Details

sample4.1m (36.6%)

Algorithm
77×intervals
Results
1.2m43465×body1280valid
57.9s17619×body10240exit
28.8s30753×body640valid
18.1s202709×body80valid
14.0s152160×body80nan
13.3s27659×body320valid
7.3s35878×body160valid
6.9s153588×pre80true
1.9s2974×body2560valid
1.1s7682×body160nan
488.0ms4146×pre10240exit
199.0ms8382×pre80false
104.0ms228×body5120valid

simplify4.0m (35.3%)

prune1.4m (12.3%)

series55.0s (8.2%)

Calls

448 calls:

1.0s
(log (exp (/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta)))))) (pow (sin phi1) 2))) (fma (sin (asin (fma (sin delta) (* (cos phi1) (cos theta)) (* (sin phi1) (cos delta))))) (sin phi1) (cos delta)))))
846.0ms
(* R (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)))
780.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
666.0ms
(fma (/ (sqrt x0) (+ (sqrt 1.0) (sqrt x1))) (/ (sqrt x0) (- (sqrt 1.0) (sqrt x1))) (- x0))
645.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))

rewrite20.2s (3.0%)

Algorithm
144×rewrite-expression-head
Calls

448 calls:

605.0ms
(* (- (/ m (/ (* v (- (* 1.0 1.0) (* m m))) (* (- (* 1.0 1.0) (* m m)) (- 1.0 m)))) 1.0) (- 1.0 m))
521.0ms
(+ (/ 1.0 x) (/ (sqrt (- 1.0 (* x x))) x))
519.0ms
(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
486.0ms
(/ (* (* -1.5 (/ a (sqrt b))) (/ c (sqrt b))) (* 3.0 a))
476.0ms
(pow (+ (* (/ 1.0 (- (pow x 3) (pow 1.0 3))) (+ (* x x) (+ (* 1.0 1.0) (* x 1.0)))) (/ x (+ x 1.0))) 3)
Rules
17158×times-frac
13703×*-un-lft-identity
11926×add-sqr-sqrt
8936×add-cube-cbrt
3865×prod-diff
2449×add-exp-log
2059×sqrt-prod
1650×add-cbrt-cube
1432×cbrt-prod
1361×difference-of-squares
1204×distribute-lft-out
1183×distribute-lft-out--
1002×associate-/r/
1000×div-inv
943×pow1
872×unpow-prod-down
803×cube-prod
780×div-exp
754×prod-exp
618×add-log-exp associate-*l*
600×associate-/r*
550×associate-*r*
458×fma-neg
450×expm1-log1p-u
449×log1p-expm1-u
416×cbrt-undiv
403×flip--
402×flip3--
401×cbrt-unprod
376×associate-/l*
353×distribute-rgt-neg-in
287×pow-exp
271×flip-+
270×flip3-+
250×log-prod
232×log-pow
206×pow-to-exp
179×sqrt-div exp-prod
163×pow-prod-down
162×fma-def
147×sqr-pow
134×unswap-sqr
132×sqrt-pow1
107×clear-num frac-2neg
103×associate-*r/
95×frac-times
94×pow1/2
91×swap-sqr
88×distribute-rgt-in *-commutative distribute-lft-in
77×sub-neg
76×associate-*l/
73×unpow3 cube-mult
68×cbrt-div
63×diff-log
62×distribute-lft-neg-in associate-/l/
60×pow-unpow
59×pow1/3
58×cos-sum
43×div-sub
41×pow-prod-up
38×log-div
36×rem-log-exp
34×rem-sqrt-square
31×pow-sqr
28×1-exp
26×exp-sum
25×distribute-rgt-out rec-exp sum-log
24×fma-udef
23×sin-sum
22×pow-pow
19×+-commutative
18×frac-add sin-diff
15×cos-diff neg-mul-1
14×associate--l+
13×cube-div associate-+r+
12×sin-cos-mult pow-plus pow2 acos-asin tan-quot sin-mult
11×associate-+l-
10×unpow2
9×exp-diff frac-sub
8×rem-cube-cbrt neg-sub0
7×rem-exp-log difference-cubes associate--r+ associate-+r-
6×acos-neg asin-acos sqrt-unprod distribute-neg-in associate-+l+ distribute-frac-neg distribute-neg-frac
5×hypot-def neg-log cos-mult associate--r-
4×log1p-udef distribute-lft1-in distribute-rgt1-in rem-square-sqrt sum-cubes distribute-rgt-neg-out
3×log1p-expm1 expm1-log1p expm1-udef
2×associate--l- inv-pow hypot-udef count-2 pow-flip rem-cbrt-cube
1×sin-neg sqrt-undiv distribute-lft-neg-out sqr-sin sub-div tanh-undef distribute-rgt-out-- tanh-def

regimes14.7s (2.2%)

Accuracy

Total 48.3b remaining (31.8%)

Threshold costs 6.5b (4.3%)

7.5b47.4%Cubic critical, narrow range
6.5b8.9%Quadratic roots, medium range
6.4b8.2%Cubic critical, medium range
5.3b51.2%Quotient of products
4.2b85.3%Quadratic roots, full range

bsearch12.0s (1.8%)

localize4.0s (0.6%)

end1.0ms (0.0%)