Details

sample426.0ms

Algorithm

intervals

Results

148.0ms	125×	body	320	valid
44.0ms	20×	body	640	valid
32.0ms	255×	body	80	nan
30.0ms	511×	pre	80	true
24.0ms	83×	body	160	valid
3.0ms	28×	body	80	valid

simplify478.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	134
5	134
4	125
3	90
2	47
1	25
0	14

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 53.3b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma (* c a) -4 (* b b)))
0.1b	(fma (* c a) -4 (* b b))
0.1b	(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
23.2b	(- (sqrt (fma (* c a) -4 (* b b))) b)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

51×	`add-sqr-sqrt`
40×	`*-un-lft-identity`
30×	`add-cube-cbrt`
20×	`sqrt-prod`
18×	`times-frac` `prod-diff`
10×	`difference-of-squares`
6×	`add-cbrt-cube` `fma-neg` `add-exp-log` `associate-/l*` `add-log-exp`
5×	`pow1` `distribute-lft-out--`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`associate-/r*`
2×	`flip3--` `flip--` `associate-/l/`
1×	`cbrt-undiv` `rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `fma-udef` `div-inv`

Counts

4 → 114

Calls

4 calls:

1.0ms	(sqrt (fma (* c a) -4 (* b b)))
0.0ms	(fma (* c a) -4 (* b b))
16.0ms	(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
17.0ms	(- (sqrt (fma (* c a) -4 (* b b))) b)

series422.0ms

Counts

4 → 12

Calls

4 calls:

135.0ms	(sqrt (fma (* c a) -4 (* b b)))
78.0ms	(fma (* c a) -4 (* b b))
85.0ms	(/ (- (sqrt (fma (* c a) -4 (* b b))) b) a)
124.0ms	(- (sqrt (fma (* c a) -4 (* b b))) b)

simplify1.1s

Counts

126 → 126

Iterations

Iter	Nodes
done	5000
2	1070
1	337
0	157

prune642.0ms

Pruning

26 alts after pruning (26 fresh and 0 done)

Merged error: 50.2b

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* c a) -4 (* b b))
0.1b	(fma (* c a) -4 (* b b))
0.1b	(/ (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) a)
52.9b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`times-frac`
6×	`add-cbrt-cube` `add-exp-log`
4×	`expm1-log1p-u` `pow1` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-/r` `fma-udef` `associate-/l`
1×	`cbrt-undiv` `clear-num` `frac-2neg` `div-exp` `div-inv`

Counts

4 → 63

Calls

4 calls:

0.0ms	(fma (* c a) -4 (* b b))
0.0ms	(fma (* c a) -4 (* b b))
4.0ms	(/ (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) a)
0.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

series1.0s

Counts

4 → 12

Calls

4 calls:

84.0ms	(fma (* c a) -4 (* b b))
54.0ms	(fma (* c a) -4 (* b b))
473.0ms	(/ (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) a)
409.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

simplify1.5s

Counts

75 → 75

Iterations

Iter	Nodes
done	5001
3	2211
2	504
1	190
0	110

prune688.0ms

Pruning

34 alts after pruning (34 fresh and 0 done)

Merged error: 50.1b

localize61.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (* c a) -4 (* b b))
0.1b	(fma (* c a) -4 (* b b))
0.2b	(* (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) (/ 1 a))
52.9b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

rewrite21.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
13×	`-un-lft-identity` `associate-r*` `add-exp-log`
12×	`add-cube-cbrt`
11×	`times-frac`
9×	`add-cbrt-cube`
6×	`pow1`
4×	`expm1-log1p-u` `prod-exp` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`associate-l` `fma-udef` `unswap-sqr`
2×	`div-exp` `cbrt-unprod`
1×	`cbrt-undiv` `rec-exp` `1-exp` `pow-prod-down` `associate-r/` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 72

Calls

4 calls:

0.0ms	(fma (* c a) -4 (* b b))
0.0ms	(fma (* c a) -4 (* b b))
19.0ms	(* (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) (/ 1 a))
1.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

series1.1s

Counts

4 → 12

Calls

4 calls:

70.0ms	(fma (* c a) -4 (* b b))
98.0ms	(fma (* c a) -4 (* b b))
547.0ms	(* (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b)) (/ 1 a))
394.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

simplify2.1s

Counts

84 → 84

Iterations

Iter	Nodes
done	5001
2	1347
1	280
0	132

prune819.0ms

Pruning

39 alts after pruning (38 fresh and 1 done)

Merged error: 50.1b

localize55.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))))
52.9b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
52.9b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
52.9b	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

20×	`add-sqr-sqrt`
16×	`cbrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
6×	`pow1/3` `swap-sqr` `associate-r` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `insert-posit16` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
3×	`fma-udef`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 76

Calls

4 calls:

8.0ms	(* (cbrt (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))))
0.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
0.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

series2.0s

Counts

4 → 12

Calls

4 calls:

781.0ms	(* (cbrt (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))) (cbrt (fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))))
378.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
413.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))
417.0ms	(fma (sqrt (sqrt (fma (* c a) -4 (* b b)))) (sqrt (sqrt (fma (* c a) -4 (* b b)))) (- b))

simplify1.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	1057
1	282
0	126

prune832.0ms

Pruning

35 alts after pruning (35 fresh and 0 done)

Merged error: 49.5b

regimes949.0ms

Accuracy

0% (3.2b remaining)

Error of 51.9b against oracle of 48.7b and baseline of 51.9b

bsearch0.0ms

simplify10.0ms

Iterations

Iter	Nodes
done	25
1	25
0	22

end0.0ms

sample6.3s

Algorithm

intervals

Results

1.9s	3666×	body	320	valid
1.1s	8268×	body	80	nan
1.1s	16268×	pre	80	true
894.0ms	2943×	body	160	valid
260.0ms	490×	body	640	valid
111.0ms	901×	body	80	valid