Details

sample75.0ms

Algorithm

intervals

Results

20.0ms	203×	body	80	valid
9.0ms	23×	body	640	valid
9.0ms	256×	pre	80	true
4.0ms	9×	body	1280	valid
3.0ms	9×	body	320	valid
2.0ms	12×	body	160	valid

simplify3.7s

Counts

1 → 1

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	106	27
3	477	26
4	2270	26
done	5001	26

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.6b

localize23.0ms

Local error

Found 3 expressions with local error:

0.0b

(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))

0.0b

(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))

3.3b

(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

53×	`*-un-lft-identity`
33×	`add-sqr-sqrt`
32×	`times-frac`
23×	`add-cube-cbrt`
10×	`distribute-lft-out`
9×	`associate-/l*`
7×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`distribute-lft-out--` `difference-of-squares`
4×	`associate-/l/`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+` `div-inv`
1×	`flip3--` `div-sub` `flip--` `fma-udef`

Counts

3 → 93

Calls

3 calls:

20.0ms

(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))

49.0ms

(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))

1.0ms

(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series482.0ms

Counts

3 → 9

Calls

3 calls:

126.0ms

(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))

122.0ms

(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))

234.0ms

(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify2.4s

Counts

102 → 102

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	172	1935
1	391	1877
2	1095	1746
3	3539	1744
done	5000	1741

prune514.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.2b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (fma 2.0 i (+ alpha beta)))
0.0b	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.2b	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
5.2b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

56×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
40×	`times-frac`
31×	`add-cube-cbrt`
19×	`add-exp-log`
13×	`associate-r` `add-cbrt-cube`
8×	`associate-/l*`
7×	`pow1` `associate-/r*` `distribute-lft-out`
5×	`div-exp` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `associate-/r/` `cbrt-unprod` `associate-/l/`
1×	`flip3--` `pow-flip` `div-sub` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `flip--` `fma-udef` `inv-pow`

Counts

4 → 134

Calls

4 calls:

8.0ms	(/ 1 (fma 2.0 i (+ alpha beta)))
25.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
54.0ms	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
0.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

series570.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ 1 (fma 2.0 i (+ alpha beta)))
137.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
81.0ms	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
230.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

simplify1.8s

Counts

146 → 146

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	216	2503
1	507	2268
2	1485	2081
done	5000	2079

prune599.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.2b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ (fma 2.0 i (+ alpha beta)) 2.0) (- beta alpha))
0.2b	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
0.4b	(/ 1 (/ (+ (fma 2.0 i (+ alpha beta)) 2.0) (- beta alpha)))
5.2b	(fma (/ 1 (/ (+ (fma 2.0 i (+ alpha beta)) 2.0) (- beta alpha))) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

rewrite129.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
187×	`*-un-lft-identity`
139×	`add-sqr-sqrt`
90×	`add-cube-cbrt`
31×	`associate-/r*`
27×	`distribute-lft-out`
26×	`add-exp-log`
21×	`distribute-lft-out--` `difference-of-squares`
16×	`add-cbrt-cube`
13×	`associate-r`
11×	`associate-/r/`
10×	`div-exp`
7×	`pow1` `div-inv` `associate-/l*`
5×	`cbrt-undiv` `flip3--` `flip--`
4×	`expm1-log1p-u` `associate-l` `prod-exp` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `flip3-+` `1-exp` `flip-+` `unswap-sqr`
2×	`frac-times` `frac-2neg` `associate-*l/` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `fma-udef` `inv-pow`

Counts

4 → 230

Calls

4 calls:

29.0ms	(/ (+ (fma 2.0 i (+ alpha beta)) 2.0) (- beta alpha))
52.0ms	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
26.0ms	(/ 1 (/ (+ (fma 2.0 i (+ alpha beta)) 2.0) (- beta alpha)))
0.0ms	(fma (/ 1 (/ (+ (fma 2.0 i (+ alpha beta)) 2.0) (- beta alpha))) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

series611.0ms

Counts

4 → 12

Calls

4 calls:

130.0ms	(/ (+ (fma 2.0 i (+ alpha beta)) 2.0) (- beta alpha))
116.0ms	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
253.0ms	(/ 1 (/ (+ (fma 2.0 i (+ alpha beta)) 2.0) (- beta alpha)))
113.0ms	(fma (/ 1 (/ (+ (fma 2.0 i (+ alpha beta)) 2.0) (- beta alpha))) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

simplify1.6s

Counts

242 → 242

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	319	5378
1	741	4784
2	1984	4336
done	5002	4279

prune813.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 12.2b

localize40.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.3b	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.4b	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
9.1b	(fma (* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite240.0ms

Algorithm

rewrite-expression-head

Rules

148×	`add-sqr-sqrt`
144×	`*-un-lft-identity`
134×	`times-frac`
83×	`sqrt-prod`
72×	`add-cube-cbrt`
41×	`associate-r`
32×	`add-exp-log`
27×	`associate-l`
20×	`add-cbrt-cube`
18×	`distribute-lft-out`
15×	`distribute-lft-out--` `difference-of-squares` `unswap-sqr`
14×	`associate-/r*`
11×	`div-exp`
8×	`pow1` `sqrt-div` `prod-exp` `associate-/r/` `associate-/l*`
6×	`cbrt-undiv`
4×	`expm1-log1p-u` `flip3-+` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`rec-exp` `pow-flip` `1-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`frac-times` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `fma-udef` `inv-pow`

Counts

4 → 238

Calls

4 calls:

181.0ms	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
25.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
21.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
1.0ms	(fma (* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series824.0ms

Counts

4 → 12

Calls

4 calls:

282.0ms	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
228.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
203.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
111.0ms	(fma (* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.8s

Counts

250 → 250

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	297	6664
1	774	6016
2	2259	5067
done	5000	5055

prune848.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 12.2b

regimes277.0ms

Accuracy

0% (0.3b remaining)

Error of 12.6b against oracle of 12.4b and baseline of 12.6b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	16	30
1	21	30
done	21	30

end0.0ms

sample2.6s

Algorithm

intervals

Results

1.1s	6315×	body	80	valid
323.0ms	8000×	pre	80	true
294.0ms	582×	body	640	valid
264.0ms	528×	body	1280	valid
90.0ms	356×	body	320	valid
34.0ms	219×	body	160	valid