Details

sample45.0ms

Algorithm

intervals

Results

22.0ms	256×	body	80	valid
9.0ms	256×	pre	80	true

simplify3.0s

Counts

1 → 1

Iterations

Iter	Nodes
8	2884
7	1046
6	573
5	339
4	177
3	95
2	46
1	22
0	9

prune11.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 19.3b

localize36.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* x x) (* y y))
0.0b	(- (/ (* x x) (+ (* x x) (* y y))) (/ (* y y) (+ (* x x) (* y y))))
17.5b	(/ (* x x) (+ (* x x) (* y y)))
24.3b	(/ (* y y) (+ (* x x) (* y y)))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
14×	`add-cbrt-cube` `add-exp-log`
10×	`*-un-lft-identity` `times-frac`
8×	`associate-/r/` `add-cube-cbrt` `add-log-exp`
6×	`associate-/r*`
5×	`flip3-+` `flip-+`
4×	`pow1` `cbrt-undiv` `div-exp` `div-inv` `difference-of-squares`
3×	`distribute-rgt-out--`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `associate-/l*`
1×	`+-commutative` `sum-log` `sub-neg` `flip3--` `diff-log` `frac-sub` `flip--` `distribute-lft-out--` `sub-div`

Counts

4 → 79

Calls

4 calls:

14.0ms	(+ (* x x) (* y y))
64.0ms	(- (/ (* x x) (+ (* x x) (* y y))) (/ (* y y) (+ (* x x) (* y y))))
30.0ms	(/ (* x x) (+ (* x x) (* y y)))
27.0ms	(/ (* y y) (+ (* x x) (* y y)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(+ (* x x) (* y y))
98.0ms	(- (/ (* x x) (+ (* x x) (* y y))) (/ (* y y) (+ (* x x) (* y y))))
66.0ms	(/ (* x x) (+ (* x x) (* y y)))
63.0ms	(/ (* y y) (+ (* x x) (* y y)))

simplify1.3s

Counts

91 → 91

Iterations

Iter	Nodes
3	3721
2	1133
1	372
0	128

prune771.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.8b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (/ (* x x) (+ (* x x) (* y y))) (log (exp (/ (* y y) (+ (* x x) (* y y))))))
2.6b	(log (exp (/ (* y y) (+ (* x x) (* y y)))))
17.5b	(/ (* x x) (+ (* x x) (* y y)))
24.3b	(/ (* y y) (+ (* x x) (* y y)))

rewrite181.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
14×	`add-cbrt-cube` `add-exp-log`
12×	`add-cube-cbrt`
11×	`log-pow`
10×	`times-frac`
9×	`exp-prod`
6×	`pow1` `log-prod` `associate-/r*` `associate-/r/`
5×	`add-log-exp`
4×	`cbrt-undiv` `div-exp`
3×	`flip3-+` `flip-+` `div-inv` `associate--r+`
2×	`clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `associate-/l*` `distribute-lft-out--` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `rem-log-exp` `flip--`

Counts

4 → 86

Calls

4 calls:

120.0ms	(- (/ (* x x) (+ (* x x) (* y y))) (log (exp (/ (* y y) (+ (* x x) (* y y))))))
33.0ms	(log (exp (/ (* y y) (+ (* x x) (* y y)))))
14.0ms	(/ (* x x) (+ (* x x) (* y y)))
13.0ms	(/ (* y y) (+ (* x x) (* y y)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(- (/ (* x x) (+ (* x x) (* y y))) (log (exp (/ (* y y) (+ (* x x) (* y y))))))
81.0ms	(log (exp (/ (* y y) (+ (* x x) (* y y)))))
65.0ms	(/ (* x x) (+ (* x x) (* y y)))
58.0ms	(/ (* y y) (+ (* x x) (* y y)))

simplify1.4s

Counts

98 → 98

Iterations

Iter	Nodes
3	3121
2	972
1	335
0	143

prune899.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.8b

localize64.0ms

Local error

Found 4 expressions with local error:

17.5b	(/ (* x x) (+ (* x x) (* y y)))
24.3b	(/ (* y y) (+ (* x x) (* y y)))
24.3b	(/ (* y y) (+ (* x x) (* y y)))
24.3b	(/ (* y y) (+ (* x x) (* y y)))

rewrite82.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-cbrt-cube` `add-exp-log`
12×	`add-sqr-sqrt` `associate-/r` `-un-lft-identity` `times-frac` `add-cube-cbrt`
8×	`cbrt-undiv` `div-exp` `associate-/r/`
4×	`pow1` `clear-num` `frac-2neg` `flip3-+` `prod-exp` `cbrt-unprod` `flip-+` `div-inv` `associate-/l*` `add-log-exp`

Counts

4 → 92

Calls

4 calls:

15.0ms	(/ (* x x) (+ (* x x) (* y y)))
17.0ms	(/ (* y y) (+ (* x x) (* y y)))
23.0ms	(/ (* y y) (+ (* x x) (* y y)))
25.0ms	(/ (* y y) (+ (* x x) (* y y)))

series325.0ms

Counts

4 → 12

Calls

4 calls:

84.0ms	(/ (* x x) (+ (* x x) (* y y)))
86.0ms	(/ (* y y) (+ (* x x) (* y y)))
76.0ms	(/ (* y y) (+ (* x x) (* y y)))
78.0ms	(/ (* y y) (+ (* x x) (* y y)))

simplify957.0ms

Counts

104 → 104

Iterations

Iter	Nodes
3	2422
2	754
1	230
0	84

prune944.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 0.8b

localize31.0ms

Local error

Found 4 expressions with local error:

2.6b	(log (exp (/ (* y y) (+ (* x x) (* y y)))))
17.5b	(/ (* x x) (+ (* x x) (* y y)))
24.3b	(/ (* y y) (+ (* x x) (* y y)))
24.3b	(/ (* y y) (+ (* x x) (* y y)))

rewrite116.0ms

Algorithm

rewrite-expression-head

Rules

19×	`add-cbrt-cube` `add-exp-log`
13×	`add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt`
12×	`times-frac`
10×	`log-pow`
9×	`exp-prod` `associate-/r*`
8×	`associate-/r/`
6×	`cbrt-undiv` `div-exp`
5×	`pow1`
4×	`flip3-+` `flip-+` `div-inv` `add-log-exp`
3×	`log-prod` `clear-num` `frac-2neg` `prod-exp` `cbrt-unprod` `associate-/l*`
1×	`rem-log-exp`

Counts

4 → 90

Calls

4 calls:

32.0ms	(log (exp (/ (* y y) (+ (* x x) (* y y)))))
26.0ms	(/ (* x x) (+ (* x x) (* y y)))
27.0ms	(/ (* y y) (+ (* x x) (* y y)))
29.0ms	(/ (* y y) (+ (* x x) (* y y)))

series297.0ms

Counts

4 → 12

Calls

4 calls:

58.0ms	(log (exp (/ (* y y) (+ (* x x) (* y y)))))
72.0ms	(/ (* x x) (+ (* x x) (* y y)))
82.0ms	(/ (* y y) (+ (* x x) (* y y)))
85.0ms	(/ (* y y) (+ (* x x) (* y y)))

simplify926.0ms

Counts

102 → 102

Iterations

Iter	Nodes
3	2511
2	813
1	277
0	117

prune1.5s

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 0.8b

regimes147.0ms

Accuracy

77.6% (4.3b remaining)

Error of 4.7b against oracle of 0.5b and baseline of 19.5b

bsearch180.0ms

Steps

Iters	Range		Point
8	5.084351179865213e-170	3.116980067791689e-166	3.050134070228654e-166
8	-1.9931419727158644e-179	-1.42601952914834e-182	-1.9618167972718326e-179
7	-3.024207974548735e-165	-2.99545875242898e-167	-4.0918058340644614e-167
9	-2.1186688695348193e+154	-5.841327702345065e+146	-1.3622257246714918e+154

simplify28.0ms

Iterations

Iter	Nodes
2	30
1	30
0	28

end0.0ms

sample1.5s

Algorithm

intervals

Results

942.0ms	8000×	body	80	valid
356.0ms	8000×	pre	80	true