Details

simplify6.5m (42.7%)

sample5.2m (34.1%)

Algorithm
78×intervals
Results
1.9m21677×body10240exit
1.3m44002×body1280valid
28.8s30671×body640valid
19.9s202829×body80valid
15.1s152220×body80nan
12.8s27697×body320valid
7.4s35848×body160valid
7.3s159048×pre80true
2.0s2961×body2560valid
1.2s7872×body160nan
479.0ms4103×pre10240exit
209.0ms230×body5120valid
206.0ms8220×pre80false

prune1.3m (8.5%)

series1.1m (7.3%)

Calls

483 calls:

1.1s
(/ (- (* (cos delta) (cos delta)) (pow (* (sin phi1) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) 2)) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)))
942.0ms
(cbrt (fma (/ (pow x 3) (pow (sqrt 1.0) 3)) -1/6 (+ (log (sqrt 1.0)) (/ x (sqrt 1.0)))))
901.0ms
(hypot (* (cos (/ (+ phi1 phi2) 2.0)) (- lambda1 lambda2)) (- phi1 phi2))
814.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
793.0ms
(/ (* (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)))

rewrite26.4s (2.9%)

Algorithm
145×rewrite-expression-head
Calls

483 calls:

1.1s
(* (+ (- (* (+ (sqrt 1.0) (sqrt m)) (/ m (/ v (- (sqrt 1.0) (sqrt m))))) 1.0) (+ (- 1.0) 1.0)) m)
810.0ms
(cbrt (pow (- (log 2) (+ (- (/ 0.09375 (pow x 4)) (log x)) (/ 0.25 (* x x)))) 3))
711.0ms
(pow (- (log 2) (+ (- (/ 0.09375 (pow x 4)) (log x)) (/ 0.25 (* x x)))) 3)
655.0ms
(- (log 2) (- (+ (/ 0.25 (* x x)) (/ 0.09375 (pow x 4))) (log x)))
519.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
Rules
13858×*-un-lft-identity
11443×times-frac
10828×add-sqr-sqrt
7914×add-cube-cbrt
5768×prod-diff
2710×unpow-prod-down
2669×add-exp-log
2518×cube-prod
1885×sqrt-prod
1771×distribute-lft-out
1710×add-cbrt-cube
1250×difference-of-squares
1212×distribute-lft-out--
1060×pow1
976×associate-/r/
923×prod-exp
744×div-exp
712×add-log-exp
671×associate-/l*
669×div-inv
610×associate-*r*
602×fma-neg
584×cbrt-prod
537×associate-/r*
509×associate-*l*
484×log1p-expm1-u
483×expm1-log1p-u
437×cbrt-unprod
392×flip--
391×flip3--
363×pow-exp
348×cbrt-undiv
338×flip-+
337×flip3-+
334×distribute-rgt-neg-in
262×pow-to-exp
259×sqr-pow
247×distribute-rgt-in distribute-lft-in
242×pow-prod-down
235×fma-def
230×log-prod
189×distribute-lft-neg-in
176×unpow3 cube-mult
160×unswap-sqr
136×sqrt-div
132×log-pow swap-sqr
120×clear-num frac-2neg
108×*-commutative
107×associate-/l/
98×sub-neg associate-*r/
93×associate-+l+
84×associate-*l/
75×diff-log
69×exp-prod
64×cbrt-div
63×cos-sum
62×neg-mul-1
56×pow1/3
55×associate-+r+
54×pow-unpow
47×frac-times
45×sum-log
44×sin-sum
43×div-sub
38×frac-add
33×log-div
32×fma-udef +-commutative
29×pow1/2 sqrt-pow1
27×pow-pow
26×exp-sum rem-log-exp
25×rem-sqrt-square unpow2 1-exp rec-exp associate--r+
22×sin-mult
20×cube-div rem-cube-cbrt
19×neg-sub0
17×tan-quot cos-mult sin-diff
13×associate-+l- neg-log
12×pow-prod-up pow-sqr
11×distribute-lft-neg-out cos-diff distribute-rgt-out sum-cubes
10×acos-asin
9×pow2 frac-sub distribute-rgt-neg-out
8×sin-cos-mult associate--l- pow-plus
7×rem-cbrt-cube
6×associate--l+
5×sqrt-undiv unsub-neg asin-acos associate--r-
4×exp-diff acos-neg distribute-frac-neg rem-exp-log
3×sin-neg un-div-inv pow-flip
2×difference-cubes sqrt-unprod inv-pow hypot-udef distribute-neg-frac associate-+r-
1×distribute-neg-out expm1-log1p rem-square-sqrt hypot-def tanh-undef sqr-cos expm1-udef tanh-def

bsearch25.8s (2.8%)

regimes11.5s (1.3%)

Accuracy

Total 22.3b remaining (20.6%)

Threshold costs 6.6b (6.1%)

5.1b54.2%Quotient of products
3.5b0%Quadratic roots, wide range
2.4b89.6%Cubic critical
2.1b0%(- (/ x0 (- 1 x1)) x0)
1.6b93.9%Quadratic roots, full range

localize3.8s (0.4%)

end1.0ms (0.0%)