Details

sample68.0ms

Algorithm

intervals

Results

17.0ms	200×	body	80	valid
8.0ms	18×	body	1280	valid
7.0ms	256×	pre	80	true
7.0ms	18×	body	640	valid
4.0ms	14×	body	320	valid
1.0ms	6×	body	160	valid

simplify2.8s

Counts

1 → 1

Iterations

Useful iterations: 3 (87.0ms)

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

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 13.1b

localize31.0ms

Local error

Found 3 expressions with local error:

0.0b

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

0.0b

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

2.4b

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

rewrite64.0ms

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

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

20.0ms

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

0.0ms

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

series430.0ms

Counts

3 → 9

Calls

3 calls:

121.0ms

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

92.0ms

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

217.0ms

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

simplify1.5s

Counts

102 → 102

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	172	1935
1	401	1877
2	1673	1748
done	5001	1746

prune454.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 12.8b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0b	(/ (+ 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))))
2.4b	(+ (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 1.0)

rewrite273.0ms

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:

51.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
40.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
120.0ms	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
46.0ms	(+ (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 1.0)

series913.0ms

Counts

4 → 12

Calls

4 calls:

145.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
109.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
359.0ms	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
300.0ms	(+ (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 1.0)

simplify2.6s

Counts

177 → 177

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	245	4140
1	725	3960
2	3991	3685
done	5001	3677

prune802.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 12.8b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
0.0b	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
2.4b	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
2.4b	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))

rewrite91.0ms

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:

32.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
49.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
1.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
6.0ms	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))

series615.0ms

Counts

4 → 12

Calls

4 calls:

114.0ms	(/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0))
101.0ms	(/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))
210.0ms	(fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)
189.0ms	(log (exp (fma (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))) 1.0)))

simplify1.3s

Counts

123 → 123

Iterations

Useful iterations: done (1.3s)

Iter	Nodes	Cost
0	199	2602
1	437	2502
2	1733	2294
done	5001	2292

prune608.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.8b

localize74.0ms

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	(pow (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 3)
2.2b	(- 1.0 (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))))
2.3b	(+ (pow (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 3) (pow 1.0 3))

rewrite222.0ms

Algorithm

rewrite-expression-head

Rules

52×	`*-un-lft-identity`
46×	`add-sqr-sqrt`
36×	`times-frac`
29×	`add-exp-log` `add-cbrt-cube`
26×	`add-cube-cbrt` `associate-l`
16×	`associate-r`
9×	`pow1` `distribute-lft-out`
8×	`cbrt-undiv` `fma-def` `div-exp` `prod-exp` `cbrt-unprod` `add-log-exp`
5×	`pow-exp` `rem-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`
3×	`cube-div` `pow-unpow` `fma-neg` `prod-diff`
2×	`cube-mult` `frac-times` `unpow-prod-down` `pow-pow` `flip3-+` `unpow3` `cube-prod` `associate-r/` `pow-prod-down` `associate-l/` `associate-/r/` `flip-+` `div-inv` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `diff-log` `sum-log` `sum-cubes` `*-commutative` `flip--`

Counts

4 → 144

Calls

4 calls:

108.0ms	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
50.0ms	(pow (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 3)
12.0ms	(- 1.0 (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))))
38.0ms	(+ (pow (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 3) (pow 1.0 3))

series17.4s

Counts

4 → 12

Calls

4 calls:

375.0ms	(* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta))))
5.1s	(pow (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 3)
435.0ms	(- 1.0 (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))))
11.5s	(+ (pow (* (/ (- beta alpha) (+ (fma 2.0 i (+ alpha beta)) 2.0)) (/ (+ alpha beta) (fma 2.0 i (+ alpha beta)))) 3) (pow 1.0 3))

simplify3.4s

Counts

156 → 156

Iterations

Useful iterations: done (3.4s)

Iter	Nodes	Cost
0	265	4562
1	853	4162
2	4985	3842
done	5000	3840

prune1.0s

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 12.8b

regimes260.0ms

Accuracy

0% (0.3b remaining)

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

bsearch0.0ms

simplify4.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	152
1	28	152
done	28	152

end0.0ms

sample2.4s

Algorithm

intervals

Results

1.0s	6419×	body	80	valid
393.0ms	516×	body	1280	valid
263.0ms	8000×	pre	80	true
165.0ms	560×	body	640	valid
75.0ms	326×	body	320	valid
26.0ms	179×	body	160	valid