Details

simplify4.3m (53.3%)

sample2.0m (24.2%)

Algorithm
77×intervals
Results
34.2s43972×body1280valid
34.2s15913×body10240exit
11.0s29783×body640valid
6.7s202058×body80valid
4.6s27684×body320valid
4.6s152509×body80nan
3.0s36124×body160valid
2.3s151934×pre80true
710.0ms2964×body2560valid
366.0ms8106×body160nan
325.0ms4022×pre10240exit
93.0ms8332×pre80false
55.0ms208×body5120valid

prune46.2s (9.5%)

series38.5s (7.9%)

Calls

460 calls:

496.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
495.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
407.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
401.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
394.0ms
(fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (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)))))))))

rewrite14.3s (2.9%)

Algorithm
142×rewrite-expression-head
Calls

460 calls:

495.0ms
(* (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))) (sqrt (- (/ x (+ x 1.0)) (/ (+ x 1.0) (- x 1.0)))))
269.0ms
(* (/ 1 (sqrt x)) (+ (/ 1.0 (sqrt x)) (/ (sqrt (- 1.0 (* x x))) (sqrt x))))
185.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))
183.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))
180.0ms
(- (/ 0.125 (pow x 3)) (+ (/ 0.0625 (pow x 5)) (/ 0.5 x)))
Rules
11937×*-un-lft-identity
9512×times-frac
9081×add-sqr-sqrt
6098×add-cube-cbrt
3406×prod-diff
2097×add-exp-log
1709×add-cbrt-cube
1462×distribute-lft-out
1401×difference-of-squares
1285×distribute-lft-out--
1134×sqrt-prod
942×associate-*r*
905×pow1
707×cbrt-prod
676×add-log-exp
634×associate-/r/
621×associate-/l*
589×associate-/r*
585×unpow-prod-down
567×prod-exp
560×div-exp
549×cube-prod
544×associate-*l*
482×div-inv
462×log1p-expm1-u expm1-log1p-u
437×cbrt-unprod
396×fma-neg
394×cbrt-undiv
343×flip--
342×flip3--
335×log-prod
289×distribute-rgt-neg-in
271×sqr-pow
244×flip-+
243×flip3-+
240×distribute-rgt-in distribute-lft-in
229×fma-def
178×pow-prod-down
150×unswap-sqr
124×swap-sqr
114×clear-num frac-2neg
103×associate-*r/
102×associate-/l/
96×*-commutative
95×associate-+l+
89×cube-mult
88×unpow3
87×sub-neg frac-times
85×distribute-lft-neg-in
78×sqrt-div
74×associate-*l/
71×exp-prod
70×log-pow
68×1-exp diff-log
62×cos-sum
60×exp-sum
48×associate-+r+
45×pow1/2 sqrt-pow1
43×sum-log
42×pow1/3 log-div
41×rec-exp cbrt-div
40×frac-sub
37×div-sub
36×fma-udef
33×pow-unpow
29×+-commutative neg-mul-1
28×frac-add
27×rem-log-exp
25×rem-sqrt-square
22×sin-sum
20×difference-cubes
19×pow-prod-up sin-diff
18×associate--l+
17×pow-exp
16×pow-flip neg-sub0
15×pow-sqr
14×pow-to-exp
13×sin-cos-mult pow-pow associate-+l-
12×tan-quot sin-mult
10×cube-div inv-pow neg-log
9×pow-plus pow2 cos-diff
8×pow-div rem-cube-cbrt distribute-rgt-out associate--r+
7×unpow2 associate--l-
6×rem-exp-log expm1-udef
5×acos-asin asin-acos
4×expm1-log1p cos-mult associate--r- rem-cbrt-cube
3×log1p-udef distribute-lft-neg-out log1p-expm1
2×sin-neg distribute-lft1-in sqrt-unprod hypot-udef rem-square-sqrt distribute-rgt-neg-out
1×exp-diff acos-neg sqrt-undiv un-div-inv exp-to-pow pow3 distribute-neg-in sin-asin sqr-sin unsub-neg distribute-frac-neg tanh-undef tanh-def

regimes8.0s (1.6%)

Accuracy

Total 40.0b remaining (32.4%)

Threshold costs 7.7b (6.2%)

7.8b45%Quadratic roots, narrow range
6.2b11.6%Quadratic roots, medium range
6.0b78.6%Cubic critical
5.7b48%Quotient of products
4.6b83.5%Quadratic roots, full range

localize2.2s (0.5%)

bsearch660.0ms (0.1%)

end1.0ms (0.0%)