Details

sample38.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
6.0ms	256×	pre	80	true

simplify7.3s

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

Iter	Nodes	Cost
0	9	15
1	23	14
2	52	14
3	113	14
4	229	14
5	461	14
6	822	14
7	1308	14
8	3296	14
done	5000	14

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.6b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
21.7b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite60.0ms

Algorithm

rewrite-expression-head

Rules

8×	`associate-/l/`
7×	`add-exp-log` `add-cbrt-cube`
5×	`flip3-+` `flip-+`
4×	`add-sqr-sqrt` `frac-times` `add-cube-cbrt` `*-un-lft-identity` `add-log-exp`
3×	`flip3--` `times-frac` `associate-/r*` `flip--`
2×	`pow1` `cbrt-undiv` `expm1-log1p-u` `associate-r/` `div-exp` `associate-l/` `associate-/r/` `log1p-expm1-u`
1×	`+-commutative` `fma-def` `frac-2neg` `prod-exp` `clear-num` `sum-log` `cbrt-unprod` `div-inv` `associate-/l*`

Counts

2 → 47

Calls

2 calls:

9.0ms	(+ (* x x) (* y y))
49.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series127.0ms

Counts

2 → 6

Calls

2 calls:

58.0ms	(+ (* x x) (* y y))
69.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.2s

Counts

53 → 53

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	95	874
1	317	764
2	1517	635
done	5000	627

prune211.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.0b

localize11.0ms

Local error

Found 4 expressions with local error:

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

rewrite147.0ms

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

Counts

4 → 146

Calls

4 calls:

0.0ms	(hypot x y)
25.0ms	(/ (+ x y) (hypot x y))
36.0ms	(/ (- x y) (hypot x y))
79.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

series500.0ms

Counts

4 → 12

Calls

4 calls:

60.0ms	(hypot x y)
165.0ms	(/ (+ x y) (hypot x y))
160.0ms	(/ (- x y) (hypot x y))
114.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

simplify1.6s

Counts

158 → 158

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	172	2247
1	478	2185
2	1652	1971
done	5000	1970

prune525.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize35.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ (+ x y) (hypot x y))
0.0b	(/ (- x y) (hypot x y))
0.0b	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
0.0b	(pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3)

rewrite178.0ms

Algorithm

rewrite-expression-head

Rules

69×	`*-un-lft-identity`
67×	`add-sqr-sqrt`
58×	`times-frac`
41×	`add-cube-cbrt`
33×	`add-exp-log` `add-cbrt-cube`
19×	`associate-l`
16×	`associate-r`
10×	`cbrt-undiv` `div-exp`
9×	`pow1` `associate-/l*`
8×	`prod-exp` `cbrt-unprod`
7×	`distribute-lft-out` `distribute-lft-out--` `difference-of-squares`
6×	`associate-/r*`
5×	`pow-exp` `rem-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `associate-/l/` `add-log-exp` `unswap-sqr`
3×	`cube-div` `pow-unpow`
2×	`frac-times` `pow-pow` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num`
1×	`cube-mult` `pow-to-exp` `unpow-prod-down` `flip3--` `flip3-+` `unpow3` `div-sub` `cube-prod` `*-commutative` `flip--` `flip-+` `sqr-pow`

Counts

4 → 169

Calls

4 calls:

30.0ms	(/ (+ x y) (hypot x y))
36.0ms	(/ (- x y) (hypot x y))
75.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
28.0ms	(pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3)

series586.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(/ (+ x y) (hypot x y))
135.0ms	(/ (- x y) (hypot x y))
170.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
159.0ms	(pow (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))) 3)

simplify1.7s

Counts

181 → 181

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	200	2774
1	561	2517
2	2096	2399
done	5001	2362

prune741.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

localize19.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (- x y) (hypot x y))))
0.0b	(* (log1p (expm1 (/ (- x y) (hypot x y)))) (/ (+ x y) (hypot x y)))
0.0b	(pow (* (log1p (expm1 (/ (- x y) (hypot x y)))) (/ (+ x y) (hypot x y))) 3)
0.8b	(expm1 (/ (- x y) (hypot x y)))

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

20×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
16×	`associate-r`
15×	`add-exp-log` `add-cbrt-cube`
14×	`add-cube-cbrt`
13×	`times-frac`
9×	`pow1`
5×	`log1p-expm1-u`
4×	`expm1-log1p-u` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`pow-unpow` `associate-l` `pow-exp` `distribute-lft-out` `rem-cube-cbrt`
2×	`cbrt-undiv` `pow-pow` `associate-*r/` `div-exp` `pow-prod-down` `unswap-sqr`
1×	`cube-div` `cube-mult` `pow-to-exp` `unpow-prod-down` `log1p-udef` `expm1-log1p` `unpow3` `cube-prod` `log1p-expm1` `*-commutative` `div-inv` `expm1-udef` `sqr-pow`

Counts

4 → 86

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (- x y) (hypot x y))))
29.0ms	(* (log1p (expm1 (/ (- x y) (hypot x y)))) (/ (+ x y) (hypot x y)))
20.0ms	(pow (* (log1p (expm1 (/ (- x y) (hypot x y)))) (/ (+ x y) (hypot x y))) 3)
1.0ms	(expm1 (/ (- x y) (hypot x y)))

series941.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(log1p (expm1 (/ (- x y) (hypot x y))))
281.0ms	(* (log1p (expm1 (/ (- x y) (hypot x y)))) (/ (+ x y) (hypot x y)))
264.0ms	(pow (* (log1p (expm1 (/ (- x y) (hypot x y)))) (/ (+ x y) (hypot x y))) 3)
172.0ms	(expm1 (/ (- x y) (hypot x y)))

simplify1.2s

Counts

98 → 98

Iterations

Useful iterations: 2 (233.0ms)

Iter	Nodes	Cost
0	122	1653
1	280	1318
2	1172	1234
done	5000	1234

prune383.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

regimes58.0ms

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	13	20
1	15	20
done	15	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

481.0ms	8000×	pre	80	true
417.0ms	8000×	body	80	valid