Details

sample35.0ms

Algorithm

intervals

Results

10.0ms	211×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	14×	body	1280	valid
2.0ms	17×	body	640	valid
1.0ms	7×	body	320	valid
0.0ms	7×	body	160	valid

simplify50.0ms

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	14
1	103	14
2	454	14
3	2127	14
4	5001	14
done	5001	14

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
0.1b	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
2.1b	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
19.8b	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

rewrite851.0ms

Algorithm

rewrite-expression-head

Rules

54×	`times-frac`
50×	`*-un-lft-identity`
26×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-exp-log` `add-cbrt-cube`
15×	`add-log-exp`
14×	`associate-/r/`
12×	`flip3-+` `flip-+` `distribute-lft-out`
10×	`associate-/l*`
9×	`associate-/l/`
7×	`cbrt-undiv` `div-exp` `associate-/r*` `sum-log` `div-inv`
4×	`pow1` `frac-times`
3×	`flip3--` `flip--`
2×	`+-commutative` `frac-2neg` `associate-r/` `associate-l/` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate-+l+`

Counts

4 → 126

Calls

4 calls:

102.0ms	(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
170.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
526.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
48.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

series666.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(+ (+ (+ alpha beta) (* 2.0 i)) 2.0)
254.0ms	(/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
299.0ms	(+ (/ (/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)) 1.0)
86.0ms	(/ (* (+ alpha beta) (- beta alpha)) (+ (+ alpha beta) (* 2.0 i)))

simplify100.0ms

Counts

138 → 138

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	732	2016
1	4108	1891
2	5002	1891
done	5002	1891

prune379.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.1b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.7b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite674.0ms

Algorithm

rewrite-expression-head

Rules

321×	`times-frac`
290×	`*-un-lft-identity`
211×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
90×	`associate-r`
44×	`distribute-lft-out`
31×	`distribute-lft-out--` `difference-of-squares`
26×	`associate-/l*`
24×	`associate-/r/`
20×	`add-exp-log` `add-cbrt-cube`
15×	`flip3-+` `flip-+`
12×	`div-inv`
7×	`cbrt-undiv` `div-exp` `associate-/r*`
6×	`pow1` `add-log-exp`
4×	`associate-l`
3×	`div-sub` `prod-exp` `cbrt-unprod` `associate-/l/` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num`
1×	`+-commutative` `flip3--` `associate-r/` `pow-prod-down` `sum-log` `-commutative` `flip--`

Counts

4 → 295

Calls

4 calls:

172.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
41.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
348.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
94.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series798.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))
81.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
246.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
298.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify63.0ms

Counts

307 → 307

Iterations

Useful iterations: 1 (26.0ms)

Iter	Nodes	Cost
0	1080	4781
1	5001	4605
done	5001	4605

prune757.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 5.1b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
2.7b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
3.6b	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

rewrite846.0ms

Algorithm

rewrite-expression-head

Rules

162×	`times-frac`
151×	`*-un-lft-identity`
116×	`add-sqr-sqrt`
90×	`associate-r`
75×	`add-cube-cbrt`
22×	`distribute-lft-out`
16×	`distribute-lft-out--` `difference-of-squares`
15×	`add-exp-log` `add-cbrt-cube`
12×	`associate-/r/`
9×	`flip3-+` `flip-+`
7×	`pow1`
6×	`div-inv` `add-log-exp`
5×	`associate-/l*`
4×	`cbrt-undiv` `log-prod` `div-exp` `associate-l` `log-pow`
3×	`exp-prod` `prod-exp` `associate-/r*` `cbrt-unprod` `unswap-sqr`
2×	`frac-times` `associate-*l/` `associate-/l/`
1×	`+-commutative` `flip3--` `frac-2neg` `div-sub` `associate-r/` `rem-log-exp` `exp-sum` `pow-prod-down` `clear-num` `sum-log` `-commutative` `flip--`

Counts

4 → 184

Calls

4 calls:

42.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
344.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
92.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
357.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

series927.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i)))
252.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
296.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)
297.0ms	(log (exp (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)))

simplify47.0ms

Counts

196 → 196

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	925	2625
1	5001	2462
done	5001	2462

prune587.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 5.1b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
0.1b	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
2.7b	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
3.6b	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

rewrite804.0ms

Algorithm

rewrite-expression-head

Rules

147×	`times-frac`
137×	`*-un-lft-identity`
102×	`add-sqr-sqrt`
90×	`associate-r`
69×	`add-cube-cbrt`
22×	`distribute-lft-out`
14×	`add-exp-log` `add-cbrt-cube`
12×	`cbrt-prod` `distribute-lft-out--` `difference-of-squares`
10×	`flip3-+` `associate-/r/` `flip-+`
7×	`pow1`
6×	`unpow-prod-down` `cube-prod` `add-log-exp`
5×	`div-inv`
4×	`cube-div` `associate-l`
3×	`cbrt-undiv` `pow-unpow` `div-exp` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cube-mult` `frac-times` `cbrt-div` `unpow3` `associate-*l/` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `pow-pow` `pow1/3` `associate-r/` `pow-prod-down` `pow-exp` `sum-log` `-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 176

Calls

4 calls:

178.0ms	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
175.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
345.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
93.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

series1.6s

Counts

4 → 12

Calls

4 calls:

781.0ms	(pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3)
299.0ms	(cbrt (pow (+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0) 3))
241.0ms	(* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0)))
296.0ms	(+ (* (+ alpha beta) (/ (/ (- beta alpha) (+ (+ alpha beta) (* 2.0 i))) (+ (+ (+ alpha beta) (* 2.0 i)) 2.0))) 1.0)

simplify49.0ms

Counts

188 → 188

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	973	3074
1	5001	2918
done	5001	2918

prune530.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 5.1b

regimes222.0ms

Accuracy

0% (6.2b remaining)

Error of 12.0b against oracle of 5.8b and baseline of 12.0b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	26	18
1	26	18
done	26	18

end0.0ms

sample822.0ms

Algorithm

intervals

Results

243.0ms	6404×	body	80	valid
111.0ms	8000×	pre	80	true
95.0ms	512×	body	1280	valid
85.0ms	551×	body	640	valid
36.0ms	332×	body	320	valid
15.0ms	201×	body	160	valid