Details

sample42.0ms

Algorithm

intervals

Results

25.0ms

646×

body

valid

simplify49.0ms

Counts

1 → 1

Iterations

Useful iterations: 2 (4.0ms)

Iter	Nodes	Cost
0	26	8
1	51	8
2	88	7
3	153	7
4	357	7
5	1572	7
6	5002	7
done	5002	7

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	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
0.0b	(* 4.0 (* b b))
0.3b	(pow (+ (* a a) (* b b)) 2.0)

rewrite369.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 84

Calls

4 calls:

8.0ms	(+ (* a a) (* b b))
334.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
15.0ms	(* 4.0 (* b b))
10.0ms	(pow (+ (* a a) (* b b)) 2.0)

series233.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(+ (* a a) (* b b))
72.0ms	(- (+ (pow (+ (* a a) (* b b)) 2.0) (* 4.0 (* b b))) 1.0)
27.0ms	(* 4.0 (* b b))
104.0ms	(pow (+ (* a a) (* b b)) 2.0)

simplify46.0ms

Counts

96 → 96

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	404	753
1	1693	603
2	5001	587
done	5001	587

prune208.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.0b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(- (fma (* 4.0 b) b (pow a 4)) 1.0)

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt` `*-un-lft-identity`
9×	`prod-diff`
8×	`add-cube-cbrt`
3×	`fma-neg` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `associate--l+` `add-cbrt-cube` `flip--` `fma-udef` `log1p-expm1-u` `distribute-lft-out--` `difference-of-squares`

Counts

1 → 29

Calls

1 calls:

7.0ms

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

series78.0ms

Counts

1 → 3

Calls

1 calls:

78.0ms

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

simplify95.0ms

Counts

32 → 32

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	142	294
1	438	208
2	2731	197
3	5001	163
done	5001	163

prune61.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.0b

localize16.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 2.0 (pow a 2))
0.0b	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
0.0b	(* 4.0 (* b b))
0.6b	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-exp-log`
11×	`add-cbrt-cube`
9×	`pow1` `add-cube-cbrt` `-un-lft-identity` `associate-r*`
6×	`associate-l` `prod-exp` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `unpow-prod-down` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down`
2×	`*-commutative` `fma-udef` `unpow2` `sqr-pow`
1×	`+-commutative` `pow-to-exp` `associate-+l+` `flip3-+` `pow-exp` `sum-log` `flip-+`

Counts

4 → 77

Calls

4 calls:

11.0ms	(* 2.0 (pow a 2))
7.0ms	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
16.0ms	(* 4.0 (* b b))
0.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

series188.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(* 2.0 (pow a 2))
65.0ms	(+ (fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4)) (* 4.0 (* b b)))
24.0ms	(* 4.0 (* b b))
73.0ms	(fma (* 2.0 (pow a 2)) (pow b 2) (pow b 4))

simplify38.0ms

Counts

89 → 89

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	291	467
1	1199	418
2	5002	407
done	5002	407

prune238.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.0b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 1.0)
0.1b	(pow (- (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 1.0) 3)
0.3b	(pow (+ (* a a) (* b b)) 2.0)
14.7b	(cbrt (pow (- (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 1.0) 3))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt` `*-un-lft-identity`
19×	`add-cube-cbrt`
16×	`cbrt-prod`
13×	`unpow-prod-down`
10×	`cube-prod`
9×	`prod-diff`
6×	`pow1` `add-exp-log` `pow-unpow` `add-log-exp`
5×	`add-cbrt-cube` `distribute-lft-out--` `difference-of-squares`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u`
3×	`flip3--` `fma-neg` `flip--` `sqr-pow`
2×	`cube-mult` `pow-to-exp` `cbrt-div` `pow-pow` `unpow3` `pow-exp`
1×	`sub-neg` `pow1/3` `diff-log` `associate--l+` `rem-cbrt-cube` `fma-udef` `rem-cube-cbrt`

Counts

4 → 108

Calls

4 calls:

6.0ms	(- (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 1.0)
11.0ms	(pow (- (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 1.0) 3)
9.0ms	(pow (+ (* a a) (* b b)) 2.0)
8.0ms	(cbrt (pow (- (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 1.0) 3))

series358.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(- (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 1.0)
104.0ms	(pow (- (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 1.0) 3)
101.0ms	(pow (+ (* a a) (* b b)) 2.0)
65.0ms	(cbrt (pow (- (fma (* 4.0 b) b (pow (+ (* a a) (* b b)) 2.0)) 1.0) 3))

simplify52.0ms

Counts

120 → 120

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	414	1359
1	1656	1215
2	5002	1203
done	5002	1203

prune303.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.0b

regimes94.0ms

Accuracy

86.7% (1.5b remaining)

Error of 1.5b against oracle of 0.1b and baseline of 11.3b

bsearch1.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	28	14
1	28	14
done	28	14

end0.0ms

sample1.2s

Algorithm

intervals

Results

747.0ms

20589×

body

valid