Details

sample150.0ms

Algorithm

intervals

Results

102.0ms

659×

body

valid

simplify2.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	18	29
1	53	27
2	172	26
3	566	26
4	2092	26
done	5002	26

prune18.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.1b

localize41.0ms

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) (+ 3.0 a)))))
0.1b	(* (* a a) (- 1.0 a))
0.3b	(pow (+ (* a a) (* b b)) 2.0)
0.8b	(* (* b b) (+ 3.0 a))

rewrite117.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt` `*-un-lft-identity`
22×	`add-cube-cbrt`
18×	`prod-diff`
15×	`pow1` `add-exp-log`
14×	`add-cbrt-cube`
13×	`distribute-rgt-in` `distribute-lft-in`
9×	`associate-r`
7×	`fma-def`
6×	`unpow-prod-down` `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` `distribute-lft-out--` `difference-of-squares`

Counts

4 → 114

Calls

4 calls:

50.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
27.0ms	(* (* a a) (- 1.0 a))
8.0ms	(pow (+ (* a a) (* b b)) 2.0)
29.0ms	(* (* b b) (+ 3.0 a))

series443.0ms

Counts

4 → 12

Calls

4 calls:

163.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
97.0ms	(* (* a a) (- 1.0 a))
143.0ms	(pow (+ (* a a) (* b b)) 2.0)
40.0ms	(* (* b b) (+ 3.0 a))

simplify548.0ms

Counts

126 → 126

Iterations

Useful iterations: done (543.0ms)

Iter	Nodes	Cost
0	235	2118
1	746	1794
done	5000	1553

prune768.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.0b

localize55.0ms

Local error

Found 4 expressions with local error:

0.1b	(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.8b	(* (* b b) (+ 3.0 a))
8.1b	(sqrt (+ (* a a) (* b b)))
8.1b	(sqrt (+ (* a a) (* b b)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `add-cbrt-cube` `add-exp-log`
7×	`add-cube-cbrt`
6×	`sqrt-prod`
4×	`expm1-log1p-u` `sqrt-div` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`flip3-+` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip-+`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-*r/` `hypot-def`
1×	`distribute-rgt-in` `distribute-lft-in` `associate-l` `*-commutative` `fma-udef` `distribute-lft-out` `unswap-sqr`

Counts

4 → 72

Calls

4 calls:

1.0ms	(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
46.0ms	(* (* b b) (+ 3.0 a))
12.0ms	(sqrt (+ (* a a) (* b b)))
13.0ms	(sqrt (+ (* a a) (* b b)))

series401.0ms

Counts

4 → 12

Calls

4 calls:

197.0ms	(fma (pow (sqrt (+ (* a a) (* b b))) 2.0) (pow (sqrt (+ (* a a) (* b b))) 2.0) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
64.0ms	(* (* b b) (+ 3.0 a))
70.0ms	(sqrt (+ (* a a) (* b b)))
70.0ms	(sqrt (+ (* a a) (* b b)))

simplify3.3s

Counts

84 → 84

Iterations

Useful iterations: done (3.3s)

Iter	Nodes	Cost
0	117	1304
1	346	908
2	2332	768
done	5001	756

prune762.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 1.0)
0.0b	(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
0.1b	(* (* a a) (- 1.0 a))
0.8b	(* (* b b) (+ 3.0 a))

rewrite256.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 125

Calls

4 calls:

141.0ms	(- (+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 1.0)
17.0ms	(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
56.0ms	(* (* a a) (- 1.0 a))
32.0ms	(* (* b b) (+ 3.0 a))

series539.0ms

Counts

4 → 12

Calls

4 calls:

191.0ms	(- (+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a))))) 1.0)
203.0ms	(+ (pow (hypot a b) (* 2 2.0)) (* 4.0 (+ (* (* a a) (- 1.0 a)) (* (* b b) (+ 3.0 a)))))
81.0ms	(* (* a a) (- 1.0 a))
64.0ms	(* (* b b) (+ 3.0 a))

simplify491.0ms

Counts

137 → 137

Iterations

Useful iterations: done (484.0ms)

Iter	Nodes	Cost
0	248	3187
1	777	2730
done	5000	2332

prune774.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize54.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot a b)
0.0b	(+ (pow (hypot a b) (* 2 2.0)) (- (* (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0) 1.0))
0.1b	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
0.8b	(* (* b b) (+ 3.0 a))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

0.0ms	(hypot a b)
35.0ms	(+ (pow (hypot a b) (* 2 2.0)) (- (* (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0) 1.0))
0.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
25.0ms	(* (* b b) (+ 3.0 a))

series354.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(hypot a b)
179.0ms	(+ (pow (hypot a b) (* 2 2.0)) (- (* (fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a))) 4.0) 1.0))
61.0ms	(fma (* a a) (- 1.0 a) (* (* b b) (+ 3.0 a)))
47.0ms	(* (* b b) (+ 3.0 a))

simplify2.5s

Counts

86 → 86

Iterations

Useful iterations: 2 (494.0ms)

Iter	Nodes	Cost
0	148	1396
1	413	1313
2	2572	1164
done	5002	1164

prune610.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

regimes205.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify6.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	19	26
1	24	26
done	24	26

end0.0ms

sample3.6s

Algorithm

intervals

Results

3.0s

20551×

body

valid