Details

sample3.5m (62.1%)

Algorithm

78×

intervals

Results

2.1m	10686×	body	10240	exit
33.9s	43657×	body	1280	valid
11.3s	30475×	body	640	valid
6.9s	203204×	body	80	valid
4.6s	151896×	body	80	nan
4.4s	27187×	body	320	valid
3.0s	36310×	body	160	valid
2.6s	161505×	pre	80	true
709.0ms	3001×	body	2560	valid
414.0ms	14986×	body	80	overflowed
369.0ms	7871×	body	160	nan
357.0ms	4119×	pre	10240	exit
98.0ms	8583×	pre	80	false
78.0ms	247×	body	5120	valid
1.0ms	2×	body	320	nan

prune57.0s (16.6%)

series34.3s (10.0%)

Calls

453 calls:

2.1s	(- (cos delta) (+ (* (sin phi1) (* (sin (fma 1 (/ PI 2) (- (* (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) 1)))) (cos (fma (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 1 (* (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) 1))))) (* (sin phi1) (* (cos (fma 1 (/ PI 2) (- (* (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) 1)))) (sin (fma (- (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta))))) 1 (* (acos (+ (* (sin phi1) (cos delta)) (* (* (cos phi1) (sin delta)) (cos theta)))) 1)))))))
521.0ms	(/ (* (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)))
428.0ms	(* (hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2)) R)
345.0ms	(hypot (* (- lambda1 lambda2) (cos (/ (+ phi1 phi2) 2.0))) (- phi1 phi2))
336.0ms	(- (- (log (+ (sqrt 1.0) 1.0)) (* 1/2 (/ (pow x 2) (* (sqrt 1.0) (+ (sqrt 1.0) 1.0))))) (fma 1/8 (/ (pow x 4) (* (pow (sqrt 1.0) 3) (+ (sqrt 1.0) 1.0))) (log x)))

rewrite14.2s (4.2%)

Algorithm

143×	rewrite-expression-head

Calls

453 calls:

465.0ms	(+ (log 2) (- (- (log x) (/ (/ 0.25 x) x)) (/ 0.09375 (pow x 4))))
397.0ms	(- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5))))
307.0ms	(- (/ (/ 2.0 (sqrt (+ 1.0 (exp (* -2.0 x))))) (sqrt (+ 1.0 (exp (* -2.0 x))))) 1.0)
300.0ms	(log (- (/ 0.125 (pow x 3)) (- (/ 0.5 x) (/ (- 0.0625) (pow x 5)))))
284.0ms	(* (- (/ m (/ v (- 1.0 m))) 1.0) (- 1.0 m))

Rules

13284×	`times-frac`
12825×	`*-un-lft-identity`
12318×	`add-sqr-sqrt`
8970×	`add-cube-cbrt`
5656×	`prod-diff`
2797×	`add-exp-log`
2626×	`sqrt-prod`
1844×	`add-cbrt-cube`
1683×	`unpow-prod-down`
1395×	`difference-of-squares`
1253×	`distribute-rgt-neg-in`
1228×	`pow1`
1156×	`associate-r`
1094×	`distribute-lft-neg-in`
1058×	`associate--r+`
944×	`distribute-lft-out`
943×	`prod-exp`
920×	`distribute-lft-out--`
866×	`div-exp`
731×	`associate-/l*`
671×	`add-log-exp`
619×	`fma-neg`
616×	`cbrt-prod`
605×	`div-inv`
595×	`sqr-pow`
574×	`cube-prod`
556×	`distribute-rgt-in` `distribute-lft-in`
521×	`associate-/r*`
507×	`associate-/r/`
489×	`cbrt-unprod`
455×	`log1p-expm1-u` `expm1-log1p-u`
443×	`cbrt-undiv`
432×	`log-prod`
387×	`associate-+r+`
377×	`associate-l`
358×	`neg-mul-1`
319×	`pow-exp`
314×	`pow-prod-down`
259×	`flip--`
258×	`flip3--`
247×	`fma-def`
237×	`pow-to-exp`
223×	`flip-+`
222×	`flip3-+`
220×	`associate--l+`
191×	`sin-sum`
186×	`unswap-sqr`
182×	`sqrt-div`
153×	`log-pow`
135×	`unpow2`
126×	`associate-*r/`
116×	`clear-num` `frac-2neg`
113×	`unpow3` `cube-mult`
111×	`associate-/l/`
97×	`*-commutative` `sub-neg`
96×	`sqrt-pow1`
91×	`cos-sum`
75×	`pow-unpow`
69×	`diff-log`
67×	`associate-*l/` `frac-times`
61×	`pow1/2`
57×	`swap-sqr`
52×	`div-sub`
50×	`sum-log`
43×	`pow-prod-up`
41×	`1-exp` `pow1/3` `exp-prod`
38×	`log-div`
36×	`rec-exp`
35×	`pow-sqr`
33×	`+-commutative` `cbrt-div`
32×	`exp-sum`
31×	`neg-sub0`
28×	`associate-+l+` `rem-sqrt-square`
27×	`rem-log-exp`
25×	`sin-mult`
24×	`fma-udef` `pow-pow`
20×	`cos-diff` `tan-quot` `cos-mult`
18×	`acos-asin` `frac-sub` `associate-+l-`
17×	`neg-log`
16×	`sin-diff`
15×	`cube-div` `distribute-rgt-out`
14×	`pow-plus`
12×	`associate--l-` `distribute-neg-frac`
11×	`frac-add` `pow-flip` `distribute-frac-neg` `associate--r-`
10×	`sin-cos-mult` `pow2`
9×	`rem-cube-cbrt`
7×	`rem-exp-log`
6×	`rem-cbrt-cube`
5×	`acos-neg` `inv-pow` `associate-+r-` `expm1-udef`
4×	`expm1-log1p` `sub-div`
3×	`exp-diff` `log1p-udef` `log1p-expm1`
2×	`un-div-inv` `distribute-lft1-in` `rem-square-sqrt` `sqrt-unprod`
1×	`distribute-rgt1-in` `sum-cubes` `hypot-udef` `hypot-def` `asin-acos` `distribute-rgt-out--` `distribute-rgt-neg-out` `exp-to-pow`

simplify13.0s (3.8%)

Algorithm

221×	egg-herbie

regimes8.6s (2.5%)

Accuracy

Total 29.4b remaining (21.9%)

Threshold costs 5.9b (4.4%)

5.7b	57.9%	Cubic critical, narrow range
5.2b	23.7%	Cubic critical, medium range
3.5b	0%	Cubic critical, wide range
2.4b	78.8%	Quotient of products
2.1b	0%	(- (/ x0 (- 1 x1)) x0)

Details

sample3.5m (62.1%)

prune57.0s (16.6%)

series34.3s (10.0%)

rewrite14.2s (4.2%)

simplify13.0s (3.8%)

regimes8.6s (2.5%)

localize2.2s (0.6%)

bsearch632.0ms (0.2%)

end1.0ms (0.0%)