Details

simplify6.8m (43.4%)

sample6.3m (39.7%)

Algorithm
78×intervals
Results
3.0m26914×body10240exit
1.3m43594×body1280valid
28.5s30452×body640valid
20.7s202965×body80valid
14.2s153461×body80nan
12.4s27959×body320valid
9.3s35956×body160valid
7.4s164300×pre80true
1.8s3110×body2560valid
1.0s4113×pre10240exit
768.0ms8154×body160nan
171.0ms8261×pre80false
126.0ms215×body5120valid
3.0ms2×body640nan

prune1.1m (7.0%)

series56.4s (6.0%)

Calls

453 calls:

796.0ms
(/ (* (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)))
697.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
661.0ms
(/ (* (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)))
656.0ms
(/ (* (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)))
500.0ms
(cbrt (* (/ 1.0 (* 2.0 a)) (+ (- g) (sqrt (- (* g g) (* h h))))))

rewrite20.7s (2.2%)

Algorithm
145×rewrite-expression-head
Calls

453 calls:

598.0ms
(* (sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))) (sqrt (+ (/ (/ 2.0 x) x) (/ 2.0 (pow x 4)))))
518.0ms
(* (/ (exp a) (+ (pow (exp a) 3) (pow (exp b) 3))) (+ (* (exp a) (exp a)) (- (* (exp b) (exp b)) (* (exp a) (exp b)))))
517.0ms
(* (* (sin phi1) (cos phi2)) (- (* (cos lambda1) (cos lambda2)) (log (exp (* (sin lambda1) (sin (- lambda2)))))))
467.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) m)
348.0ms
(- (/ x (+ 1.0 x)) (/ (+ 1.0 x) (pow (cbrt (- x 1.0)) 3)))
Rules
10840×*-un-lft-identity
10044×times-frac
8703×add-sqr-sqrt
6920×add-cube-cbrt
4247×prod-diff
3893×add-exp-log
1802×add-cbrt-cube
1525×sqrt-prod
1447×prod-exp
1438×div-exp
1318×distribute-lft-out
1228×unpow-prod-down
1113×cbrt-prod
1045×cube-prod
889×pow1
707×difference-of-squares
636×add-log-exp
618×pow-exp
592×distribute-lft-out--
576×associate-/r/
566×div-inv
560×associate-/r*
482×associate-/l*
470×cbrt-undiv
459×associate-*l* associate-*r*
456×log1p-expm1-u
453×expm1-log1p-u
452×cbrt-unprod
440×pow-to-exp
331×fma-neg
265×flip--
264×flip3--
258×flip-+
257×flip3-+
214×sqr-pow
167×unpow3 cube-mult
157×fma-def
155×pow-prod-down
145×distribute-rgt-in distribute-lft-in
137×1-exp
127×rec-exp log-prod
116×unswap-sqr
115×associate-*r/
111×clear-num frac-2neg
109×distribute-rgt-neg-in
104×log-pow
97×sub-neg
92×sqrt-div
88×*-commutative
86×cbrt-div
82×associate-*l/
73×frac-times
72×pow-unpow associate-/l/
69×distribute-lft-neg-in
66×diff-log
59×cos-sum
58×cube-div
47×pow1/2 exp-prod sqrt-pow1
44×sin-sum
43×log-div
37×pow1/3 div-sub
33×pow-pow
32×swap-sqr
30×rem-sqrt-square fma-udef
26×frac-add hypot-def sum-log exp-sum
24×rem-log-exp
23×neg-mul-1
21×+-commutative
19×rem-cube-cbrt pow-flip
18×sin-diff
17×cos-mult
15×sin-mult
14×sin-cos-mult pow-prod-up
13×associate--l+
12×tan-quot frac-sub
11×inv-pow cos-diff
9×pow-sqr acos-asin sum-cubes
8×associate--r-
7×associate--l- neg-sub0 rem-cbrt-cube associate--r+
6×unpow2
5×pow-plus sin-neg un-div-inv pow2 expm1-log1p neg-log distribute-rgt-neg-out expm1-udef
4×exp-neg associate-+l- rem-exp-log
3×exp-diff acos-neg distribute-frac-neg asin-acos exp-to-pow
2×sqrt-undiv sqrt-pow2 log1p-udef sqrt-unprod log1p-expm1 sub-div rem-square-sqrt distribute-rgt-out
1×remove-double-div pow3 associate-+l+ tanh-undef distribute-rgt-out-- tanh-def log-rec

regimes12.0s (1.3%)

Accuracy

Total 41.5b remaining (29.8%)

Threshold costs 5.1b (3.7%)

7.9b42.5%Quadratic roots, narrow range
7.0b0%Cubic critical, medium range
4.6b84.2%Quadratic roots, full range
4.6b84.2%Cubic critical
3.4b0%Quadratic roots, wide range

localize3.9s (0.4%)

bsearch1.1s (0.1%)

end0.0ms (0.0%)