Details

sample59.0ms

Algorithm

intervals

Results

17.0ms	216×	body	80	valid
6.0ms	256×	pre	80	true
6.0ms	15×	body	1280	valid
3.0ms	11×	body	640	valid
2.0ms	7×	body	320	valid
1.0ms	7×	body	160	valid

simplify2.1s

Counts

1 → 1

Iterations

Useful iterations: 3 (77.0ms)

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

prune16.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 9.2b

localize22.0ms

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))

2.1b

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

rewrite70.0ms

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:

40.0ms

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

25.0ms

(/ (- 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)

series429.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms

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

133.0ms

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

202.0ms

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

simplify1.3s

Counts

102 → 102

Iterations

Useful iterations: done (1.3s)

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

prune438.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.9b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.2b	(exp (log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))
2.1b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
4.0b	(log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0))

rewrite43.0ms

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:

34.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
3.0ms	(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)
1.0ms	(log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0))

series858.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
192.0ms	(exp (log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))
183.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
331.0ms	(log (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0))

simplify847.0ms

Counts

101 → 101

Iterations

Useful iterations: done (841.0ms)

Iter	Nodes	Cost
0	159	2494
1	356	2417
2	1263	2114
done	5000	2112

prune531.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 8.9b

localize34.0ms

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	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
0.4b	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
5.5b	(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)

rewrite165.0ms

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:

105.0ms	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
14.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
34.0ms	(/ (- beta alpha) (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)

series751.0ms

Counts

4 → 12

Calls

4 calls:

263.0ms	(* (/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
199.0ms	(/ 1 (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
175.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
114.0ms	(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)

simplify585.0ms

Counts

250 → 250

Iterations

Useful iterations: done (575.0ms)

Iter	Nodes	Cost
0	297	6664
1	839	6044
done	5000	5127

prune951.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.9b

localize42.0ms

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)))
4.8b	(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)

rewrite213.0ms

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:

34.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
140.0ms	(* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
30.0ms	(/ (- 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)

series731.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
277.0ms	(* (pow (+ (fma 2.0 i (+ alpha beta)) 2.0) -1/2) (/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0))))
224.0ms	(/ (- beta alpha) (sqrt (+ (fma 2.0 i (+ alpha beta)) 2.0)))
128.0ms	(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)

simplify3.1s

Counts

200 → 200

Iterations

Useful iterations: done (3.1s)

Iter	Nodes	Cost
0	272	5030
1	677	4713
2	3940	4440
done	5000	4434

prune1.0s

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 8.9b

regimes209.0ms

Accuracy

0% (0.3b remaining)

Error of 12.0b against oracle of 11.7b and baseline of 12.0b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	50
1	22	50
done	22	50

end0.0ms

sample2.4s

Algorithm

intervals

Results

711.0ms	6412×	body	80	valid
636.0ms	497×	body	1280	valid
346.0ms	8000×	pre	80	true
175.0ms	560×	body	640	valid
127.0ms	342×	body	320	valid
30.0ms	189×	body	160	valid