Details

sample34.0ms

Algorithm

intervals

Results

8.0ms	217×	body	80	valid
4.0ms	256×	pre	80	true
3.0ms	16×	body	1280	valid
1.0ms	9×	body	640	valid
1.0ms	7×	body	320	valid
1.0ms	7×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 3 (104.0ms)

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.2b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

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

2.1b

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

rewrite66.0ms

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:

27.0ms

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

28.0ms

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

1.0ms

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

series431.0ms

Counts

3 → 9

Calls

3 calls:

135.0ms

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

122.0ms

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

173.0ms

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

simplify2.9s

Counts

102 → 102

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	172	1935
1	391	1877
2	1094	1746
3	3541	1744
done	5002	1741

prune355.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 9.0b

localize17.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0b	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
0.1b	(* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
2.4b	(fma (* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite121.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 133

Calls

4 calls:

23.0ms	(/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))
27.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
62.0ms	(* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.0ms	(fma (* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series489.0ms

Counts

4 → 12

Calls

4 calls:

95.0ms	(/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))
91.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
113.0ms	(* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0)))
189.0ms	(fma (* (- beta alpha) (/ 1 (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.5s

Counts

145 → 145

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	213	2499
1	496	2253
2	1488	2040
done	5000	2039

prune504.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 9.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
0.3b	(/ (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.4b	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
5.3b	(fma (/ (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite197.0ms

Algorithm

rewrite-expression-head

Rules

614×	`times-frac`
573×	`*-un-lft-identity`
389×	`add-sqr-sqrt`
352×	`sqrt-prod`
261×	`add-cube-cbrt`
92×	`distribute-lft-out`
64×	`distribute-lft-out--` `difference-of-squares`
50×	`associate-/l*`
20×	`sqrt-div` `associate-/r/`
17×	`associate-/r*`
13×	`add-exp-log` `add-cbrt-cube`
11×	`flip3-+` `flip-+` `div-inv`
5×	`cbrt-undiv` `div-exp` `associate-/l/`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `div-sub` `clear-num`
1×	`flip3--` `flip--` `fma-udef`

Counts

4 → 466

Calls

4 calls:

38.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
62.0ms	(/ (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
26.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.0ms	(fma (/ (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series628.0ms

Counts

4 → 12

Calls

4 calls:

113.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
130.0ms	(/ (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
198.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
187.0ms	(fma (/ (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.8s

Counts

478 → 478

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	465	18827
1	1054	16321
2	2562	15340
done	5001	14583

prune940.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 9.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.3b	(* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))
0.4b	(/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
5.8b	(fma (/ (* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite280.0ms

Algorithm

rewrite-expression-head

Rules

186×	`add-sqr-sqrt`
185×	`sqrt-prod`
162×	`times-frac`
137×	`*-un-lft-identity`
77×	`add-cube-cbrt`
62×	`add-exp-log`
56×	`associate-r`
36×	`associate-l` `add-cbrt-cube`
28×	`unswap-sqr`
27×	`div-exp`
17×	`associate-/r*`
16×	`prod-exp`
14×	`cbrt-undiv` `sqrt-div` `distribute-lft-out`
10×	`distribute-lft-out--` `difference-of-squares`
9×	`pow1`
8×	`associate-/r/` `cbrt-unprod`
5×	`rec-exp` `pow-flip` `1-exp`
4×	`expm1-log1p-u` `sqrt-pow1` `flip3-+` `flip-+` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`associate-/l/`
2×	`frac-times` `frac-2neg` `pow1/2` `associate-r/` `associate-l/` `clear-num`
1×	`pow-prod-down` `*-commutative` `fma-udef` `inv-pow`

Counts

4 → 269

Calls

4 calls:

81.0ms	(/ (* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
157.0ms	(* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))
16.0ms	(/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.0ms	(fma (/ (* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series948.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(/ (* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
262.0ms	(* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))))
349.0ms	(/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
111.0ms	(fma (/ (* (/ 1 (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify2.1s

Counts

281 → 281

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	374	9723
1	967	7593
2	3007	6372
done	5000	6356

prune897.0ms

Pruning

6 alts after pruning (4 fresh and 2 done)

Merged error: 9.0b

regimes145.0ms

Accuracy

0% (0.2b remaining)

Error of 12.2b against oracle of 12.0b and baseline of 12.2b

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	20	28
done	20	28

end0.0ms

sample1.4s

Algorithm

intervals

Results

409.0ms	6366×	body	80	valid
188.0ms	8000×	pre	80	true
175.0ms	538×	body	1280	valid
141.0ms	536×	body	640	valid
64.0ms	335×	body	320	valid
27.0ms	225×	body	160	valid