Details

sample68.0ms

Algorithm

intervals

Results

18.0ms	220×	body	80	valid
13.0ms	256×	pre	80	true
7.0ms	17×	body	1280	valid
3.0ms	10×	body	640	valid
2.0ms	6×	body	320	valid
1.0ms	3×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	15	29
1	31	29
2	106	27
3	477	26
4	2270	26
done	5001	26

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 8.7b

localize29.0ms

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)

rewrite99.0ms

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:

46.0ms

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

48.0ms

(/ (- 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)

series450.0ms

Counts

3 → 9

Calls

3 calls:

93.0ms

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

160.0ms

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

197.0ms

(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

prune489.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 8.5b

localize35.0ms

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	(log (exp (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)

rewrite99.0ms

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:

37.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
50.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
7.0ms	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))
1.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

series756.0ms

Counts

4 → 12

Calls

4 calls:

110.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
148.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
262.0ms	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))
236.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)

simplify2.4s

Counts

123 → 123

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	199	2602
1	423	2502
2	1137	2292
3	3616	2289
done	5000	2283

prune656.0ms

Pruning

12 alts after pruning (11 fresh and 1 done)

Merged error: 8.5b

localize16.0ms

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))
0.1b	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
1.3b	(+ (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 1.0)

rewrite161.0ms

Algorithm

rewrite-expression-head

Rules

96×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
68×	`times-frac`
42×	`add-cube-cbrt`
26×	`associate-l`
20×	`add-exp-log` `add-cbrt-cube`
18×	`distribute-lft-out`
16×	`associate-r`
9×	`associate-/l*` `distribute-lft-out--` `difference-of-squares`
7×	`associate-/r*`
6×	`pow1` `cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `flip3-+` `prod-exp` `associate-/r/` `cbrt-unprod` `flip-+` `log1p-expm1-u` `div-inv` `associate-/l/` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`+-commutative` `frac-times` `flip3--` `fma-def` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `sum-log` `*-commutative` `flip--`

Counts

4 → 165

Calls

4 calls:

20.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
27.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
79.0ms	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
28.0ms	(+ (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 1.0)

series822.0ms

Counts

4 → 12

Calls

4 calls:

102.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
141.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
335.0ms	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
243.0ms	(+ (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 1.0)

simplify2.1s

Counts

177 → 177

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	245	4140
1	694	3960
2	2437	3667
done	5002	3666

prune761.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 8.5b

localize47.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
0.1b	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
0.6b	(- 1.0 (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))))
1.3b	(+ (pow (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 3) (pow 1.0 3))

rewrite228.0ms

Algorithm

rewrite-expression-head

Rules

93×	`*-un-lft-identity`
83×	`add-sqr-sqrt`
72×	`times-frac`
52×	`associate-l`
43×	`add-cube-cbrt`
32×	`associate-r`
28×	`add-exp-log` `add-cbrt-cube`
17×	`distribute-lft-out`
8×	`pow1` `cbrt-undiv` `fma-def` `div-exp` `prod-exp` `cbrt-unprod` `distribute-lft-out--` `add-log-exp` `difference-of-squares` `unswap-sqr`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `div-inv`
3×	`flip3-+` `fma-neg` `prod-diff` `flip-+`
2×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`
1×	`+-commutative` `cube-mult` `sub-neg` `unpow-prod-down` `flip3--` `diff-log` `unpow3` `cube-prod` `sum-log` `sum-cubes` `flip--` `sqr-pow`

Counts

4 → 179

Calls

4 calls:

83.0ms	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
88.0ms	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
9.0ms	(- 1.0 (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))))
35.0ms	(+ (pow (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 3) (pow 1.0 3))

series12.4s

Counts

4 → 12

Calls

4 calls:

362.0ms	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
324.0ms	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
426.0ms	(- 1.0 (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))))
11.3s	(+ (pow (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 3) (pow 1.0 3))

simplify1.9s

Counts

191 → 191

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	222	5702
1	657	5443
2	2502	4902
done	5000	4898

prune1.2s

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 8.5b

regimes279.0ms

Accuracy

0% (0.3b remaining)

Error of 12.1b against oracle of 11.8b and baseline of 12.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

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

end0.0ms

sample2.5s

Algorithm

intervals

Results

1.1s	6390×	body	80	valid
314.0ms	8000×	pre	80	true
245.0ms	491×	body	1280	valid
222.0ms	549×	body	640	valid
136.0ms	381×	body	320	valid
29.0ms	189×	body	160	valid