Details

sample210.0ms

Algorithm

intervals

Results

46.0ms	113×	body	320	valid
42.0ms	306×	body	80	nan
35.0ms	562×	pre	80	true
23.0ms	90×	body	160	valid
8.0ms	16×	body	640	valid
5.0ms	37×	body	80	valid

simplify89.0ms

Counts

1 → 1

Iterations

Iter	Nodes
8	102
7	102
6	101
5	99
4	91
3	73
2	41
1	22
0	12

prune19.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 50.7b

localize39.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (fma -3 (* c a) (* b b)))
0.1b	(fma -3 (* c a) (* b b))
0.2b	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
24.7b	(- (sqrt (fma -3 (* c a) (* b b))) b)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 102

Calls

4 calls:

1.0ms	(sqrt (fma -3 (* c a) (* b b)))
0.0ms	(fma -3 (* c a) (* b b))
25.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
8.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

series389.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(sqrt (fma -3 (* c a) (* b b)))
84.0ms	(fma -3 (* c a) (* b b))
94.0ms	(/ (- (sqrt (fma -3 (* c a) (* b b))) b) (* 3 a))
88.0ms	(- (sqrt (fma -3 (* c a) (* b b))) b)

simplify2.3s

Counts

114 → 114

Iterations

Iter	Nodes
3	3402
2	935
1	329
0	152

prune634.0ms

Pruning

25 alts after pruning (25 fresh and 0 done)

Merged error: 47.6b

localize66.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma -3 (* c a) (* b b))
0.1b	(fma -3 (* c a) (* b b))
0.2b	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
50.3b	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

0.0ms	(fma -3 (* c a) (* b b))
0.0ms	(fma -3 (* c a) (* b b))
14.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
1.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series1.2s

Counts

4 → 12

Calls

4 calls:

69.0ms	(fma -3 (* c a) (* b b))
74.0ms	(fma -3 (* c a) (* b b))
617.0ms	(/ (fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b)) (* 3 a))
391.0ms	(fma (sqrt (sqrt (fma -3 (* c a) (* b b)))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify1.0s

Counts

69 → 69

Iterations

Iter	Nodes
3	2206
2	614
1	230
0	112

prune694.0ms

Pruning

30 alts after pruning (30 fresh and 0 done)

Merged error: 47.6b

localize52.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
0.5b	(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
0.5b	(cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))))
50.3b	(fma (sqrt (sqrt (cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
12×	`add-sqr-sqrt`
11×	`add-cbrt-cube` `add-exp-log`
9×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-plus` `pow-prod-up`
6×	`associate-r`
5×	`fma-udef`
4×	`expm1-log1p-u` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow2` `swap-sqr` `pow-sqr`
2×	`distribute-rgt-in` `distribute-lft-in` `pow3` `*-commutative` `unswap-sqr`
1×	`cbrt-prod` `pow1/3` `rem-cbrt-cube`

Counts

4 → 87

Calls

4 calls:

16.0ms	(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
6.0ms	(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
18.0ms	(cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))))
0.0ms	(fma (sqrt (sqrt (cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series746.0ms

Counts

4 → 12

Calls

4 calls:

172.0ms	(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
84.0ms	(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
60.0ms	(cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))))
430.0ms	(fma (sqrt (sqrt (cbrt (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify3.1s

Counts

99 → 99

Iterations

Iter	Nodes
3	4299
2	1009
1	312
0	140

prune1.1s

Pruning

36 alts after pruning (35 fresh and 1 done)

Merged error: 47.5b

localize82.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
0.5b	(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
4.5b	(pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3)
49.8b	(fma (sqrt (sqrt (pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

50×	`pow1`
17×	`add-exp-log`
13×	`add-sqr-sqrt` `pow-plus` `pow-prod-up`
12×	`pow-pow`
11×	`add-cbrt-cube`
10×	`*-un-lft-identity` `add-cube-cbrt`
7×	`pow-prod-down` `prod-exp`
6×	`associate-r`
5×	`pow2` `pow-sqr` `fma-udef`
4×	`expm1-log1p-u` `associate-l` `cbrt-unprod` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `swap-sqr` `pow-exp`
2×	`distribute-rgt-in` `distribute-lft-in` `pow3` `*-commutative` `unswap-sqr`
1×	`pow-to-exp` `unpow-prod-down` `unpow1/3` `sqr-pow`

Counts

4 → 106

Calls

4 calls:

40.0ms	(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
7.0ms	(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
15.0ms	(pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3)
0.0ms	(fma (sqrt (sqrt (pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

series966.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b)))
110.0ms	(* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b)))
219.0ms	(pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3)
440.0ms	(fma (sqrt (sqrt (pow (* (* (fma -3 (* c a) (* b b)) (fma -3 (* c a) (* b b))) (fma -3 (* c a) (* b b))) 1/3))) (sqrt (sqrt (fma -3 (* c a) (* b b)))) (- b))

simplify4.2s

Counts

118 → 118

Iterations

Iter	Nodes
3	5382
2	1322
1	417
0	175

prune808.0ms

Pruning

38 alts after pruning (37 fresh and 1 done)

Merged error: 47.5b

regimes1.0s

Accuracy

0% (2.1b remaining)

Error of 51.2b against oracle of 49.1b and baseline of 51.2b

bsearch0.0ms

simplify8.0ms

Iterations

Iter	Nodes
2	25
1	25
0	22

end0.0ms

sample6.2s

Algorithm

intervals

Results

2.0s	3647×	body	320	valid
1.3s	2922×	body	160	valid
1.1s	8238×	body	80	nan
973.0ms	16238×	pre	80	true
240.0ms	503×	body	640	valid
135.0ms	928×	body	80	valid