Details

sample36.0ms

Algorithm

intervals

Results

14.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify3.2s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	35
1	33	35
2	111	35
3	550	35
4	4087	35
done	5000	35

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 2.1b

localize30.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

0.1b

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

1.9b

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

804×	`times-frac`
583×	`*-un-lft-identity`
339×	`add-sqr-sqrt` `add-cube-cbrt`
122×	`distribute-lft-out`
82×	`associate-/l*`
54×	`associate-/r/`
28×	`flip3-+` `flip-+`
27×	`div-inv`
19×	`add-exp-log` `add-cbrt-cube`
10×	`cbrt-undiv` `div-exp` `associate-/r*`
4×	`associate-/l/`
3×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

3 → 450

Calls

3 calls:

497.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

783.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

494.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series541.0ms

Counts

3 → 9

Calls

3 calls:

205.0ms

(/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0)))

232.0ms

(/ (/ (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ alpha beta) (* 2.0 1.0))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))

104.0ms

(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.5s

Counts

459 → 459

Iterations

Useful iterations: done (2.5s)

Iter	Nodes	Cost
0	580	25719
1	1395	24955
2	4628	24032
done	5000	23292

prune1.7s

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.4b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
0.0b	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
0.1b	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
1.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite3.5s

Algorithm

rewrite-expression-head

Rules

18109×	`times-frac`
9724×	`*-un-lft-identity`
6724×	`add-sqr-sqrt` `add-cube-cbrt`
1500×	`distribute-lft-out`
792×	`associate-/l*`
684×	`div-inv`
572×	`associate-/r/`
245×	`flip3-+` `flip-+`
154×	`add-exp-log`
134×	`div-exp`
84×	`associate-/r*`
61×	`add-cbrt-cube`
41×	`cbrt-undiv`
30×	`1-exp`
12×	`rec-exp`
6×	`associate-/l/`
4×	`pow1` `frac-2neg` `clear-num` `add-log-exp`

Counts

4 → 4911

Calls

4 calls:

318.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
730.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
860.0ms	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
481.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series756.0ms

Counts

4 → 12

Calls

4 calls:

232.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
203.0ms	(/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
215.0ms	(/ (/ (/ 1 1) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
105.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify2.9s

Counts

4923 → 4923

Iterations

Useful iterations: 0 (808.0ms)

Iter	Nodes	Cost
0	5274	351082
done	5274	351082

prune24.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (/ (/ 1 1) (* (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
0.1b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
0.1b	(/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
15.8b	(* (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))

rewrite1.4s

Algorithm

rewrite-expression-head

Rules

819×	`add-exp-log`
659×	`div-exp`
390×	`times-frac`
226×	`*-un-lft-identity`
203×	`add-sqr-sqrt`
179×	`1-exp`
163×	`add-cube-cbrt`
160×	`prod-exp`
116×	`rec-exp`
113×	`add-cbrt-cube`
67×	`cbrt-undiv`
50×	`associate-r`
37×	`associate-/r/`
28×	`distribute-lft-out`
26×	`associate-/l*`
23×	`associate-/r*`
22×	`div-inv`
18×	`associate-l` `cbrt-unprod`
12×	`unswap-sqr`
11×	`flip3-+` `flip-+`
10×	`pow1`
6×	`frac-times` `associate-r/` `associate-l/`
4×	`add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/`
2×	`pow-flip` `inv-pow` `pow-div`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 519

Calls

4 calls:

360.0ms	(/ (/ (/ 1 1) (* (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
157.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
180.0ms	(/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
611.0ms	(* (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))

series536.0ms

Counts

4 → 12

Calls

4 calls:

250.0ms	(/ (/ (/ 1 1) (* (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))) (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0))
25.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0))))
65.0ms	(/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0))
196.0ms	(* (/ 1 (+ (+ (+ alpha beta) (* beta alpha)) 1.0)) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ 1 (+ (+ alpha beta) (* 2.0 1.0)))))

simplify1.7s

Counts

531 → 531

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	901	23374
1	1866	18619
done	5000	17003

prune1.1s

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize37.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
0.0b	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
0.2b	(/ (/ 1 1) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
1.9b	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

rewrite2.2s

Algorithm

rewrite-expression-head

Rules

238×	`times-frac`
174×	`*-un-lft-identity`
131×	`add-sqr-sqrt`
122×	`add-cube-cbrt`
114×	`add-exp-log`
72×	`div-exp`
59×	`associate-r`
52×	`add-cbrt-cube`
26×	`distribute-lft-out`
25×	`cbrt-undiv`
24×	`prod-exp`
23×	`associate-/r/`
22×	`associate-/r*`
20×	`1-exp` `associate-/l*`
14×	`flip3-+` `flip-+`
13×	`div-inv`
9×	`cbrt-unprod`
8×	`rec-exp`
6×	`pow1`
5×	`associate-/l/`
4×	`frac-times` `associate-l` `associate-*l/` `add-log-exp`
3×	`frac-2neg` `clear-num` `unswap-sqr`
2×	`associate-*r/`
1×	`pow-prod-down` `*-commutative`

Counts

4 → 292

Calls

4 calls:

353.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
1.1s	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
234.0ms	(/ (/ 1 1) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
501.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

series873.0ms

Counts

4 → 12

Calls

4 calls:

188.0ms	(/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))
358.0ms	(* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))))
217.0ms	(/ (/ 1 1) (* (+ (+ (+ alpha beta) (* 2.0 1.0)) 1.0) (/ (+ (+ alpha beta) (* 2.0 1.0)) (/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0))))))
109.0ms	(/ (+ (+ (+ alpha beta) (* beta alpha)) 1.0) (+ (+ alpha beta) (* 2.0 1.0)))

simplify1.0s

Counts

304 → 304

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	442	12734
1	1104	11934
done	5000	10745

prune1.1s

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

Details

sample36.0ms

simplify3.2s

prune4.0ms

localize30.0ms

rewrite1.8s

series541.0ms

simplify2.5s

prune1.7s

localize38.0ms

rewrite3.5s

series756.0ms

simplify2.9s

prune24.3s

localize22.0ms

rewrite1.4s

series536.0ms

simplify1.7s

prune1.1s

localize37.0ms

rewrite2.2s

series873.0ms

simplify1.0s

prune1.1s

regimes109.0ms

bsearch2.0ms