Details

sample41.0ms

Algorithm

intervals

Results

15.0ms	256×	body	80	valid
7.0ms	256×	pre	80	true

simplify6.8s

Counts

1 → 1

Iterations

Useful iterations: 1 (5.0ms)

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

prune6.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 23.2b

localize15.0ms

Local error

Found 2 expressions with local error:

0.0b	(+ (* x x) (* y y))
23.3b	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

rewrite52.0ms

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:

10.0ms	(+ (* x x) (* y y))
39.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

series126.0ms

Counts

2 → 6

Calls

2 calls:

39.0ms	(+ (* x x) (* y y))
87.0ms	(/ (* (- x y) (+ x y)) (+ (* x x) (* y y)))

simplify1.0s

Counts

53 → 53

Iterations

Useful iterations: done (1.0s)

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

prune146.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.0b

localize8.0ms

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

rewrite109.0ms

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))
57.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
18.0ms	(/ (- x y) (hypot x y))

series730.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(hypot x y)
100.0ms	(/ (+ x y) (hypot x y))
450.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
132.0ms	(/ (- x y) (hypot x y))

simplify1.5s

Counts

158 → 158

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	172	2247
1	479	2185
2	1642	1971
done	5001	1970

prune556.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0b

localize12.0ms

Local error

Found 4 expressions with local error:

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

rewrite126.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 152

Calls

4 calls:

18.0ms	(/ (+ x y) (hypot x y))
5.0ms	(log (exp (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))))
75.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
21.0ms	(/ (- x y) (hypot x y))

series517.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(/ (+ x y) (hypot x y))
119.0ms	(log (exp (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))))
145.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
114.0ms	(/ (- x y) (hypot x y))

simplify1.5s

Counts

164 → 164

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	185	2550
1	490	2457
2	1661	2203
done	5000	2202

prune525.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0b

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))))
0.0b	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
0.0b	(/ (- x y) (hypot x y))
0.4b	(expm1 (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))))

rewrite100.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 123

Calls

4 calls:

0.0ms	(log1p (expm1 (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))))
63.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
31.0ms	(/ (- x y) (hypot x y))
1.0ms	(expm1 (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))))

series576.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(log1p (expm1 (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))))
129.0ms	(* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y)))
143.0ms	(/ (- x y) (hypot x y))
149.0ms	(expm1 (* (/ (- x y) (hypot x y)) (/ (+ x y) (hypot x y))))

simplify1.3s

Counts

135 → 135

Iterations

Useful iterations: 2 (309.0ms)

Iter	Nodes	Cost
0	170	2214
1	466	2140
2	1591	1898
done	5000	1898

prune503.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0b

regimes40.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify2.0ms

Iterations

Useful iterations: 0 (0.0ms)

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

end0.0ms

sample705.0ms

Algorithm

intervals

Results

300.0ms	8000×	body	80	valid
136.0ms	8000×	pre	80	true