Details

simplify10.8m (43.2%)

sample9.0m (36.0%)

Algorithm
78×intervals
Results
4.7m26288×body10240exit
1.8m43571×body1280valid
39.7s30540×body640valid
25.3s202536×body80valid
19.1s150771×body80nan
16.5s27686×body320valid
14.2s36538×body160valid
9.7s163277×pre80true
2.2s3037×body2560valid
1.4s4104×pre10240exit
1.1s8004×body160nan
217.0ms202×body5120valid
1.0msbody320nan

prune2.5m (9.9%)

series1.5m (5.8%)

Calls

453 calls:

2.5s
(expm1 (log1p (log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1))))
2.4s
(fma (* (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0)) (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- (* (* (log1p (expm1 (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0)))) (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0))) (* 1.0 1.0))))
1.7s
(log1p (log1p (fma (fma 1/4 (- a b) 1) (sqrt E) -1)))
1.4s
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
1.2s
(fma (* (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0)) (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0))) (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (- (* (* (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0)) (- (* (* (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (/ 2.0 (+ 1.0 (exp (* -2.0 x))))) (* (* 1.0 1.0) 1.0))) (* 1.0 1.0))))

regimes33.3s (2.2%)

Accuracy

Total 59.3b remaining (34.9%)

Threshold costs 4.8b (2.8%)

8.5b38%Quadratic roots, narrow range
8.4b38.4%Cubic critical, narrow range
6.0b14.9%Cubic critical, medium range
5.9b15%Quadratic roots, medium range
5.4b81.6%Cubic critical

rewrite32.9s (2.2%)

Algorithm
145×rewrite-expression-head
Calls

453 calls:

1.0s
(/ (* (* (* -1.5 -1.5) -1.5) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* a a) a) (* (* 3.0 3.0) 3.0)))
951.0ms
(cbrt (/ (* (* (* -1.5 -1.5) -1.5) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* a a) a) (* (* 3.0 3.0) 3.0))))
712.0ms
(* (- (/ (/ (* (* (- 1.0 m) (+ m 1.0)) m) (+ 1.0 m)) v) 1.0) (- 1.0 m))
711.0ms
(cbrt (* (* (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0) (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)) (- (/ 2.0 (+ 1.0 (exp (* -2.0 x)))) 1.0)))
614.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
Rules
13040×add-exp-log
12344×add-cbrt-cube
8688×prod-exp
8321×cbrt-unprod
7046×*-un-lft-identity
6715×add-sqr-sqrt
6484×times-frac
4743×add-cube-cbrt
2481×div-exp
2394×prod-diff
2194×cbrt-undiv
1666×pow1
1415×sqrt-prod
768×difference-of-squares
630×add-log-exp
572×distribute-lft-out
539×distribute-lft-out--
535×flip--
534×flip3--
492×associate-*r*
483×cbrt-div
458×expm1-log1p-u
456×log1p-expm1-u
454×frac-times
442×associate-/l*
434×associate-*l*
431×pow-prod-down
392×div-inv
390×associate-/r*
384×distribute-rgt-neg-in
380×distribute-lft-neg-in
354×fma-neg associate-/r/
336×sqrt-div
275×cbrt-prod
265×pow-exp
264×pow-prod-up
250×distribute-rgt-in distribute-lft-in
245×associate-*r/
242×associate-*l/
185×pow-to-exp
182×flip-+
181×flip3-+
170×exp-prod
150×pow-sqr
147×log-prod
146×unswap-sqr
141×pow-plus
113×fma-def
110×sub-neg
108×*-commutative
100×clear-num frac-2neg
93×pow1/3
91×swap-sqr
89×associate-/l/
87×neg-mul-1
86×log-pow
84×tan-quot
73×pow2
68×diff-log
58×cos-sum
50×div-sub
48×unpow-prod-down
47×associate--l+
46×fma-udef
44×sin-sum
40×pow1/2 sqrt-pow1
33×log-div
29×pow-flip
26×rem-sqrt-square
25×1-exp rec-exp cos-mult
22×sum-log rem-log-exp
20×+-commutative
18×sin-diff
17×pow3 cos-diff frac-sub
16×exp-sum
15×neg-sub0
14×associate-+r+
12×associate--r+
11×sin-mult
10×exp-diff sin-cos-mult distribute-frac-neg acos-asin
log1p-udef inv-pow log1p-expm1 frac-add expm1-log1p expm1-udef exp-neg distribute-rgt-neg-out
pow-unpow difference-cubes sqr-pow associate--l-
sin-neg
rem-exp-log acos-neg
un-div-inv
pow-pow sqrt-unprod hypot-udef hypot-def associate--r- tanh-def rem-cbrt-cube
cube-unmult rem-square-sqrt distribute-rgt-out tanh-undef asin-acos

localize9.5s (0.6%)

bsearch1.5s (0.1%)

end2.0ms (0.0%)