Details

simplify1.3hr

Calls

39595 calls:

Slowest
1.8s
(/ (* (* (* -3/2 -3/2) -3/2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 3 a) (* 3 a)) (* 3 a)))
1.5s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.5s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a c) (* a c)) (* a c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))
1.5s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 a) (* 2 a)) (* 2 a)))
1.4s
(/ (* (* (* -2 -2) -2) (/ (* (* (* a a) a) (* (* c c) c)) (* (* b b) b))) (* (* (* 2 2) 2) (* (* a a) a)))

sample12.1m

Algorithm
66×intervals
Results
9.4m73583×body10240exit
50.6s27303×body1280valid
23.7s163102×body80valid
21.2s19714×body640valid
20.1s143432×body80nan
13.6s19522×body320valid
11.5s31074×body160valid
8.4s123490×pre80true
2.0s2151×body2560valid
1.9s4165×pre10240exit
1.4s7864×body160nan
209.0ms228×body5120valid

prune5.5m

rewrite2.3m

Algorithm
126×rewrite-expression-head
Calls

406 calls:

Slowest
24.1s
(/ (+ (pow (+ (* (* (* x x) -1/3) x) x) 3) (pow (* (pow x 5) 2/15) 3)) (+ (* (+ (* (* (* x x) -1/3) x) x) (+ (* (* (* x x) -1/3) x) x)) (- (* (* (pow x 5) 2/15) (* (pow x 5) 2/15)) (* (+ (* (* (* x x) -1/3) x) x) (* (pow x 5) 2/15)))))
22.9s
(* (* (- (/ m (* (/ v (- (pow 1 3) (pow m 3))) (+ (+ (* m m) m) 1))) 1) (sqrt m)) (sqrt m))
8.3s
(* (- (/ (- m (* (* m m) (* m m))) (* v (+ (* 1 1) (+ (* m m) (* 1 m))))) 1) (- 1 m))
7.4s
(* (- (/ m (* (/ v (- (pow 1 3) (pow m 3))) (+ (+ (* m m) m) 1))) 1) (sqrt m))
7.3s
(* (- (/ m (* (/ v (- (pow 1 3) (pow m 3))) (+ (+ (* m m) m) 1))) 1) m)
Rules
98530×*-un-lft-identity
75572×add-sqr-sqrt
66799×times-frac
50367×associate-*l*
44197×add-cube-cbrt
41172×associate-/l*
35973×associate-/r*
27125×distribute-lft-out
20653×frac-add
19018×frac-sub
18567×frac-times
15771×associate-*r*
14698×cbrt-prod
14626×unpow-prod-down
14614×associate-/l/
12582×associate-*l/
11164×unswap-sqr
9150×log-div
8158×distribute-lft-out--
8028×sqrt-prod
7885×difference-of-squares
6002×clear-num
5983×frac-2neg
5350×cube-prod
4153×*-commutative
3026×swap-sqr
2966×sqr-pow
2951×add-exp-log
2758×add-cbrt-cube
2048×div-inv
1272×flip-+
1271×flip3-+
1188×pow1
1187×prod-exp
1102×cbrt-undiv
1098×cbrt-unprod
988×div-exp
870×associate-*r/
795×associate-/r/
701×pow-exp
643×add-log-exp
618×pow-unpow
528×flip--
527×flip3--
472×sum-cubes
406×insert-posit16
353×pow-to-exp
310×sqrt-div
278×pow-prod-down
245×log-prod
243×distribute-rgt-out--
195×difference-of-sqr-1
180×cbrt-div
176×log-pow
159×exp-prod
140×difference-cubes
131×1-exp
130×rec-exp
100×pow-prod-up
95×sub-neg
80×tan-quot
75×diff-log
74×+-commutative
70×pow-sqr
69×distribute-rgt-neg-in
67×exp-diff
54×pow-plus
52×distribute-rgt-in distribute-lft-in
50×un-div-inv
49×sum-log sqrt-pow1
43×pow1/2
42×pow2
36×rem-sqrt-square
35×div-sub cube-mult
31×pow1/3
30×difference-of-sqr--1
28×rem-log-exp
25×distribute-rgt-out
20×associate-+l+
19×associate--l+ sub-div
16×associate-+r+
14×acos-asin
13×cos-mult
12×cos-diff
10×pow-flip associate--l- exp-sum
inv-pow
cos-sum
sin-mult remove-double-div
pow-pow distribute-rgt1-in
distribute-frac-neg associate--r+ associate-+l-
log-rec sin-PI/3 acos-neg
sin-sum sqrt-unprod associate--r-
remove-posit16 sin-cos-mult distribute-lft1-in sub0-neg pow3 tanh-undef tanh-def exp-to-pow asin-acos rem-exp-log sin-diff

series39.1s

Calls

406 calls:

Slowest
910.0ms
(cbrt (/ (- (- g) (sqrt (- (* g g) (* h h)))) (/ (cbrt a) (sqrt 1/2))))
791.0ms
(/ (* (/ (cbrt a2) (cbrt b2)) (* (/ (cbrt a2) (cbrt b2)) a1)) b1)
746.0ms
(/ (* (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)))
696.0ms
(cos (/ (- (* (/ (acos (/ g h)) (* (cbrt 3) (cbrt 3))) 3/2) (* (cbrt 3) PI)) (* (cbrt 3) 3/2)))
576.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

regimes11.6s

Accuracy

Total 50.2b remaining (31.4%)

8.1b41.4%Quadratic roots, narrow range
7.6b45.7%Cubic critical, narrow range
6.8b54.4%Equirectangular approximation to distance on a great circle
6.2b14.1%Cubic critical, medium range
5.8b16.4%Quadratic roots, medium range

localize3.3s

bsearch966.0ms

end1.0ms