Details

sample73.0ms

Algorithm

intervals

Results

19.0ms	201×	body	80	valid
9.0ms	20×	body	1280	valid
8.0ms	256×	pre	80	true
7.0ms	20×	body	640	valid
3.0ms	11×	body	320	valid
1.0ms	4×	body	160	valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 3 (62.0ms)

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

prune9.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 13.0b

localize15.0ms

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))

0.9b

(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:

33.0ms

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

32.0ms

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

0.0ms

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

series447.0ms

Counts

3 → 9

Calls

3 calls:

98.0ms

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

117.0ms

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

233.0ms

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

simplify1.2s

Counts

102 → 102

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	172	1935
1	401	1877
2	1674	1748
done	5000	1746

prune420.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.8b

localize28.0ms

Local error

Found 4 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))
0.9b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
0.9b	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))

rewrite59.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 111

Calls

4 calls:

19.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
33.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
3.0ms	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))

series590.0ms

Counts

4 → 12

Calls

4 calls:

81.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
116.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
195.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
198.0ms	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))

simplify1.2s

Counts

123 → 123

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	199	2602
1	437	2502
2	1733	2294
done	5000	2292

prune699.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 12.8b

localize40.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.9b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) 1.0)
0.9b	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) 1.0)))
2.6b	(log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))))

rewrite80.0ms

Algorithm

rewrite-expression-head

Rules

54×	`*-un-lft-identity`
36×	`add-sqr-sqrt`
32×	`times-frac`
26×	`add-cube-cbrt`
21×	`log-pow`
19×	`exp-prod`
9×	`distribute-lft-out`
7×	`log-prod`
6×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`rem-log-exp` `associate-/r/` `fma-udef` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `flip3--` `frac-2neg` `flip3-+` `div-sub` `div-exp` `exp-sum` `clear-num` `flip--` `flip-+`

Counts

4 → 106

Calls

4 calls:

36.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) 1.0)
4.0ms	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) 1.0)))
35.0ms	(log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))))

series598.0ms

Counts

4 → 12

Calls

4 calls:

101.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
202.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) 1.0)
214.0ms	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) 1.0)))
82.0ms	(log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))))

simplify828.0ms

Counts

118 → 118

Iterations

Useful iterations: done (822.0ms)

Iter	Nodes	Cost
0	206	2547
1	403	2332
2	1324	2121
done	5000	2119

prune532.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.8b

localize31.0ms

Local error

Found 4 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))
0.9b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) 1.0)
2.6b	(log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))))

rewrite124.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
44×	`times-frac`
43×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
17×	`log-pow`
16×	`exp-prod`
13×	`distribute-lft-out`
9×	`associate-/l*`
8×	`add-exp-log` `add-cbrt-cube`
7×	`associate-/r*`
5×	`pow1` `distribute-lft-out--` `difference-of-squares`
4×	`expm1-log1p-u` `log1p-expm1-u` `associate-/l/` `add-log-exp`
3×	`log-prod` `div-inv`
2×	`cbrt-undiv` `frac-2neg` `flip3-+` `div-exp` `clear-num` `associate-/r/` `flip-+`
1×	`flip3--` `div-sub` `rem-log-exp` `flip--` `fma-udef`

Counts

4 → 123

Calls

4 calls:

30.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
51.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
1.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) 1.0)
38.0ms	(log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))))

series495.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
132.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
193.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))) 1.0)
77.0ms	(log (exp (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))))

simplify1.1s

Counts

135 → 135

Iterations

Useful iterations: done (1.1s)

Iter	Nodes	Cost
0	215	2430
1	455	2277
2	1776	2119
done	5000	2115

prune573.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 12.8b

regimes163.0ms

Accuracy

0% (0.3b remaining)

Error of 11.9b against oracle of 11.6b and baseline of 11.9b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	28
1	17	28
done	17	28

end0.0ms

sample2.0s

Algorithm

intervals

Results

930.0ms	6415×	body	80	valid
276.0ms	8000×	pre	80	true
153.0ms	492×	body	1280	valid
135.0ms	549×	body	640	valid
73.0ms	350×	body	320	valid
58.0ms	194×	body	160	valid