Details

sample90.0ms

Algorithm

intervals

Results

25.0ms	203×	body	80	valid
18.0ms	256×	pre	80	true
10.0ms	18×	body	1280	valid
4.0ms	10×	body	640	valid
3.0ms	15×	body	160	valid
3.0ms	10×	body	320	valid

simplify4.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	2366
3	465
2	101
1	31
0	15

prune28.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.7b

localize40.0ms

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))

3.5b

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

rewrite90.0ms

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:

29.0ms

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

54.0ms

(/ (- 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)

series644.0ms

Counts

3 → 9

Calls

3 calls:

141.0ms

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

183.0ms

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

320.0ms

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

simplify5.2s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
3	4838
2	1169
1	401
0	172

prune1.1s

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 11.5b

localize73.0ms

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))))
0.4b	(/ (- 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)

rewrite308.0ms

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:

188.0ms	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
63.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
28.0ms	(/ 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)

series947.0ms

Counts

4 → 12

Calls

4 calls:

293.0ms	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
231.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
260.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
162.0ms	(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)

simplify3.4s

Counts

250 → 250

Iterations

Iter	Nodes
done	5001
2	2300
1	820
0	297

prune2.3s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.5b

localize81.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
0.3b	(* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
0.4b	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
5.9b	(fma (* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite275.0ms

Algorithm

rewrite-expression-head

Rules

115×	`*-un-lft-identity`
104×	`add-sqr-sqrt`
88×	`times-frac`
53×	`add-cube-cbrt`
47×	`sqrt-prod`
41×	`associate-r`
21×	`add-exp-log`
16×	`distribute-lft-out`
15×	`distribute-lft-out--` `difference-of-squares`
13×	`add-cbrt-cube`
10×	`associate-/r*`
9×	`associate-/l*` `unswap-sqr`
8×	`associate-l`
7×	`unpow-prod-down`
6×	`prod-exp`
5×	`div-exp`
4×	`pow1` `expm1-log1p-u` `sqrt-div` `associate-/r/` `log1p-expm1-u` `associate-/l/` `add-log-exp` `sqr-pow`
3×	`cbrt-undiv` `flip3-+` `flip-+` `div-inv`
2×	`pow-to-exp` `frac-2neg` `pow-exp` `clear-num` `cbrt-unprod`
1×	`flip3--` `div-sub` `associate-r/` `-commutative` `flip--` `fma-udef`

Counts

4 → 188

Calls

4 calls:

38.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
168.0ms	(* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
51.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
1.0ms	(fma (* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series836.0ms

Counts

4 → 12

Calls

4 calls:

148.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
283.0ms	(* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
251.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
154.0ms	(fma (* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify3.4s

Counts

200 → 200

Iterations

Iter	Nodes
done	5000
2	2132
1	677
0	272

prune2.1s

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 11.5b

localize163.0ms

Local error

Found 4 expressions with local error:

0.4b	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
5.9b	(fma (* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
5.9b	(fma (* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
5.9b	(fma (* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

rewrite78.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
40×	`add-sqr-sqrt`
35×	`times-frac`
24×	`add-cube-cbrt` `sqrt-prod`
8×	`distribute-lft-out--` `difference-of-squares`
7×	`associate-/r*`
6×	`add-exp-log` `add-cbrt-cube` `distribute-lft-out`
5×	`associate-/l*`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`fma-udef`
2×	`sqrt-div` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `clear-num` `flip--` `flip-+` `div-inv`

Counts

4 → 96

Calls

4 calls:

64.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
1.0ms	(fma (* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
1.0ms	(fma (* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
1.0ms	(fma (* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series754.0ms

Counts

4 → 12

Calls

4 calls:

270.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
162.0ms	(fma (* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
162.0ms	(fma (* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
160.0ms	(fma (* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify3.6s

Counts

108 → 108

Iterations

Iter	Nodes
done	5006
3	2655
2	833
1	340
0	152

prune1.4s

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.4b

regimes1.5s

Accuracy

0% (0.3b remaining)

Error of 12.2b against oracle of 11.9b and baseline of 12.2b

bsearch0.0ms

simplify6.0ms

Iterations

Iter	Nodes
done	24
1	24
0	20

end0.0ms

sample3.3s

Algorithm

intervals

Results

1.2s	588×	body	640	valid
885.0ms	6366×	body	80	valid
360.0ms	494×	body	1280	valid
293.0ms	8000×	pre	80	true
108.0ms	335×	body	320	valid
47.0ms	217×	body	160	valid