Details

sample31.0ms

Algorithm

intervals

Results

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

simplify4.4s

Counts

1 → 1

Iterations

Useful iterations: 1 (2.0ms)

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

prune12.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 17.3b

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
17.4b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite46.0ms

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:

8.0ms	(+ (* x x) (* y y))
37.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series107.0ms

Counts

2 → 6

Calls

2 calls:

36.0ms	(+ (* x x) (* y y))
71.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify2.4s

Counts

53 → 53

Iterations

Useful iterations: done (2.4s)

Iter	Nodes	Cost
0	95	874
1	352	767
2	2743	639
done	5000	635

prune262.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.0b

localize10.0ms

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)))

rewrite123.0ms

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:

1.0ms	(hypot x y)
37.0ms	(/ (+ x y) (hypot x y))
19.0ms	(/ (- x y) (hypot x y))
55.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

series447.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(hypot x y)
128.0ms	(/ (+ x y) (hypot x y))
119.0ms	(/ (- x y) (hypot x y))
135.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))

simplify2.2s

Counts

158 → 158

Iterations

Useful iterations: done (2.2s)

Iter	Nodes	Cost
0	172	2247
1	508	2185
2	2840	1981
done	5002	1971

prune485.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0b

localize24.0ms

Local error

Found 4 expressions with local error:

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

rewrite229.0ms

Algorithm

rewrite-expression-head

Rules

161×	`add-sqr-sqrt`
130×	`*-un-lft-identity`
128×	`times-frac`
100×	`cbrt-prod`
80×	`add-cube-cbrt`
61×	`unpow-prod-down` `cube-prod`
47×	`associate-l`
22×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-r`
14×	`add-exp-log` `unswap-sqr`
12×	`add-cbrt-cube`
8×	`div-inv`
7×	`pow1`
5×	`associate-/l*` `sqr-pow`
4×	`cube-div` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `cube-mult` `pow-unpow` `cbrt-div` `unpow3` `div-exp` `associate-/r*` `distribute-lft-out`
2×	`pow-exp` `prod-exp` `cbrt-unprod` `associate-/l/` `rem-cube-cbrt`
1×	`frac-times` `pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip--` `rem-cbrt-cube`

Counts

4 → 251

Calls

4 calls:

29.0ms	(/ (- x y) (hypot x y))
135.0ms	(* (cbrt (pow (/ (- x y) (hypot x y)) 3)) (/ (+ x y) (hypot x y)))
21.0ms	(cbrt (pow (/ (- x y) (hypot x y)) 3))
23.0ms	(pow (/ (- x y) (hypot x y)) 3)

series466.0ms

Counts

4 → 12

Calls

4 calls:

112.0ms	(/ (- x y) (hypot x y))
125.0ms	(* (cbrt (pow (/ (- x y) (hypot x y)) 3)) (/ (+ x y) (hypot x y)))
95.0ms	(cbrt (pow (/ (- x y) (hypot x y)) 3))
134.0ms	(pow (/ (- x y) (hypot x y)) 3)

simplify421.0ms

Counts

263 → 263

Iterations

Useful iterations: done (412.0ms)

Iter	Nodes	Cost
0	250	4961
1	849	4205
done	5001	3966

prune683.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0b

localize28.0ms

Local error

Found 4 expressions with local error:

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

rewrite397.0ms

Algorithm

rewrite-expression-head

Rules

151×	`add-sqr-sqrt`
140×	`log-pow`
134×	`*-un-lft-identity`
133×	`exp-prod`
122×	`times-frac`
112×	`cbrt-prod`
86×	`add-cube-cbrt`
71×	`unpow-prod-down` `cube-prod`
55×	`associate-l`
21×	`distribute-lft-out--` `difference-of-squares`
16×	`associate-r`
14×	`pow1`
10×	`add-exp-log` `unswap-sqr`
8×	`add-cbrt-cube` `div-inv`
5×	`sqr-pow`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cube-mult` `pow-unpow` `log-prod` `unpow3` `distribute-lft-out`
2×	`prod-exp` `cbrt-unprod`
1×	`cbrt-undiv` `pow-to-exp` `log-div` `pow-pow` `exp-diff` `pow1/3` `div-sub` `associate-r/` `div-exp` `rem-log-exp` `pow-prod-down` `pow-exp` `-commutative` `rem-cbrt-cube` `rem-cube-cbrt`

Counts

4 → 259

Calls

4 calls:

25.0ms	(log (exp (/ (- x y) (hypot x y))))
258.0ms	(* (cbrt (pow (log (exp (/ (- x y) (hypot x y)))) 3)) (/ (+ x y) (hypot x y)))
47.0ms	(cbrt (pow (log (exp (/ (- x y) (hypot x y)))) 3))
51.0ms	(pow (log (exp (/ (- x y) (hypot x y)))) 3)

series546.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(log (exp (/ (- x y) (hypot x y))))
141.0ms	(* (cbrt (pow (log (exp (/ (- x y) (hypot x y)))) 3)) (/ (+ x y) (hypot x y)))
132.0ms	(cbrt (pow (log (exp (/ (- x y) (hypot x y)))) 3))
150.0ms	(pow (log (exp (/ (- x y) (hypot x y)))) 3)

simplify3.6s

Counts

271 → 271

Iterations

Useful iterations: 2 (934.0ms)

Iter	Nodes	Cost
0	288	5641
1	874	4235
2	4844	3886
done	5000	3886

prune679.0ms

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0b

regimes57.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	15	20
done	15	20

end0.0ms

sample1.4s

Algorithm

intervals

Results

582.0ms	8000×	body	80	valid
520.0ms	8000×	pre	80	true