Details

simplify1.2hr

Calls

32297 calls:

Slowest
3.0s
(/ (* (* (* 4 4) 4) (* (* (* c a) (* c a)) (* c a))) (* (* (* (* 2 a) (* 2 a)) (* 2 a)) (* (* (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))) (- (- b) (sqrt (- (* b b) (* (* 4 a) c))))) (- (- b) (sqrt (- (* b b) (* (* 4 a) c)))))))
1.4s
(* (* (* (* 3 a) (* 3 a)) (* 3 a)) (* (* (+ (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -3 (* c a) (* b b))) b))) (+ (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -3 (* c a) (* b b))) b)))) (+ (* (sqrt (fma -3 (* c a) (* b b))) (sqrt (fma -3 (* c a) (* b b)))) (+ (* b b) (* (sqrt (fma -3 (* c a) (* b b))) b)))))
1.2s
(/ (- (exp x) (exp (- x))) (* (+ (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))
1.2s
(/ (- (exp x) (exp (- x))) (* (+ (exp x) (exp (- x))) (+ (exp x) (exp (- x)))))
1.2s
(* (/ (+ x 1) 1) (- (- x 1)))

sample12.1m

Algorithm
65×intervals
Results
9.5m81165×body10240exit
50.8s26427×body1280valid
21.6s166555×body80valid
19.7s19602×body640valid
17.1s131789×body80nan
13.3s21661×body320valid
8.3s120349×pre80true
8.2s24550×body160valid
1.9s4165×pre10240exit
1.6s1113×body2560valid
1.5s7864×body160nan
109.0ms120×body5120valid

prune4.6m

series49.5s

Calls

393 calls:

Slowest
909.0ms
(cbrt (fma 2/15 (pow x 5) x))
879.0ms
(cbrt (fma 2/15 (pow x 5) x))
870.0ms
(cbrt (fma 2/15 (pow x 5) x))
798.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
672.0ms
(* (hypot (* (- lambda1 lambda2) (cos (* (+ phi1 phi2) 1/2))) (- phi1 phi2)) R)

rewrite29.8s

Algorithm
119×rewrite-expression-head
Calls

393 calls:

Slowest
2.1s
(/ (- (* (sqrt (fma b b (* a (* c -4)))) (fma b b (* a (* c -4)))) (* b (* b b))) (* a (* 2 (+ (* (sqrt (fma c (* -4 a) (* b b))) (sqrt (fma c (* -4 a) (* b b)))) (+ (* b b) (* (sqrt (fma c (* -4 a) (* b b))) b))))))
1.6s
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- t))))) c_n)))
1.2s
(* (- (/ (/ (- m (* m (* m m))) v) (+ 1 m)) 1) (- 1 m))
1.2s
(* (- (* (* (- 1 m) m) (/ 1 v)) 1) (- 1 m))
1.0s
(* (* (- (/ m (/ v (- 1 m))) 1) (sqrt m)) (sqrt m))
Rules
51118×add-sqr-sqrt
40592×*-un-lft-identity
28667×times-frac
27565×add-cube-cbrt
19947×associate-/r*
18555×associate-/l*
14495×associate-*l*
11075×associate-*r*
10736×prod-diff
10144×frac-sub
9959×frac-times
9724×frac-add
9578×cbrt-prod
8973×unswap-sqr
7255×unpow-prod-down
6756×associate-/l/
4928×associate-*l/
4787×log-div
4659×difference-of-squares
4009×distribute-lft-out
3800×swap-sqr
3487×clear-num
3482×frac-2neg
2788×*-commutative
2756×sqrt-prod
2500×add-exp-log
2015×add-cbrt-cube
1889×sqr-pow
1690×distribute-lft-out--
1151×pow1
1086×div-inv
1027×prod-exp
971×associate-/r/
832×div-exp
777×cbrt-unprod
766×cbrt-undiv
701×pow-exp
636×fma-neg
556×add-log-exp
547×flip-+
546×flip3-+
479×distribute-rgt-neg-in
474×distribute-lft-in distribute-rgt-in
411×associate-*r/
399×expm1-log1p-u
395×log1p-expm1-u
393×insert-posit16
368×distribute-lft-neg-in
348×pow-to-exp
264×flip--
263×flip3--
240×pow-prod-down
220×difference-of-sqr-1
182×cbrt-div
173×exp-prod
145×cube-unmult
142×fma-def
139×pow-prod-up
130×1-exp
129×rec-exp
127×distribute-rgt-out--
124×neg-mul-1
94×log-prod
89×fma-udef
87×log-pow
85×pow-sqr
81×pow-plus
76×sqrt-div
73×sub-neg
72×tan-quot
70×difference-cubes
66×sqrt-pow1
60×pow1/2
52×diff-log
48×pow2
37×pow1/3
34×+-commutative
33×sin-sum pow-pow
32×rem-sqrt-square
30×sum-log
25×cos-sum
23×div-sub
19×pow-flip sub-div
18×neg-sub0 pow3
16×pow-unpow
15×rem-log-exp
14×un-div-inv
11×log1p-expm1
10×associate-+r+ inv-pow associate-+l-
neg-log associate--r+
associate--l+ log1p-udef exp-neg
exp-diff exp-sum rem-cbrt-cube
acos-asin
remove-double-div sin-mult expm1-def
unpow-prod-up log-rec sqrt-unprod rem-square-sqrt rem-exp-log distribute-rgt-out
expm1-log1p expm1-udef associate--l- unpow1/3 cos-diff associate--r-
remove-posit16 distribute-rgt1-in distribute-frac-neg tanh-undef tanh-def exp-to-pow asin-acos hypot-udef acos-neg sin-diff e-exp-1

regimes9.9s

Accuracy

Total 24.4b remaining (11.2%)

6.8b26.6%Cubic critical, narrow range
3.9b85.7%Cubic critical
3.4b0%Cubic critical, medium range
2.0b0%2-ancestry mixing, positive discriminant
1.8b0%Quadratic roots, wide range

localize3.0s

bsearch898.0ms

end1.0ms