Details

sample73.0ms

Algorithm

intervals

Results

17.0ms	256×	pre	80	true
16.0ms	205×	body	80	valid
7.0ms	24×	body	640	valid
6.0ms	13×	body	1280	valid
2.0ms	9×	body	320	valid
1.0ms	5×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 3 (81.0ms)

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: 12.1b

localize14.0ms

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))

1.3b

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

rewrite81.0ms

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:

39.0ms

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

30.0ms

(/ (- 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)

series459.0ms

Counts

3 → 9

Calls

3 calls:

102.0ms

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

123.0ms

(/ (- 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)

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

prune466.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 11.8b

localize33.0ms

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))))
3.0b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

rewrite105.0ms

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:

6.0ms	(/ 1 (fma 2.0 i (+ alpha beta)))
32.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
62.0ms	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
1.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta)))) 1.0)

series639.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(/ 1 (fma 2.0 i (+ alpha beta)))
160.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
121.0ms	(* (+ alpha beta) (/ 1 (fma 2.0 i (+ alpha beta))))
233.0ms	(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

prune602.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 11.8b

localize18.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.1b	(exp (log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))
1.3b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
3.2b	(log (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

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

Counts

4 → 89

Calls

4 calls:

50.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
4.0ms	(exp (log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))
0.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
2.0ms	(log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0))

series958.0ms

Counts

4 → 12

Calls

4 calls:

142.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
214.0ms	(exp (log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))
215.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
387.0ms	(log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0))

simplify1.8s

Counts

101 → 101

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	159	2494
1	345	2417
2	878	2112
3	2726	2109
done	5002	2094

prune612.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 11.8b

localize24.0ms

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))
1.3b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
1.4b	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))

rewrite69.0ms

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)))
43.0ms	(/ (- 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)))

series720.0ms

Counts

4 → 12

Calls

4 calls:

93.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
135.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
244.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
248.0ms	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))

simplify2.2s

Counts

123 → 123

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	199	2602
1	423	2502
2	1132	2292
3	3607	2289
done	5001	2283

prune552.0ms

Pruning

14 alts after pruning (12 fresh and 2 done)

Merged error: 11.8b

regimes550.0ms

Accuracy

0% (0.3b remaining)

Error of 12.4b against oracle of 12.1b and baseline of 12.4b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample2.6s

Algorithm

intervals

Results

812.0ms	6347×	body	80	valid
731.0ms	524×	body	1280	valid
261.0ms	8000×	pre	80	true
239.0ms	561×	body	640	valid
88.0ms	357×	body	320	valid
34.0ms	211×	body	160	valid