Details

sample55.0ms

Algorithm

intervals

Results

37.0ms

660×

body

valid

simplify2.2s

Counts

1 → 1

Iterations

Useful iterations: 2 (14.0ms)

Iter	Nodes	Cost
0	19	31
1	55	29
2	158	28
3	443	28
4	1206	28
5	3442	28
done	5000	28

prune7.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize20.0ms

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))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.4b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite61.0ms

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×	`sub-neg` `associate-+r+` `flip3-+` `associate-l` `*-commutative` `flip-+` `unswap-sqr` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `flip3--` `pow-pow` `pow-exp` `sum-log` `flip--` `distribute-lft-out`

Counts

4 → 100

Calls

4 calls:

28.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
14.0ms	(* (* a a) (+ 1.0 a))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)
13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series317.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
52.0ms	(* (* a a) (+ 1.0 a))
103.0ms	(pow (+ (* a a) (* b b)) 2.0)
53.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify1.1s

Counts

112 → 112

Iterations

Useful iterations: 2 (434.0ms)

Iter	Nodes	Cost
0	201	1802
1	550	1621
2	2267	1446
done	5000	1446

prune344.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* b b) (- 1.0 (* 3.0 a)))
0.4b	(* (* b b) (- 1.0 (* 3.0 a)))
7.5b	(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))
7.5b	(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

16×	`pow1` `add-sqr-sqrt`
14×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity` `prod-diff`
10×	`distribute-rgt-in` `distribute-lft-in`
6×	`associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `associate-*r/` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 96

Calls

4 calls:

13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
1.0ms	(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))
1.0ms	(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))

series517.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
49.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
205.0ms	(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))
207.0ms	(sqrt (fma (fma (pow a 2) (+ 1.0 a) (* (* b b) (- 1.0 (* 3.0 a)))) 4.0 (pow (fma a a (* b b)) 2.0)))

simplify2.5s

Counts

108 → 108

Iterations

Useful iterations: 3 (1.3s)

Iter	Nodes	Cost
0	129	2220
1	324	2078
2	1139	1844
3	4573	1818
done	5000	1818

prune441.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize20.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (* b b) (- 1.0 (* 3.0 a)))
19.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
19.5b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

21×	`cbrt-prod`
14×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
9×	`pow1` `add-exp-log` `unpow-prod-down` `add-cbrt-cube`
6×	`prod-diff`
5×	`distribute-rgt-in` `distribute-lft-in`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-r` `pow-prod-down` `prod-exp` `cbrt-unprod` `sqr-pow`
2×	`sub-neg` `associate-*r/`
1×	`flip3--` `associate-l` `*-commutative` `flip--` `unswap-sqr`

Counts

4 → 84

Calls

4 calls:

13.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
7.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
4.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series514.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
156.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
159.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
149.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.4s

Counts

96 → 96

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	132	1508
1	310	1389
2	1066	1248
3	4207	1230
done	5000	1224

prune441.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow a 4) (fma 2 (* (pow a 2) (pow b 2)) (pow b 4)))
0.0b	(- (+ (pow a 4) (fma 2 (* (pow a 2) (pow b 2)) (pow b 4))) 1.0)
0.0b	(fma 2 (* (pow a 2) (pow b 2)) (pow b 4))
3.0b	(* (pow a 2) (pow b 2))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
33×	`*-un-lft-identity`
18×	`add-cube-cbrt`
17×	`unpow-prod-down`
16×	`add-exp-log` `unswap-sqr`
12×	`prod-diff`
11×	`add-log-exp` `sqr-pow`
10×	`unpow2`
9×	`prod-exp`
8×	`associate-r` `associate-l`
7×	`fma-def`
6×	`pow-to-exp` `pow-exp` `add-cbrt-cube` `distribute-lft-out`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
2×	`diff-log` `sum-log` `fma-udef` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `associate-+r+` `flip3--` `flip3-+` `pow-prod-down` `associate--l+` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `difference-of-squares`

Counts

4 → 120

Calls

4 calls:

8.0ms	(+ (pow a 4) (fma 2 (* (pow a 2) (pow b 2)) (pow b 4)))
55.0ms	(- (+ (pow a 4) (fma 2 (* (pow a 2) (pow b 2)) (pow b 4))) 1.0)
0.0ms	(fma 2 (* (pow a 2) (pow b 2)) (pow b 4))
9.0ms	(* (pow a 2) (pow b 2))

series211.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(+ (pow a 4) (fma 2 (* (pow a 2) (pow b 2)) (pow b 4)))
54.0ms	(- (+ (pow a 4) (fma 2 (* (pow a 2) (pow b 2)) (pow b 4))) 1.0)
77.0ms	(fma 2 (* (pow a 2) (pow b 2)) (pow b 4))
32.0ms	(* (pow a 2) (pow b 2))

simplify673.0ms

Counts

132 → 132

Iterations

Useful iterations: done (669.0ms)

Iter	Nodes	Cost
0	169	2359
1	372	2083
2	1340	1801
done	5000	1775

prune343.0ms

Pruning

5 alts after pruning (1 fresh and 4 done)

Merged error: 0.0b

regimes148.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	20	57
1	23	57
done	23	57

end0.0ms

sample1.7s

Algorithm

intervals

Results

1.3s

20612×

body

valid