Details

sample168.0ms

Algorithm

intervals

Results

117.0ms

711×

body

valid

simplify5.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1724
3	551
2	177
1	55
0	19

prune34.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize74.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (* 3.0 a))
0.0b	(fma 4.0 (fma (- 1.0 (* 3.0 a)) (* b b) (* (+ a 1.0) (* a a))) (pow (fma b b (* a a)) 2.0))
0.1b	(* (+ a 1.0) (* a a))
0.3b	(pow (fma b b (* a a)) 2.0)

rewrite107.0ms

Algorithm

rewrite-expression-head

Rules

11×	`*-un-lft-identity`
10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cube-cbrt` `add-cbrt-cube`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
3×	`unpow-prod-down` `pow-unpow` `fma-neg` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`associate-*l/`
1×	`pow-to-exp` `sub-neg` `flip3--` `pow-pow` `flip3-+` `diff-log` `associate-r` `pow-exp` `*-commutative` `flip--` `flip-+` `fma-udef` `distribute-lft-out` `unswap-sqr` `sqr-pow`

Counts

4 → 73

Calls

4 calls:

16.0ms	(- 1.0 (* 3.0 a))
1.0ms	(fma 4.0 (fma (- 1.0 (* 3.0 a)) (* b b) (* (+ a 1.0) (* a a))) (pow (fma b b (* a a)) 2.0))
79.0ms	(* (+ a 1.0) (* a a))
7.0ms	(pow (fma b b (* a a)) 2.0)

series1.0s

Counts

4 → 12

Calls

4 calls:

123.0ms	(- 1.0 (* 3.0 a))
325.0ms	(fma 4.0 (fma (- 1.0 (* 3.0 a)) (* b b) (* (+ a 1.0) (* a a))) (pow (fma b b (* a a)) 2.0))
172.0ms	(* (+ a 1.0) (* a a))
415.0ms	(pow (fma b b (* a a)) 2.0)

simplify2.5s

Counts

85 → 85

Iterations

Iter	Nodes
done	5003
2	1230
1	368
0	148

prune929.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize123.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (fma b b (* a a)) 2.0)
0.3b	(pow (fma b b (* a a)) 2.0)
8.3b	(sqrt (fma 4.0 (fma (- 1.0 (* 3.0 a)) (* b b) (* (+ a 1.0) (* a a))) (pow (fma b b (* a a)) 2.0)))
8.3b	(sqrt (fma 4.0 (fma (- 1.0 (* 3.0 a)) (* b b) (* (+ a 1.0) (* a a))) (pow (fma b b (* a a)) 2.0)))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow1`
6×	`add-exp-log` `unpow-prod-down` `pow-unpow` `sqrt-prod`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-to-exp` `rem-sqrt-square` `pow-pow` `sqrt-pow1` `pow1/2` `pow-exp` `sqr-pow`

Counts

4 → 68

Calls

4 calls:

6.0ms	(pow (fma b b (* a a)) 2.0)
6.0ms	(pow (fma b b (* a a)) 2.0)
4.0ms	(sqrt (fma 4.0 (fma (- 1.0 (* 3.0 a)) (* b b) (* (+ a 1.0) (* a a))) (pow (fma b b (* a a)) 2.0)))
4.0ms	(sqrt (fma 4.0 (fma (- 1.0 (* 3.0 a)) (* b b) (* (+ a 1.0) (* a a))) (pow (fma b b (* a a)) 2.0)))

series1.7s

Counts

4 → 12

Calls

4 calls:

323.0ms	(pow (fma b b (* a a)) 2.0)
276.0ms	(pow (fma b b (* a a)) 2.0)
486.0ms	(sqrt (fma 4.0 (fma (- 1.0 (* 3.0 a)) (* b b) (* (+ a 1.0) (* a a))) (pow (fma b b (* a a)) 2.0)))
580.0ms	(sqrt (fma 4.0 (fma (- 1.0 (* 3.0 a)) (* b b) (* (+ a 1.0) (* a a))) (pow (fma b b (* a a)) 2.0)))

simplify3.1s

Counts

80 → 80

Iterations

Iter	Nodes
done	5001
3	1784
2	540
1	220
0	101

prune1.2s

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 0.1b

localize208.0ms

Local error

Found 4 expressions with local error:

8.3b	(sqrt (fma 4.0 (fma (- 1.0 (* 3.0 a)) (* b b) (* (+ a 1.0) (* a a))) (* (* (cbrt (pow (fma b b (* a a)) 2.0)) (cbrt (pow (fma b b (* a a)) 2.0))) (cbrt (pow (fma b b (* a a)) 2.0)))))
18.0b	(cbrt (pow (fma b b (* a a)) 2.0))
18.0b	(cbrt (pow (fma b b (* a a)) 2.0))
18.0b	(cbrt (pow (fma b b (* a a)) 2.0))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`add-sqr-sqrt`
11×	`add-cube-cbrt` `*-un-lft-identity`
9×	`unpow-prod-down`
5×	`pow1`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `sqrt-prod` `sqr-pow`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 66

Calls

4 calls:

4.0ms	(sqrt (fma 4.0 (fma (- 1.0 (* 3.0 a)) (* b b) (* (+ a 1.0) (* a a))) (* (* (cbrt (pow (fma b b (* a a)) 2.0)) (cbrt (pow (fma b b (* a a)) 2.0))) (cbrt (pow (fma b b (* a a)) 2.0)))))
5.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
6.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
6.0ms	(cbrt (pow (fma b b (* a a)) 2.0))

series2.0s

Counts

4 → 12

Calls

4 calls:

704.0ms	(sqrt (fma 4.0 (fma (- 1.0 (* 3.0 a)) (* b b) (* (+ a 1.0) (* a a))) (* (* (cbrt (pow (fma b b (* a a)) 2.0)) (cbrt (pow (fma b b (* a a)) 2.0))) (cbrt (pow (fma b b (* a a)) 2.0)))))
415.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
426.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
470.0ms	(cbrt (pow (fma b b (* a a)) 2.0))

simplify5.7s

Counts

78 → 78

Iterations

Iter	Nodes
done	5000
4	4214
3	1391
2	507
1	219
0	112

prune1.3s

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 0.1b

localize324.0ms

Local error

Found 4 expressions with local error:

11.4b	(sqrt (pow (fma b b (* a a)) 2.0))
11.4b	(sqrt (pow (fma b b (* a a)) 2.0))
18.0b	(cbrt (pow (fma b b (* a a)) 2.0))
18.0b	(cbrt (pow (fma b b (* a a)) 2.0))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`cbrt-prod` `unpow-prod-down` `sqrt-prod`
12×	`add-cube-cbrt` `*-un-lft-identity`
6×	`rem-sqrt-square` `sqr-pow`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`sqrt-pow1` `pow1/2` `pow1/3`

Counts

4 → 76

Calls

4 calls:

9.0ms	(sqrt (pow (fma b b (* a a)) 2.0))
9.0ms	(sqrt (pow (fma b b (* a a)) 2.0))
5.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
5.0ms	(cbrt (pow (fma b b (* a a)) 2.0))

series1.6s

Counts

4 → 12

Calls

4 calls:

342.0ms	(sqrt (pow (fma b b (* a a)) 2.0))
324.0ms	(sqrt (pow (fma b b (* a a)) 2.0))
434.0ms	(cbrt (pow (fma b b (* a a)) 2.0))
514.0ms	(cbrt (pow (fma b b (* a a)) 2.0))

simplify3.8s

Counts

88 → 88

Iterations

Iter	Nodes
done	5000
4	1733
3	683
2	286
1	142
0	82

prune1.5s

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 0.1b

regimes426.0ms

Accuracy

0% (0.1b remaining)

Error of 0.2b against oracle of 0.1b and baseline of 0.2b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
done	20
1	20
0	17

end0.0ms

sample5.8s

Algorithm

intervals

Results

5.0s

20252×

body

valid