Details

sample23.3m (71.4%)

Algorithm
76×intervals
Results
20.0m130696×body10240exit
1.0m34339×body1280valid
25.8s25601×body640valid
25.7s199950×body80valid
20.6s151831×body80nan
13.8s26228×body320valid
13.3s35258×body160valid
11.8s179111×pre80true
2.5s2981×body2560valid
1.8s7962×body160nan
853.0ms4064×pre10240exit
252.0ms250×body5120valid

simplify5.2m (16.0%)

prune2.9m (8.9%)

series38.2s (2.0%)

Calls

421 calls:

635.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
587.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
582.0ms
(/ (* (pow (/ 1 (+ 1 (exp (- s)))) c_p) (pow (- 1 (/ 1 (+ 1 (exp (- s))))) c_n)) (* (pow (/ 1 (+ 1 (exp (- t)))) c_p) (pow (+ 1/2 (- (* (* 1/48 (* t t)) t) (* 1/4 t))) c_n)))
581.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
559.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))

rewrite15.0s (0.8%)

Algorithm
132×rewrite-expression-head
Calls

421 calls:

625.0ms
(+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x)))
386.0ms
(log (+ x (+ (+ (/ -1/8 (* (* x x) x)) x) (/ 1/2 x))))
330.0ms
(sqrt (+ (* (* (- lambda1 lambda2) (* (* (cbrt (cos (/ (+ phi1 phi2) 2))) (cbrt (cos (/ (+ phi1 phi2) 2)))) (cbrt (cos (/ (+ phi1 phi2) 2))))) (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2)))) (* (- phi1 phi2) (- phi1 phi2))))
312.0ms
(cbrt (+ (/ x0 (- 1 x1)) x0))
264.0ms
(+ (- (/ 1/8 (* (* x x) x)) (/ 1/2 x)) (/ -1/16 (* (* x x) (* (* x x) x))))
Rules
5368×times-frac
4964×add-sqr-sqrt
4694×*-un-lft-identity
4344×add-exp-log
3346×add-cube-cbrt
1908×prod-exp
1708×add-cbrt-cube
1677×div-exp
1671×pow1
1383×pow-exp
1202×associate-*l/
931×flip--
930×flip3--
866×frac-times
741×associate-*r*
692×pow-to-exp
664×add-log-exp
618×difference-of-squares
606×sqrt-prod
604×sqrt-div associate-*l*
571×associate-/r*
492×cbrt-unprod
475×frac-add
461×associate-*r/
454×cbrt-prod
429×associate-/l*
421×insert-posit16
395×cbrt-undiv
357×div-inv
336×pow-prod-down
318×distribute-lft-out--
296×pow-prod-up
286×flip-+
285×flip3-+
279×1-exp rec-exp
261×distribute-lft-out
257×associate-/r/
197×log-prod
186×unswap-sqr
179×cbrt-div
160×pow-plus
134×pow-sqr
112×frac-2neg clear-num
109×*-commutative
106×tanh-def
100×tan-quot
98×pow2
96×sub-neg
94×log-pow
86×associate-/l/ diff-log
73×swap-sqr
66×associate--l+
64×associate--r+
58×distribute-rgt-in distribute-lft-in
57×difference-of-sqr-1 unpow-prod-down
52×frac-sub
51×log-div
50×sqrt-pow1
49×exp-prod
48×sum-log
40×pow1/2
34×+-commutative
29×div-sub
26×rem-sqrt-square
24×pow1/3
23×distribute-rgt-out--
21×sin-mult
20×cos-sum
19×rem-log-exp
17×pow-flip
15×associate--l- pow3
14×inv-pow
13×sqr-pow
12×cos-diff associate--r-
11×acos-asin
9×exp-sum distribute-rgt-neg-out pow-unpow distribute-rgt-neg-in distribute-lft-neg-in distribute-rgt-out
8×pow-pow associate-+l-
7×difference-of-sqr--1
6×exp-diff
5×associate-+l+
4×distribute-lft1-in associate-+r+ cube-mult asin-acos rem-cbrt-cube
3×unsub-neg distribute-frac-neg neg-mul-1 sum-cubes un-div-inv acos-neg
2×rem-cube-cbrt sin-sum associate-+r- rem-exp-log distribute-rgt1-in
1×remove-posit16 cube-prod cos-mult sin-cos-mult cube-unmult unpow3 sqrt-unprod tanh-undef sin-diff

regimes12.0s (0.6%)

Accuracy

Total 62.5b remaining (35.3%)

Threshold costs 5.2b (2.9%)

7.2b46.8%Quadratic roots, narrow range
7.1b46.5%Cubic critical, narrow range
6.2b77.7%Cubic critical
6.1b78.1%Quadratic roots, full range
5.9b12.3%Quadratic roots, medium range

localize5.0s (0.3%)

bsearch1.7s (0.1%)

end1.0ms (0.0%)