Details

sample94.0ms

Algorithm

intervals

Results

57.0ms

644×

body

valid

simplify3.9s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
6	3761
5	474
4	154
3	87
2	50
1	26
0	12

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
0.0b	(+ (* a a) (* b b))
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `pow1` `add-exp-log`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-cube-cbrt`
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` `sum-log` `flip3-+` `flip-+` `sqr-pow`
1×	`pow-to-exp` `pow-pow` `associate-r` `pow-exp` `*-commutative` `unswap-sqr`

Counts

4 → 74

Calls

4 calls:

95.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
12.0ms	(+ (* a a) (* b b))
15.0ms	(* 4.0 (* b b))
8.0ms	(pow (+ (* a a) (* b b)) 2.0)

series306.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
37.0ms	(+ (* a a) (* b b))
51.0ms	(* 4.0 (* b b))
131.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.3s

Counts

86 → 86

Iterations

Iter	Nodes
done	5000
2	2253
1	399
0	125

prune475.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow a 4) (pow b 4))
0.0b	(- (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4))) 1.0)
0.0b	(fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4)))
0.2b	(* (* a b) (* a b))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

43×	`pow1`
19×	`*-un-lft-identity`
17×	`pow-prod-down`
16×	`add-cbrt-cube` `add-exp-log`
15×	`add-sqr-sqrt`
13×	`add-cube-cbrt`
9×	`prod-diff`
8×	`prod-exp` `cbrt-unprod` `add-log-exp`
7×	`fma-def`
5×	`unpow-prod-down`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow-plus` `fma-udef` `distribute-lft-out`
1×	`pow2` `+-commutative` `sum-log` `sub-neg` `flip3-+` `flip3--` `diff-log` `swap-sqr` `associate-r` `associate-l` `associate--l+` `*-commutative` `flip-+` `flip--` `distribute-lft-out--` `difference-of-squares` `sqr-pow`

Counts

4 → 97

Calls

4 calls:

14.0ms	(+ (pow a 4) (pow b 4))
6.0ms	(- (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4))) 1.0)
0.0ms	(fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4)))
24.0ms	(* (* a b) (* a b))

series268.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(+ (pow a 4) (pow b 4))
101.0ms	(- (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4))) 1.0)
59.0ms	(fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4)))
35.0ms	(* (* a b) (* a b))

simplify714.0ms

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	1443
1	331
0	134

prune578.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* a b) (* a b))
0.2b	(fma (sqrt (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4)))) (sqrt (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4)))) (- 1.0))
13.9b	(sqrt (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4))))
13.9b	(sqrt (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

45×	`pow1`
17×	`pow-prod-down`
16×	`add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `prod-exp` `cbrt-unprod`
6×	`*-un-lft-identity` `add-cube-cbrt` `sqrt-prod`
4×	`expm1-log1p-u` `pow-sqr` `pow-prod-up` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow-plus` `pow1/2`
1×	`pow2` `swap-sqr` `associate-r` `associate-l` `*-commutative` `fma-udef`

Counts

4 → 76

Calls

4 calls:

41.0ms	(* (* a b) (* a b))
0.0ms	(fma (sqrt (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4)))) (sqrt (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4)))) (- 1.0))
2.0ms	(sqrt (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4))))
2.0ms	(sqrt (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4))))

series542.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(* (* a b) (* a b))
248.0ms	(fma (sqrt (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4)))) (sqrt (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4)))) (- 1.0))
114.0ms	(sqrt (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4))))
122.0ms	(sqrt (fma 2 (* (* a b) (* a b)) (+ (pow a 4) (pow b 4))))

simplify600.0ms

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	828
1	170
0	77

prune509.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

localize20.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 4.0 (* b b))
0.0b	(fma (* (* (* 2.0 a) a) b) b (pow b 4))
0.5b	(* (* (* 2.0 a) a) b)

rewrite106.0ms

Algorithm

rewrite-expression-head

Rules

17×	`pow1` `add-cbrt-cube` `add-exp-log`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
6×	`add-sqr-sqrt`
5×	`*-un-lft-identity` `add-cube-cbrt`
4×	`associate-r` `associate-l`
3×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`*-commutative`
1×	`fma-udef` `unswap-sqr`

Counts

3 → 54

Calls

3 calls:

25.0ms	(* 4.0 (* b b))
0.0ms	(fma (* (* (* 2.0 a) a) b) b (pow b 4))
77.0ms	(* (* (* 2.0 a) a) b)

series201.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(* 4.0 (* b b))
120.0ms	(fma (* (* (* 2.0 a) a) b) b (pow b 4))
44.0ms	(* (* (* 2.0 a) a) b)

simplify1.3s

Counts

63 → 63

Iterations

Iter	Nodes
done	5000
2	1924
1	265
0	102

prune300.0ms

Pruning

4 alts after pruning (0 fresh and 4 done)

Merged error: 0b

regimes323.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Iter	Nodes
done	15
1	15
0	12

end0.0ms

sample3.0s

Algorithm

intervals

Results

2.2s

20523×

body

valid