Details

sample106.0ms

Algorithm

intervals

Results

86.0ms

688×

body

valid

simplify3.8s

Counts

1 → 1

Iterations

Iter	Nodes
6	4855
5	1985
4	584
3	159
2	60
1	27
0	12

prune17.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.1b

localize42.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
0.0b	(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1)
0.0b	(* 4 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2)

rewrite501.0ms

Algorithm

rewrite-expression-head

Rules

21×	`add-sqr-sqrt`
19×	`*-un-lft-identity`
16×	`add-cube-cbrt`
11×	`add-exp-log` `add-log-exp`
10×	`pow1`
9×	`add-cbrt-cube` `prod-diff`
8×	`fma-def`
6×	`unpow-prod-down`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u`
3×	`pow-unpow` `fma-neg` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`sum-log` `diff-log` `unpow2` `difference-of-squares` `sqr-pow`
1×	`pow-to-exp` `+-commutative` `expm1-def` `sub-neg` `pow-pow` `flip3-+` `flip3--` `difference-of-sqr-1` `associate-r` `pow-exp` `associate--l+` `*-commutative` `flip-+` `flip--` `distribute-lft-out--` `unswap-sqr`

Counts

4 → 99

Calls

4 calls:

63.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
407.0ms	(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1)
14.0ms	(* 4 (* b b))
15.0ms	(pow (+ (* a a) (* b b)) 2)

series284.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b)))
107.0ms	(- (+ (pow (+ (* a a) (* b b)) 2) (* 4 (* b b))) 1)
45.0ms	(* 4 (* b b))
55.0ms	(pow (+ (* a a) (* b b)) 2)

simplify3.1s

Counts

111 → 111

Iterations

Iter	Nodes
3	4906
2	1164
1	385
0	155

prune1.1s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize31.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 4 (* b b))
0.0b	(* (* a a) 2)
0.2b	(fma (* b b) (fma b b (* (* a a) 2)) (* (* a a) (* a a)))
0.2b	(* (* a a) (* a a))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

125×	`pow1`
36×	`pow-prod-up`
29×	`pow-prod-down`
26×	`add-cbrt-cube` `add-exp-log`
22×	`pow-sqr`
18×	`pow-plus`
14×	`prod-exp` `cbrt-unprod`
13×	`pow2`
8×	`add-sqr-sqrt`
6×	`*-un-lft-identity` `add-cube-cbrt`
5×	`associate-r` `associate-l`
4×	`expm1-log1p-u` `insert-posit16` `log1p-expm1-u` `add-log-exp`
3×	`*-commutative` `unswap-sqr`
1×	`swap-sqr` `fma-udef`

Counts

4 → 121

Calls

4 calls:

16.0ms	(* 4 (* b b))
23.0ms	(* (* a a) 2)
0.0ms	(fma (* b b) (fma b b (* (* a a) 2)) (* (* a a) (* a a)))
36.0ms	(* (* a a) (* a a))

series198.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(* 4 (* b b))
32.0ms	(* (* a a) 2)
76.0ms	(fma (* b b) (fma b b (* (* a a) 2)) (* (* a a) (* a a)))
52.0ms	(* (* a a) (* a a))

simplify1.4s

Counts

133 → 133

Iterations

Iter	Nodes
3	2739
2	903
1	325
0	128

prune1.5s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

localize28.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (fma (* b b) (fma b b (* (* a a) 2)) (pow a 4)) (* 4 (* b b))) 1)
0.0b	(* 4 (* b b))
0.0b	(* (* a a) 2)
0.2b	(fma (* b b) (fma b b (* (* a a) 2)) (pow a 4))

rewrite92.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`add-exp-log`
14×	`pow1` `add-cbrt-cube`
13×	`add-cube-cbrt`
9×	`prod-diff` `add-log-exp`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg`
2×	`diff-log` `*-commutative` `difference-of-squares` `unswap-sqr`
1×	`expm1-def` `sum-log` `sub-neg` `flip3--` `difference-of-sqr-1` `associate--l+` `fma-udef` `flip--` `distribute-lft-out--`

Counts

4 → 89

Calls

4 calls:

55.0ms	(- (+ (fma (* b b) (fma b b (* (* a a) 2)) (pow a 4)) (* 4 (* b b))) 1)
20.0ms	(* 4 (* b b))
15.0ms	(* (* a a) 2)
0.0ms	(fma (* b b) (fma b b (* (* a a) 2)) (pow a 4))

series258.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(- (+ (fma (* b b) (fma b b (* (* a a) 2)) (pow a 4)) (* 4 (* b b))) 1)
41.0ms	(* 4 (* b b))
38.0ms	(* (* a a) 2)
95.0ms	(fma (* b b) (fma b b (* (* a a) 2)) (pow a 4))

simplify1.9s

Counts

101 → 101

Iterations

Iter	Nodes
3	3849
2	1045
1	359
0	156

prune1.2s

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.1b

localize46.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ (+ (* (* b b) (+ (+ (* a a) (* a a)) (* b b))) (pow a 4)) (* 4 (* b b))) 1)
0.0b	(* 4 (* b b))
0.0b	(+ (* a a) (* a a))
1.4b	(* (* b b) (+ (+ (* a a) (* a a)) (* b b)))

rewrite1.6s

Algorithm

rewrite-expression-head

Rules

19×	`add-sqr-sqrt`
16×	`*-un-lft-identity`
15×	`add-exp-log` `add-log-exp`
14×	`pow1` `add-cbrt-cube`
13×	`add-cube-cbrt`
9×	`prod-diff`
6×	`pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `sum-log` `associate-r` `associate-l` `insert-posit16` `log1p-expm1-u`
3×	`fma-neg` `diff-log`
2×	`flip3-+` `associate-r/` `-commutative` `flip-+` `difference-of-squares` `unswap-sqr`
1×	`distribute-rgt-in` `+-commutative` `expm1-def` `sub-neg` `fma-def` `distribute-lft-in` `distribute-rgt-out` `flip3--` `count-2` `difference-of-sqr-1` `associate--l+` `flip--` `distribute-lft-out` `distribute-lft-out--`

Counts

4 → 101

Calls

4 calls:

1.4s	(- (+ (+ (* (* b b) (+ (+ (* a a) (* a a)) (* b b))) (pow a 4)) (* 4 (* b b))) 1)
26.0ms	(* 4 (* b b))
9.0ms	(+ (* a a) (* a a))
92.0ms	(* (* b b) (+ (+ (* a a) (* a a)) (* b b)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(- (+ (+ (* (* b b) (+ (+ (* a a) (* a a)) (* b b))) (pow a 4)) (* 4 (* b b))) 1)
50.0ms	(* 4 (* b b))
64.0ms	(+ (* a a) (* a a))
88.0ms	(* (* b b) (+ (+ (* a a) (* a a)) (* b b)))

simplify7.8s

Counts

113 → 113

Iterations

Iter	Nodes
3	9422
2	1749
1	467
0	170

prune1.3s

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

regimes228.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify5.0ms

Iterations

Iter	Nodes
2	21
1	21
0	15

end0.0ms

sample3.6s

Algorithm

intervals

Results

3.2s

20839×

body

valid