Details

sample13.2m (63.8%)

Algorithm
78×intervals
Results
9.9m58993×body10240exit
1.3m43594×body1280valid
29.0s30501×body640valid
21.0s204871×body80valid
12.9s152369×body80nan
12.2s27609×body320valid
10.3s197675×pre80true
8.6s36214×body160valid
2.3s3141×body2560valid
850.0ms7851×body160nan
615.0ms4168×pre10240exit
172.0ms231×body5120valid
159.0ms8421×pre80false
1.0ms1×body640nan

simplify4.4m (21.4%)

prune1.3m (6.2%)

series1.1m (5.4%)

Calls

447 calls:

1.3s
(cbrt (pow (pow (log (+ 1.0 (exp x))) (sqrt 3)) (sqrt 3)))
1.1s
(pow (log (fma (sqrt (- x (sqrt 1.0))) (sqrt (+ x (sqrt 1.0))) x)) 3)
1.1s
(/ (fma (cos delta) (cos delta) (- (* (pow (sin phi1) 2) (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))))))) (fma (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1) (cos delta)))
1.0s
(/ (- (* (cos delta) (cos delta)) (* (* (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta)))))) (pow (sin phi1) 2))) (fma (sin (asin (fma (sin phi1) (cos delta) (* (* (cos phi1) (sin delta)) (cos theta))))) (sin phi1) (cos delta)))
785.0ms
(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)

rewrite20.5s (1.7%)

Algorithm
143×rewrite-expression-head
Calls

447 calls:

964.0ms
(- (log (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n))) (fma (log (/ 1.0 (+ 1.0 (exp (- t))))) c_p (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))) c_n)))
498.0ms
(* (* (sqrt (sqrt m)) (* (sqrt (sqrt m)) (- (/ (* m (- 1.0 m)) v) 1.0))) (sqrt m))
471.0ms
(* (/ x (+ x 1.0)) (- (/ x (+ x 1.0)) (/ 1.0 (- x 1.0))))
471.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))
454.0ms
(* (- (/ m (/ v (- 1.0 m))) 1.0) m)
Rules
11347×*-un-lft-identity
9419×add-sqr-sqrt
9330×times-frac
6825×add-cube-cbrt
4983×prod-diff
2345×add-exp-log
1899×cbrt-prod
1553×add-cbrt-cube
1243×distribute-lft-out
1149×difference-of-squares
1127×sqrt-prod
1023×pow1
1017×distribute-lft-out--
955×associate-/r/
930×unpow-prod-down
831×cube-prod
781×prod-exp
760×distribute-rgt-in distribute-lft-in
673×div-exp
613×div-inv
603×add-log-exp
476×associate-/r*
467×fma-neg
465×associate-/l*
451×log1p-expm1-u
448×expm1-log1p-u
437×associate-*r*
413×flip--
412×flip3--
383×cbrt-unprod
347×cbrt-undiv
337×associate-*l*
329×distribute-rgt-neg-in
316×flip-+
315×flip3-+
304×pow-exp
261×distribute-lft-neg-in
225×pow-prod-down
213×pow-to-exp
193×log-prod
133×log-pow
118×sqrt-pow1
114×associate-*r/
113×unswap-sqr
102×fma-def
100×frac-times
99×clear-num frac-2neg
98×exp-prod
97×sub-neg
95×associate-*l/
87×neg-mul-1
81×*-commutative
80×sqrt-div
77×associate-/l/
76×pow1/2
73×swap-sqr
70×pow-unpow sqr-pow
63×diff-log
53×cbrt-div
52×unpow3 cube-mult
51×pow1/3
49×cos-sum
42×div-sub
41×rem-sqrt-square rem-log-exp
39×fma-udef pow-prod-up
36×log-div
33×sin-sum associate--l+
31×pow-sqr sin-mult
25×1-exp rec-exp
23×pow2
22×pow-pow
20×frac-sub cos-mult
19×sin-diff
18×sum-log
16×exp-sum
15×rem-cube-cbrt sin-cos-mult pow-plus
14×neg-sub0
12×+-commutative
11×pow-flip
10×cube-div cos-diff
8×distribute-frac-neg associate--l- acos-asin tan-quot neg-log
7×associate-+l- rem-cbrt-cube associate--r+
6×sub-div unpow2
5×expm1-log1p hypot-def expm1-udef
4×acos-neg sin-neg sum-cubes log1p-udef sqrt-unprod inv-pow log1p-expm1 distribute-rgt-neg-out
3×associate-+r+ sqr-sin associate-+l+ hypot-udef rem-square-sqrt
2×exp-diff associate--r- rem-exp-log
1×associate-+r- frac-add tanh-undef asin-acos sqr-cos tanh-def

regimes13.8s (1.1%)

Accuracy

Total 44.5b remaining (29.4%)

Threshold costs 5.6b (3.7%)

7.9b44%Cubic critical, narrow range
6.9b0%Cubic critical, medium range
6.9b0%Quadratic roots, medium range
6.0b48.4%Quotient of products
3.5b0%Cubic critical, wide range

localize4.5s (0.4%)

bsearch761.0ms (0.1%)

end1.0ms (0.0%)