Details

sample42.0ms

Algorithm

intervals

Results

23.0ms

644×

body

valid

simplify51.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (5.0ms)

Iter	Nodes	Cost
0	26	8
1	51	8
2	88	7
3	153	7
4	357	7
5	1572	7
6	5002	7
done	5002	7

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.0b	(+ (* a a) (* b b))
0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.4b	(pow (+ (* a a) (* b b)) 2.0)

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

10×	`pow1` `add-exp-log` `add-sqr-sqrt`
9×	`add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube`
8×	`fma-def` `add-log-exp`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`+-commutative` `flip3-+` `sum-log` `flip-+` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

17.0ms	(* 4.0 (* b b))
8.0ms	(+ (* a a) (* b b))
62.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
10.0ms	(pow (+ (* a a) (* b b)) 2.0)

series235.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 4.0 (* b b))
29.0ms	(+ (* a a) (* b b))
72.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
108.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify43.0ms

Counts

86 → 86

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	339	438
1	1458	396
2	5002	385
done	5002	385

prune225.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4.0 (* b b))
0.0b	(fma a a (* b b))
0.0b	(+ (pow (fma a a (* b b)) 2.0) (* 4.0 (* b b)))
0.4b	(pow (fma a a (* b b)) 2.0)

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

16.0ms	(* 4.0 (* b b))
0.0ms	(fma a a (* b b))
14.0ms	(+ (pow (fma a a (* b b)) 2.0) (* 4.0 (* b b)))
3.0ms	(pow (fma a a (* b b)) 2.0)

series252.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(* 4.0 (* b b))
35.0ms	(fma a a (* b b))
65.0ms	(+ (pow (fma a a (* b b)) 2.0) (* 4.0 (* b b)))
120.0ms	(pow (fma a a (* b b)) 2.0)

simplify126.0ms

Counts

82 → 82

Iterations

Useful iterations: 3 (121.0ms)

Iter	Nodes	Cost
0	267	375
1	1043	338
2	4174	329
3	5001	326
done	5001	326

prune209.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
14.2b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.2b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
14.2b	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

rewrite341.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
18×	`cbrt-div`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`flip3-+` `pow1/3` `flip-+`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 95

Calls

4 calls:

244.0ms	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
30.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
33.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
30.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

series733.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(* (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))) (cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))))
194.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
195.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))
190.0ms	(cbrt (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))))

simplify139.0ms

Counts

107 → 107

Iterations

Useful iterations: 3 (125.0ms)

Iter	Nodes	Cost
0	272	1903
1	1000	1779
2	4603	1626
3	5001	1617
done	5001	1617

prune337.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 2 (pow a 2))
0.0b	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
0.5b	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

13×	`add-sqr-sqrt`
9×	`*-un-lft-identity`
8×	`add-exp-log` `associate-r`
7×	`add-cube-cbrt`
5×	`add-cbrt-cube` `add-log-exp`
4×	`unpow-prod-down` `unswap-sqr`
3×	`pow1` `expm1-log1p-u` `fma-def` `associate-l` `prod-exp` `log1p-expm1-u`
2×	`fma-udef` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `flip3-+` `pow-exp` `sum-log` `*-commutative` `cbrt-unprod` `flip-+` `distribute-lft-out`

Counts

3 → 57

Calls

3 calls:

16.0ms	(* 2 (pow a 2))
8.0ms	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
0.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

series148.0ms

Counts

3 → 9

Calls

3 calls:

25.0ms	(* 2 (pow a 2))
55.0ms	(+ (fma (* 2 (pow a 2)) (pow b 2) (pow b 4)) (pow a 4))
69.0ms	(fma (* 2 (pow a 2)) (pow b 2) (pow b 4))

simplify33.0ms

Counts

66 → 66

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	215	372
1	971	344
2	5001	343
done	5001	343

prune199.0ms

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 0b

regimes90.0ms

Accuracy

0% (0.2b remaining)

Error of 0.2b against oracle of 0.0b and baseline of 0.2b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	7
1	13	7
done	13	7

end0.0ms

sample1.2s

Algorithm

intervals

Results

728.0ms

20599×

body

valid