Details

sample101.0ms

Algorithm

intervals

Results

66.0ms

693×

body

valid

simplify2.5s

Counts

1 → 1

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	19	31
1	55	29
2	179	28
3	594	28
4	2383	28
done	5000	28

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize38.0ms

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)
1.4b	(* (* b b) (- 1.0 (* 3.0 a)))

rewrite254.0ms

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:

127.0ms	(+ (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))
13.0ms	(pow (+ (* a a) (* b b)) 2.0)
57.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

series423.0ms

Counts

4 → 12

Calls

4 calls:

143.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (+ 1.0 a)) (* (* b b) (- 1.0 (* 3.0 a))))))
70.0ms	(* (* a a) (+ 1.0 a))
145.0ms	(pow (+ (* a a) (* b b)) 2.0)
64.0ms	(* (* b b) (- 1.0 (* 3.0 a)))

simplify3.3s

Counts

112 → 112

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	201	1802
1	618	1631
2	4429	1447
done	5000	1446

prune485.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize39.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (* b b) (- 1.0 (* 3.0 a)))
1.4b	(* (* b b) (- 1.0 (* 3.0 a)))
7.4b	(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)))
7.4b	(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)))

rewrite84.0ms

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:

38.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
37.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms	(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)))
2.0ms	(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)))

series809.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
74.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
313.0ms	(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)))
346.0ms	(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)))

simplify2.0s

Counts

108 → 108

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	129	2220
1	348	2078
2	2041	1844
done	5001	1820

prune609.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0b

localize41.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (* b b) (- 1.0 (* 3.0 a)))
7.4b	(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)))
7.4b	(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)))
7.4b	(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)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 78

Calls

4 calls:

42.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
2.0ms	(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)))
3.0ms	(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)))
3.0ms	(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)))

series920.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
298.0ms	(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)))
245.0ms	(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)))
292.0ms	(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)))

simplify2.0s

Counts

90 → 90

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	129	2252
1	348	2049
2	2041	1866
done	5001	1848

prune546.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0b

localize48.0ms

Local error

Found 4 expressions with local error:

1.4b	(* (* b b) (- 1.0 (* 3.0 a)))
15.3b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
15.3b	(cbrt (pow (+ (* a a) (* b b)) 2.0))
15.3b	(cbrt (pow (+ (* a a) (* b b)) 2.0))

rewrite119.0ms

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:

63.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
17.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
17.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
17.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

series810.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(* (* b b) (- 1.0 (* 3.0 a)))
259.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
239.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))
242.0ms	(cbrt (pow (+ (* a a) (* b b)) 2.0))

simplify2.1s

Counts

96 → 96

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	132	1508
1	334	1389
2	1951	1252
done	5000	1230

prune717.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0b

regimes172.0ms

Accuracy

0% (0.2b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	22	87
1	26	87
done	26	87

end0.0ms

sample4.8s

Algorithm

intervals

Results

3.9s

20552×

body

valid