Details

sample9.8m (81.5%)

Algorithm
78×intervals
Results
8.4m54462×body10240exit
33.4s43059×body1280valid
11.3s30737×body640valid
7.0s204556×body80valid
4.6s152888×body80nan
4.6s27959×body320valid
3.1s194088×pre80true
2.9s36056×body160valid
752.0ms2960×body2560valid
375.0ms8261×body160nan
341.0ms4143×pre10240exit
118.0ms253×body5120valid
90.0ms8282×pre80false

prune49.4s (6.8%)

series43.5s (6.0%)

Calls

483 calls:

851.0ms
(- 1.0 (+ (pow (- (* (sin (/ phi1 2.0)) (cos (/ phi2 2.0))) (* (cos (/ phi1 2.0)) (sin (/ phi2 2.0)))) 2.0) (* (* (* (cos phi1) (cos phi2)) (- (* (sin (/ lambda1 2.0)) (cos (/ lambda2 2.0))) (* (cos (/ lambda1 2.0)) (sin (/ lambda2 2.0))))) (sin (/ (- lambda1 lambda2) 2.0)))))
640.0ms
(/ (+ 0 (* 3.0 (* a c))) (- (- b) (* (fabs (cbrt (- (* b b) (* (* 3.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 3.0 a) c)))))))
619.0ms
(log (+ (/ 1.0 x) (/ (log1p (expm1 (sqrt (- 1.0 (* x x))))) x)))
614.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
606.0ms
(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))

rewrite13.4s (1.9%)

Algorithm
146×rewrite-expression-head
Calls

483 calls:

392.0ms
(* (- (- (* 1.0 (/ m v)) (/ (pow m 2) v)) 1.0) (- 1.0 m))
328.0ms
(* (- (/ (* m (- (pow 1.0 3) (pow m 3))) (* (fma 1.0 1.0 (fma m m (* 1.0 m))) v)) 1.0) (- 1.0 m))
318.0ms
(* (- (/ (* m (- (pow 1.0 3) (pow m 3))) (* (fma 1.0 1.0 (fma m m (* 1.0 m))) v)) 1.0) (- m))
195.0ms
(* (- (/ 1 (/ v (* m (- 1.0 m)))) 1.0) m)
166.0ms
(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))
Rules
8272×*-un-lft-identity
7243×add-sqr-sqrt
6023×times-frac
5221×add-cube-cbrt
3503×prod-diff
2866×add-exp-log
1866×add-cbrt-cube
1173×unpow-prod-down
1061×associate-*r*
975×cube-prod
965×prod-exp
945×pow1
909×div-exp
882×sqrt-prod
841×difference-of-squares
778×distribute-lft-out
704×distribute-lft-out--
698×add-log-exp
632×distribute-rgt-in distribute-lft-in
573×associate-/l*
523×associate-*l*
495×associate-/r/
488×log1p-expm1-u
484×expm1-log1p-u
469×cbrt-unprod
468×cbrt-undiv
465×associate-/r*
445×sqr-pow
408×div-inv
357×cbrt-prod
350×distribute-rgt-neg-in
297×pow-exp
262×fma-neg
261×flip--
260×flip3--
247×distribute-lft-neg-in
239×unpow3 cube-mult
236×swap-sqr
226×fma-def
222×flip-+
221×flip3-+
217×pow-to-exp
200×unswap-sqr
199×log-prod
154×pow-prod-down
127×associate-*r/
118×associate-/l/
113×clear-num frac-2neg
102×*-commutative
88×sqrt-div
86×sub-neg
85×associate-*l/
82×neg-mul-1
76×log-pow
71×frac-times
69×diff-log
68×1-exp
66×pow-unpow
64×exp-prod
60×cos-sum
55×cbrt-div pow1/3
50×sqrt-pow1
47×pow1/2 pow-pow
44×rec-exp sum-log
43×div-sub log-div
34×unpow2
33×frac-sub
30×rem-sqrt-square
29×+-commutative
27×neg-sub0
26×associate-+l+ tan-quot rem-log-exp
23×fma-udef sin-sum
22×pow-prod-up
20×pow-sqr
19×associate--l+
18×neg-log associate-+l-
17×sin-diff
16×difference-cubes pow2 pow-plus sin-mult
15×cos-diff pow-flip distribute-rgt-out
13×sin-cos-mult associate--l-
12×exp-sum
11×frac-add
10×cube-div
9×associate-+r+ distribute-frac-neg acos-asin
8×expm1-udef
7×sum-cubes hypot-udef rem-cbrt-cube associate--r+
6×rem-cube-cbrt log1p-udef inv-pow log1p-expm1 expm1-log1p distribute-rgt-out-- distribute-rgt-neg-out
5×exp-diff acos-neg
4×rem-exp-log un-div-inv associate-+r- cos-mult
3×sqrt-unprod
2×sin-neg distribute-lft1-in exp-neg rem-square-sqrt hypot-def associate--r-
1×distribute-neg-in sub-div asin-acos exp-to-pow

simplify13.0s (1.8%)

Algorithm
224×egg-herbie

regimes10.9s (1.5%)

Accuracy

Total 31.9b remaining (27.3%)

Threshold costs 5.7b (4.9%)

7.5b45.7%Cubic critical, narrow range
5.6b20.1%Cubic critical, medium range
3.5b0.6%Cubic critical, wide range
3.4b67.9%Quotient of products
2.7b89.9%Cubic critical

localize2.4s (0.3%)

bsearch685.0ms (0.1%)

end1.0ms (0.0%)