Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	256×	body	80	valid
5.0ms	256×	pre	80	true

simplify5.2s

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	9	15
1	23	14
2	52	14
3	115	14
4	249	14
5	516	14
6	1111	14
7	4552	14
done	5000	14

prune7.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.1b

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (* y y))
0.1b	(* (- x y) (/ (+ x y) (fma x x (* y y))))
18.3b	(/ (+ x y) (fma x x (* y y)))

rewrite79.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
28×	`add-sqr-sqrt`
25×	`times-frac`
21×	`add-cube-cbrt`
16×	`associate-r`
10×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out`
5×	`pow1` `associate-l`
4×	`associate-/l*`
3×	`expm1-log1p-u` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `frac-times` `flip3--` `div-exp` `associate-*l/` `prod-exp` `flip--` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`frac-2neg` `flip3-+` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip-+` `fma-udef` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 88

Calls

3 calls:

0.0ms	(fma x x (* y y))
54.0ms	(* (- x y) (/ (+ x y) (fma x x (* y y))))
22.0ms	(/ (+ x y) (fma x x (* y y)))

series234.0ms

Counts

3 → 9

Calls

3 calls:

51.0ms	(fma x x (* y y))
106.0ms	(* (- x y) (/ (+ x y) (fma x x (* y y))))
77.0ms	(/ (+ x y) (fma x x (* y y)))

simplify1.8s

Counts

97 → 97

Iterations

Useful iterations: done (1.8s)

Iter	Nodes	Cost
0	123	1506
1	332	1469
2	2255	1265
done	5000	1259

prune265.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (hypot y x))
0.0b	(* (/ 1 (hypot y x)) (/ (+ x y) (hypot y x)))
0.0b	(/ (+ x y) (hypot y x))
0.1b	(* (- x y) (* (/ 1 (hypot y x)) (/ (+ x y) (hypot y x))))

rewrite187.0ms

Algorithm

rewrite-expression-head

Rules

64×	`add-exp-log`
56×	`add-sqr-sqrt`
55×	`*-un-lft-identity`
49×	`times-frac`
38×	`add-cbrt-cube`
37×	`add-cube-cbrt`
25×	`prod-exp`
19×	`div-exp`
18×	`associate-l`
17×	`associate-r`
13×	`cbrt-unprod`
12×	`pow1`
10×	`cbrt-undiv` `frac-times`
7×	`associate-r/` `distribute-lft-out` `associate-/l`
6×	`associate-l/` `associate-/r` `unswap-sqr`
5×	`rec-exp` `1-exp`
4×	`expm1-log1p-u` `flip3--` `pow-prod-down` `flip--` `log1p-expm1-u` `div-inv` `add-log-exp`
2×	`frac-2neg` `clear-num` `*-commutative` `associate-/l/`
1×	`pow-flip` `flip3-+` `flip-+` `distribute-lft-out--` `inv-pow` `difference-of-squares`

Counts

4 → 172

Calls

4 calls:

9.0ms	(/ 1 (hypot y x))
40.0ms	(* (/ 1 (hypot y x)) (/ (+ x y) (hypot y x)))
21.0ms	(/ (+ x y) (hypot y x))
104.0ms	(* (- x y) (* (/ 1 (hypot y x)) (/ (+ x y) (hypot y x))))

series524.0ms

Counts

4 → 12

Calls

4 calls:

77.0ms	(/ 1 (hypot y x))
134.0ms	(* (/ 1 (hypot y x)) (/ (+ x y) (hypot y x)))
163.0ms	(/ (+ x y) (hypot y x))
149.0ms	(* (- x y) (* (/ 1 (hypot y x)) (/ (+ x y) (hypot y x))))

simplify429.0ms

Counts

184 → 184

Iterations

Useful iterations: done (422.0ms)

Iter	Nodes	Cost
0	209	2894
1	638	2733
done	5001	2227

prune581.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.0b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (hypot y x))
0.0b	(/ (+ x y) (hypot y x))
0.0b	(* (/ (+ x y) (hypot y x)) (/ (- x y) (hypot y x)))
0.3b	(expm1 (* (/ (+ x y) (hypot y x)) (/ (- x y) (hypot y x))))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

68×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
58×	`times-frac`
40×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
16×	`associate-l`
9×	`associate-/l*`
7×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r*`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `expm1-log1p` `flip3--` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+` `expm1-udef`

Counts

4 → 147

Calls

4 calls:

18.0ms	(/ (- x y) (hypot y x))
29.0ms	(/ (+ x y) (hypot y x))
60.0ms	(* (/ (+ x y) (hypot y x)) (/ (- x y) (hypot y x)))
1.0ms	(expm1 (* (/ (+ x y) (hypot y x)) (/ (- x y) (hypot y x))))

series573.0ms

Counts

4 → 12

Calls

4 calls:

140.0ms	(/ (- x y) (hypot y x))
118.0ms	(/ (+ x y) (hypot y x))
130.0ms	(* (/ (+ x y) (hypot y x)) (/ (- x y) (hypot y x)))
186.0ms	(expm1 (* (/ (+ x y) (hypot y x)) (/ (- x y) (hypot y x))))

simplify2.6s

Counts

159 → 159

Iterations

Useful iterations: 2 (487.0ms)

Iter	Nodes	Cost
0	180	2420
1	525	2362
2	3202	2114
done	5002	2114

prune543.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (- x y) (hypot y x))
0.0b	(/ (+ x y) (hypot y x))
0.0b	(* (/ (+ x y) (hypot y x)) (/ (- x y) (hypot y x)))
0.3b	(expm1 (log (exp (* (/ (+ x y) (hypot y x)) (/ (- x y) (hypot y x))))))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

68×	`*-un-lft-identity`
66×	`add-sqr-sqrt`
58×	`times-frac`
40×	`add-cube-cbrt`
20×	`add-exp-log` `add-cbrt-cube`
19×	`associate-r`
16×	`associate-l`
9×	`associate-/l*`
7×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`pow1` `cbrt-undiv` `div-exp` `associate-/r*`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `expm1-log1p` `flip3--` `flip3-+` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--` `flip-+` `expm1-udef`

Counts

4 → 147

Calls

4 calls:

17.0ms	(/ (- x y) (hypot y x))
21.0ms	(/ (+ x y) (hypot y x))
51.0ms	(* (/ (+ x y) (hypot y x)) (/ (- x y) (hypot y x)))
1.0ms	(expm1 (log (exp (* (/ (+ x y) (hypot y x)) (/ (- x y) (hypot y x))))))

series494.0ms

Counts

4 → 12

Calls

4 calls:

128.0ms	(/ (- x y) (hypot y x))
120.0ms	(/ (+ x y) (hypot y x))
118.0ms	(* (/ (+ x y) (hypot y x)) (/ (- x y) (hypot y x)))
127.0ms	(expm1 (log (exp (* (/ (+ x y) (hypot y x)) (/ (- x y) (hypot y x))))))

simplify2.6s

Counts

159 → 159

Iterations

Useful iterations: done (2.6s)

Iter	Nodes	Cost
0	183	2446
1	524	2362
2	3237	2132
done	5000	2114

prune598.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

regimes48.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify3.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	12	19
1	14	19
done	14	19

end0.0ms

sample937.0ms

Algorithm

intervals

Results

512.0ms	8000×	body	80	valid
171.0ms	8000×	pre	80	true