Details

sample58.0ms

Algorithm

intervals

Results

15.0ms	190×	body	80	valid
9.0ms	22×	body	1280	valid
7.0ms	16×	body	2560	valid
5.0ms	9×	body	5120	valid
3.0ms	11×	body	640	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	12	15
1	24	10
2	30	10
3	32	10
done	32	10

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 14.2b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* (+ (hypot re im) re) 2.0))
0.6b	(+ (hypot re im) re)

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `*-un-lft-identity`
5×	`add-log-exp`
4×	`add-sqr-sqrt` `add-cube-cbrt`
3×	`expm1-log1p-u` `fma-def` `add-cbrt-cube` `add-exp-log` `log1p-expm1-u`
2×	`sqrt-pow1` `flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`+-commutative` `hypot-udef` `sum-log` `pow1/2` `pow-prod-down` `sqrt-prod` `distribute-lft-out`

Counts

3 → 42

Calls

3 calls:

0.0ms	(hypot re im)
12.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
7.0ms	(+ (hypot re im) re)

series408.0ms

Counts

3 → 9

Calls

3 calls:

63.0ms	(hypot re im)
277.0ms	(sqrt (* (+ (hypot re im) re) 2.0))
68.0ms	(+ (hypot re im) re)

simplify1.7s

Counts

51 → 51

Iterations

Useful iterations: done (1.7s)

Iter	Nodes	Cost
0	86	414
1	187	381
2	612	358
3	3673	349
done	5000	348

prune371.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 13.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (+ (hypot re im) re))
0.0b	(hypot re im)
0.4b	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
0.6b	(+ (hypot re im) re)

rewrite66.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

9.0ms	(sqrt (+ (hypot re im) re))
0.0ms	(hypot re im)
45.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
9.0ms	(+ (hypot re im) re)

series594.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(sqrt (+ (hypot re im) re))
59.0ms	(hypot re im)
273.0ms	(* (sqrt (+ (hypot re im) re)) (sqrt 2.0))
93.0ms	(+ (hypot re im) re)

simplify786.0ms

Counts

93 → 93

Iterations

Useful iterations: done (783.0ms)

Iter	Nodes	Cost
0	135	898
1	307	831
2	1287	784
done	5001	771

prune578.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 13.7b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(hypot re im)
0.2b	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
0.5b	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
8.9b	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
22×	`pow1`
19×	`sqrt-prod`
12×	`*-un-lft-identity` `add-cube-cbrt`
10×	`sqrt-pow1`
9×	`pow1/2`
8×	`swap-sqr`
6×	`add-cbrt-cube` `associate-r` `associate-l` `add-exp-log` `add-log-exp`
5×	`pow-prod-up`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `unswap-sqr`
3×	`pow-sqr`
2×	`flip3-+` `sqrt-div` `associate-*l/` `flip-+`
1×	`pow2` `+-commutative` `hypot-udef` `sum-log` `rem-square-sqrt` `fma-def` `pow-plus` `sqrt-unprod` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 90

Calls

4 calls:

0.0ms	(hypot re im)
12.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
11.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
10.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

series492.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(hypot re im)
255.0ms	(sqrt (* (+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re) 2.0))
83.0ms	(* (sqrt (hypot re im)) (sqrt (hypot re im)))
77.0ms	(+ (* (sqrt (hypot re im)) (sqrt (hypot re im))) re)

simplify842.0ms

Counts

102 → 102

Iterations

Useful iterations: done (840.0ms)

Iter	Nodes	Cost
0	129	1271
1	291	695
2	1169	638
done	5000	623

prune486.0ms

Pruning

12 alts after pruning (10 fresh and 2 done)

Merged error: 13.7b

localize46.0ms

Local error

Found 4 expressions with local error:

0.2b	(sqrt (* (+ (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re) 2.0))
0.3b	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
0.7b	(pow (sqrt (sqrt (hypot re im))) 3)
11.3b	(+ (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re)

rewrite94.0ms

Algorithm

rewrite-expression-head

Rules

88×	`sqrt-prod`
66×	`add-sqr-sqrt`
27×	`unpow-prod-down` `cube-prod`
24×	`associate-l` `unswap-sqr`
21×	`*-un-lft-identity` `add-cube-cbrt`
11×	`pow1`
10×	`add-exp-log`
9×	`associate-r`
7×	`add-cbrt-cube`
6×	`sqrt-pow1` `add-log-exp`
5×	`pow-pow` `sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `pow1/2` `prod-exp`
2×	`cube-mult` `pow-to-exp` `flip3-+` `sqrt-div` `unpow3` `associate-*l/` `pow-exp` `flip-+`
1×	`+-commutative` `sum-log` `fma-def` `pow-plus` `pow-prod-down` `*-commutative` `pow-prod-up` `cbrt-unprod` `sqrt-pow2` `rem-cube-cbrt`

Counts

4 → 144

Calls

4 calls:

30.0ms	(sqrt (* (+ (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re) 2.0))
31.0ms	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
5.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
24.0ms	(+ (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re)

series630.0ms

Counts

4 → 12

Calls

4 calls:

299.0ms	(sqrt (* (+ (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re) 2.0))
72.0ms	(* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im))))
167.0ms	(pow (sqrt (sqrt (hypot re im))) 3)
92.0ms	(+ (* (pow (sqrt (sqrt (hypot re im))) 3) (sqrt (sqrt (hypot re im)))) re)

simplify1.8s

Counts

156 → 156

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	177	2729
1	484	1862
2	2159	1702
done	5002	1357

prune608.0ms

Pruning

16 alts after pruning (14 fresh and 2 done)

Merged error: 13.7b

regimes314.0ms

Accuracy

0% (0.3b remaining)

Error of 13.6b against oracle of 13.3b and baseline of 13.6b

bsearch0.0ms

simplify1.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	10
1	12	10
done	12	10

end0.0ms

sample2.2s

Algorithm

intervals

Results

608.0ms	169×	body	320	valid
585.0ms	5974×	body	80	valid
278.0ms	696×	body	2560	valid
169.0ms	501×	body	1280	valid
148.0ms	301×	body	5120	valid
110.0ms	275×	body	640	valid
10.0ms	84×	body	160	valid