Details

sample41.0ms

Algorithm

intervals

Results

10.0ms	204×	body	80	valid
4.0ms	256×	pre	80	true
4.0ms	17×	body	1280	valid
2.0ms	16×	body	320	valid
2.0ms	12×	body	640	valid
1.0ms	7×	body	160	valid

simplify2.4s

Counts

1 → 1

Iterations

Useful iterations: 3 (397.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	106	27
3	478	26
4	2726	26
done	5000	26

prune16.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.5b

localize30.0ms

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)))

2.5b

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

rewrite62.0ms

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:

31.0ms

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

26.0ms

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

0.0ms

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

series473.0ms

Counts

3 → 9

Calls

3 calls:

116.0ms

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

123.0ms

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

234.0ms

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

simplify1.1s

Counts

102 → 102

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	172	1935
1	401	1877
2	1673	1748
done	5001	1746

prune727.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.2b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0b	(/ 1 (fma 2.0 i (+ alpha beta)))
0.2b	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
3.7b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

rewrite93.0ms

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:

39.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
6.0ms	(/ 1 (fma 2.0 i (+ alpha beta)))
38.0ms	(* (+ 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)

series541.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
127.0ms	(/ 1 (fma 2.0 i (+ alpha beta)))
93.0ms	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
183.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

simplify3.4s

Counts

146 → 146

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	216	2503
1	534	2341
2	3307	2083
done	5000	2081

prune822.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 12.2b

localize33.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.4b	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.4b	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
7.1b	(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)

rewrite195.0ms

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:

131.0ms	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
27.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
15.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.0ms	(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)

series757.0ms

Counts

4 → 12

Calls

4 calls:

254.0ms	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
225.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
167.0ms	(/ 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)

simplify510.0ms

Counts

250 → 250

Iterations

Useful iterations: done (497.0ms)

Iter	Nodes	Cost
0	297	6664
1	839	6044
done	5000	5580

prune1.3s

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.2b

localize58.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.4b	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.5b	(/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
8.6b	(fma (* (/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite188.0ms

Algorithm

rewrite-expression-head

Rules

572×	`times-frac`
522×	`sqrt-prod`
451×	`*-un-lft-identity`
309×	`add-sqr-sqrt`
287×	`add-cube-cbrt`
71×	`distribute-lft-out`
35×	`associate-/l*`
32×	`sqrt-div`
28×	`associate-/r/`
27×	`associate-/r*`
19×	`add-exp-log`
14×	`pow1` `flip3-+` `flip-+` `div-inv`
13×	`add-cbrt-cube`
11×	`sqrt-pow1` `distribute-lft-out--` `difference-of-squares`
9×	`pow-flip` `div-exp`
8×	`pow-div`
7×	`pow1/2`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`frac-2neg` `clear-num` `associate-/l/` `inv-pow`
2×	`rec-exp` `1-exp`
1×	`flip3--` `div-sub` `flip--` `fma-udef`

Counts

4 → 483

Calls

4 calls:

42.0ms	(/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
19.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
75.0ms	(/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.0ms	(fma (* (/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series1.2s

Counts

4 → 12

Calls

4 calls:

225.0ms	(/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
200.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
694.0ms	(/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
100.0ms	(fma (* (/ (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (- beta alpha) (sqrt (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify1.1s

Counts

495 → 495

Iterations

Useful iterations: done (1.0s)

Iter	Nodes	Cost
0	575	18793
1	1413	15998
done	5000	14900

prune1.7s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.2b

regimes419.0ms

Accuracy

0% (0.4b remaining)

Error of 12.1b against oracle of 11.7b and baseline of 12.1b

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	78
1	33	78
done	33	78

end0.0ms

sample2.4s

Algorithm

intervals

Results

622.0ms	6400×	body	80	valid
532.0ms	478×	body	1280	valid
350.0ms	581×	body	640	valid
249.0ms	8000×	pre	80	true
139.0ms	368×	body	320	valid
27.0ms	173×	body	160	valid