Details

sample38.0ms

Algorithm

intervals

Results

23.0ms

620×

body

valid

simplify3.6s

Counts

1 → 1

Iterations

Useful iterations: 2 (6.0ms)

Iter	Nodes	Cost
0	12	17
1	26	16
2	49	15
3	80	15
4	136	15
5	284	15
6	886	15
7	3991	15
done	5000	15

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

3.0ms	(+ (* a a) (* b b))
6.0ms	(* 4.0 (* b b))
29.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
4.0ms	(pow (+ (* a a) (* b b)) 2.0)

series215.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(+ (* a a) (* b b))
24.0ms	(* 4.0 (* b b))
64.0ms	(+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b)))
100.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify2.2s

Counts

86 → 86

Iterations

Useful iterations: 3 (830.0ms)

Iter	Nodes	Cost
0	125	1011
1	335	844
2	1150	772
3	4664	766
done	5000	766

prune214.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0))) (cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0))))
15.0b	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
15.0b	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
15.0b	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

25×	`cbrt-prod`
23×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `*-un-lft-identity`
11×	`pow1`
9×	`pow1/3`
6×	`add-exp-log` `swap-sqr` `associate-r` `associate-l`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0))) (cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0))))
0.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
0.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
1.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))

series804.0ms

Counts

4 → 12

Calls

4 calls:

211.0ms	(* (cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0))) (cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0))))
196.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
198.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))
199.0ms	(cbrt (fma 4.0 (* b b) (pow (fma a a (* b b)) 2.0)))

simplify683.0ms

Counts

93 → 93

Iterations

Useful iterations: 3 (248.0ms)

Iter	Nodes	Cost
0	105	2580
1	206	2420
2	549	2217
3	1753	1816
done	5000	1816

prune297.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize12.0ms

Local error

Found 2 expressions with local error:

0.0b	(- (+ (pow a 4) (fma (* (* a a) (* b b)) 2 (pow b 4))) 1.0)
2.6b	(* (* a a) (* b b))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

30×	`pow1`
23×	`*-un-lft-identity`
14×	`add-exp-log` `pow-prod-down` `add-cbrt-cube`
12×	`add-sqr-sqrt` `prod-diff`
10×	`add-cube-cbrt`
8×	`prod-exp` `cbrt-unprod`
7×	`add-log-exp`
5×	`distribute-lft-out`
4×	`pow-plus` `fma-neg` `pow-prod-up`
2×	`pow2` `expm1-log1p-u` `diff-log` `pow-sqr` `log1p-expm1-u` `distribute-lft-out--`
1×	`sub-neg` `flip3--` `associate-r` `associate-l` `associate--l+` `sum-log` `*-commutative` `flip--` `difference-of-squares` `unswap-sqr`

Counts

2 → 66

Calls

2 calls:

48.0ms	(- (+ (pow a 4) (fma (* (* a a) (* b b)) 2 (pow b 4))) 1.0)
14.0ms	(* (* a a) (* b b))

series82.0ms

Counts

2 → 6

Calls

2 calls:

48.0ms	(- (+ (pow a 4) (fma (* (* a a) (* b b)) 2 (pow b 4))) 1.0)
34.0ms	(* (* a a) (* b b))

simplify453.0ms

Counts

72 → 72

Iterations

Useful iterations: done (451.0ms)

Iter	Nodes	Cost
0	111	1439
1	261	1275
2	902	1091
done	5001	1060

prune140.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0b

localize11.0ms

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)) (* 4.0 (* b b)))
1.0b	(fma (* 2.0 (* a a)) (* b b) (pow b 4))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt`
5×	`add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`expm1-log1p-u` `fma-def` `associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u`
2×	`fma-udef`
1×	`+-commutative` `associate-+l+` `flip3-+` `associate-r` `sum-log` `*-commutative` `flip-+` `unswap-sqr`

Counts

3 → 48

Calls

3 calls:

6.0ms	(* 4.0 (* b b))
4.0ms	(+ (fma (* 2.0 (* a a)) (* b b) (pow b 4)) (* 4.0 (* b b)))
0.0ms	(fma (* 2.0 (* a a)) (* b b) (pow b 4))

series163.0ms

Counts

3 → 9

Calls

3 calls:

27.0ms	(* 4.0 (* b b))
64.0ms	(+ (fma (* 2.0 (* a a)) (* b b) (pow b 4)) (* 4.0 (* b b)))
71.0ms	(fma (* 2.0 (* a a)) (* b b) (pow b 4))

simplify1.5s

Counts

57 → 57

Iterations

Useful iterations: 3 (508.0ms)

Iter	Nodes	Cost
0	80	825
1	194	762
2	666	671
3	2504	619
done	5000	619

prune139.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0b

regimes83.0ms

Accuracy

0% (0.5b remaining)

Error of 0.5b against oracle of 0.0b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	46
1	14	46
done	14	46

end0.0ms

sample1.1s

Algorithm

intervals

Results

750.0ms

20313×

body

valid