Details

sample98.0ms

Algorithm

intervals

Results

69.0ms

612×

body

valid

simplify3.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	1809
3	551
2	177
1	55
0	19

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize49.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
0.1b	(* (* a a) (+ 1.0 a))
0.2b	(* (* b b) (- 1.0 (* 3.0 a)))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1` `add-exp-log`
14×	`add-sqr-sqrt` `*-un-lft-identity` `add-cbrt-cube`
12×	`add-cube-cbrt`
7×	`distribute-rgt-in` `fma-def` `distribute-lft-in` `associate-r`
6×	`unpow-prod-down` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod` `add-log-exp`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`pow-unpow`
2×	`associate-+r+` `sub-neg` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `sum-log` `pow-pow` `flip3--` `pow-exp` `flip--` `distribute-lft-out`

Counts

4 → 100

Calls

4 calls:

73.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
39.0ms	(* (* a a) (+ 1.0 a))
29.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
8.0ms	(pow (+ (* a a) (* b b)) 2.0)

series508.0ms

Counts

4 → 12

Calls

4 calls:

207.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
97.0ms	(* (* a a) (+ 1.0 a))
61.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
143.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.1s

Counts

112 → 112

Iterations

Iter	Nodes
done	5007
2	2251
1	583
0	201

prune938.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.1b

localize67.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
11.8b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
11.8b	(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 80

Calls

4 calls:

17.0ms	(pow (+ (* a a) (* b b)) 2.0)
17.0ms	(pow (+ (* a a) (* b b)) 2.0)
26.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
26.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))

series743.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(pow (+ (* a a) (* b b)) 2.0)
135.0ms	(pow (+ (* a a) (* b b)) 2.0)
237.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
209.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify3.3s

Counts

92 → 92

Iterations

Iter	Nodes
done	5006
4	3513
3	981
2	353
1	154
0	74

prune914.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize68.0ms

Local error

Found 4 expressions with local error:

9.1b	(sqrt (sqrt (pow (+ (* a a) (* b b)) 2.0)))
11.8b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
11.8b	(sqrt (pow (+ (* a a) (* b b)) 2.0))
11.8b	(sqrt (pow (+ (* a a) (* b b)) 2.0))

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

41×	`sqrt-prod`
22×	`add-sqr-sqrt`
16×	`unpow-prod-down`
13×	`rem-sqrt-square` `*-un-lft-identity` `add-cube-cbrt`
8×	`sqr-pow`
7×	`sqrt-pow1`
5×	`pow1` `pow1/2`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`

Counts

4 → 90

Calls

4 calls:

23.0ms	(sqrt (sqrt (pow (+ (* a a) (* b b)) 2.0)))
13.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
14.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
13.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))

series885.0ms

Counts

4 → 12

Calls

4 calls:

252.0ms	(sqrt (sqrt (pow (+ (* a a) (* b b)) 2.0)))
202.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
213.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))
217.0ms	(sqrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.3s

Counts

102 → 102

Iterations

Iter	Nodes
done	5000
4	1732
3	652
2	284
1	147
0	85

prune994.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.0b

localize153.0ms

Local error

Found 4 expressions with local error:

13.1b	(sqrt (* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0))))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.6b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite46.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
12×	`pow1`
10×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
9×	`unpow-prod-down` `sqrt-pow1` `pow1/3`
4×	`expm1-log1p-u` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u` `add-log-exp`
3×	`sqr-pow`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `rem-sqrt-square` `pow-plus` `pow1/2` `sqrt-prod`

Counts

4 → 72

Calls

4 calls:

23.0ms	(sqrt (* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0))))
7.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
7.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
7.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series907.0ms

Counts

4 → 12

Calls

4 calls:

245.0ms	(sqrt (* (cbrt (pow (+ (* a a) (* b b)) 2.0)) (cbrt (pow (+ (* a a) (* b b)) 2.0))))
177.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
250.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
235.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.9s

Counts

84 → 84

Iterations

Iter	Nodes
done	5002
5	3947
4	1309
3	507
2	242
1	142
0	81

prune1.1s

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.0b

regimes505.0ms

Accuracy

0% (0.2b remaining)

Error of 0.3b against oracle of 0.1b and baseline of 0.3b

bsearch0.0ms

simplify7.0ms

Iterations

Iter	Nodes
done	38
1	38
0	29

end0.0ms

sample4.1s

Algorithm

intervals

Results

3.5s

20694×

body

valid