Details

rewrite29.5s (9.4%)

Algorithm

144×	rewrite-expression-head

Calls

508 calls:

5.6s	(sqrt (+ (- (+ (* (pow (cos (* 0.5 phi2)) 2) (* (pow (cos (* 0.5 phi1)) 2) (pow lambda2 2))) (+ (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2)) (* (pow (sin (* 0.5 phi2)) 2) (* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2))))) (+ (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (pow lambda2 2))))) (+ (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (pow lambda2 2)))))))) (* (- phi1 phi2) (- phi1 phi2))))
1.1s	(- (+ (* (pow (cos (* 0.5 phi2)) 2) (* (pow (cos (* 0.5 phi1)) 2) (pow lambda2 2))) (+ (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2)) (* (pow (sin (* 0.5 phi2)) 2) (* (pow lambda2 2) (pow (sin (* 0.5 phi1)) 2))))) (+ (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (pow lambda2 2))))) (+ (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1))) (* (cos (* 0.5 phi1)) (* (sin (* 0.5 phi2)) (* (cos (* 0.5 phi2)) (* (sin (* 0.5 phi1)) (pow lambda2 2))))))))
708.0ms	(sqrt (+ (- (+ (* (pow lambda2 2) (pow (- (* (cos (* phi2 0.5)) (cos (* phi1 0.5))) (* (sin (* phi2 0.5)) (sin (* phi1 0.5)))) 2)) (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) (pow lambda1 2))) (* 2 (* lambda2 (* (pow (cos (* 0.5 (+ phi2 phi1))) 2) lambda1)))) (* (- phi1 phi2) (- phi1 phi2))))
604.0ms	(/ (* 4.0 a) (/ (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))) c))
603.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (- b) (sqrt (/ (- (pow b 6) (pow (* (* 4.0 a) c) 3)) (+ (* (* (* 4.0 a) c) (+ (* (* 4.0 a) c) (pow b 2))) (* (* b b) (* b b)))))))

Rules

6387×	times-frac
6331×	*-un-lft-identity
6089×	add-sqr-sqrt
3820×	add-cube-cbrt
2573×	add-exp-log
1946×	add-cbrt-cube
1300×	pow1
1157×	associate-*r*
1047×	sqrt-prod
887×	add-log-exp
844×	difference-of-squares
809×	distribute-lft-out--
791×	prod-exp
780×	associate-/l*
678×	associate-*l*
671×	div-exp
562×	associate-/r*
502×	cbrt-unprod
455×	flip--
454×	flip3--
447×	unpow-prod-down
431×	cbrt-undiv
430×	distribute-lft-out
359×	sqrt-div
341×	distribute-rgt-neg-in
332×	div-inv
304×	associate-/r/
299×	cube-prod
292×	pow-prod-down
273×	log-prod
257×	cbrt-prod
244×	associate-*l/
233×	flip-+
232×	unswap-sqr flip3-+
225×	exp-prod
208×	frac-times
204×	log-pow
174×	associate-*r/
158×	frac-add
141×	sqr-pow
125×	diff-log
121×	sub-neg
117×	clear-num frac-2neg
110×	*-commutative
101×	associate-/l/
98×	swap-sqr pow-exp
93×	distribute-lft-neg-in
92×	pow-to-exp
88×	sum-log pow-prod-up
75×	1-exp sqrt-pow1
62×	unpow3 cube-mult
60×	div-sub
58×	pow1/2 pow-sqr
52×	rec-exp unpow2
51×	frac-sub
49×	log-div
46×	pow-plus
43×	+-commutative
42×	pow-unpow
41×	rem-log-exp
38×	distribute-rgt-in distribute-lft-in
37×	rem-sqrt-square
35×	pow2 associate-+r+
33×	cbrt-div
32×	neg-sub0
31×	neg-mul-1
30×	associate-+l-
27×	pow1/3
25×	cos-sum
24×	associate--l+
22×	neg-log pow-pow
21×	exp-sum
20×	cos-diff tan-quot
19×	sin-mult
18×	distribute-rgt-out sin-diff
17×	associate--l- associate-+l+ cos-mult
16×	rem-cube-cbrt
14×	associate--r+
13×	cube-div rem-exp-log
12×	acos-asin associate--r-
10×	sin-cos-mult
9×	exp-diff inv-pow pow-flip
7×	sqrt-unprod associate-+r- distribute-frac-neg
6×	log-rec
5×	sin-sum rem-cbrt-cube
4×	acos-neg distribute-rgt-neg-out
3×	distribute-lft1-in
2×	un-div-inv distribute-rgt-out-- unsub-neg asin-acos sum-cubes
1×	sqrt-undiv rem-square-sqrt sub-div tanh-undef exp-to-pow tanh-def