2b (5.4%)

8.3b38.7%Cubic critical, narrow range
6.1b11.3%Quadratic roots, medium range
5.1b54.2%Quotient of products
4.5b84.3%Quadratic roots, full range
2.4b89.6%Cubic critical

localize3.5s (0.4%)

end1.0ms (0.0%)