Details

sample15.0ms

Algorithm

intervals

Results

7.0ms

256×

body

valid

simplify22.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	20	9
1	40	9
2	78	9
3	134	9
4	200	9
5	233	9
6	239	9
7	239	9

prune5.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 31.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
3.5b	(- (* x x) (* (* y 4.0) y))
31.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

8.0ms	(+ (* x x) (* (* y 4.0) y))
8.0ms	(- (* x x) (* (* y 4.0) y))
27.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series154.0ms

Counts

3 → 9

Calls

3 calls:

36.0ms	(+ (* x x) (* (* y 4.0) y))
39.0ms	(- (* x x) (* (* y 4.0) y))
79.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify43.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	254	719
1	1175	657
2	5001	641

prune183.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize0.0ms

rewrite0.0ms

Algorithm

rewrite-expression-head

Rules

Counts

0 → 0

series0.0ms

Counts: 0 → 0

simplify3.0ms

Algorithm

egg-herbie

Counts

0 → 0

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	0	0

prune5.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.3b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x x (* (* y 4.0) y))
0.0b	(/ 1 (/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
3.5b	(- (* x x) (* (* y 4.0) y))
31.3b	(/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*` `add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `expm1-log1p-u` `log1p-expm1-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `pow-flip` `fma-neg` `diff-log` `prod-diff` `fma-udef` `inv-pow`

Counts

4 → 143

Calls

4 calls:

0.0ms	(fma x x (* (* y 4.0) y))
20.0ms	(/ 1 (/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
11.0ms	(- (* x x) (* (* y 4.0) y))
13.0ms	(/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(fma x x (* (* y 4.0) y))
66.0ms	(/ 1 (/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
39.0ms	(- (* x x) (* (* y 4.0) y))
67.0ms	(/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

simplify75.0ms

Algorithm

egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	449	2045
1	2179	1867
2	5001	1725

prune292.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.3b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1 (/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
0.5b	(expm1 (/ 1 (/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))))
3.5b	(- (* x x) (* (* y 4.0) y))
31.3b	(/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
56×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
18×	`associate-/r*`
17×	`add-exp-log`
11×	`associate-/r/` `add-cbrt-cube`
8×	`div-exp`
6×	`flip3--` `flip--` `div-inv` `associate-/l*` `add-log-exp`
5×	`pow1` `log1p-expm1-u`
4×	`cbrt-undiv` `expm1-log1p-u`
2×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`sub-neg` `expm1-log1p` `pow-flip` `fma-neg` `diff-log` `prod-diff` `inv-pow` `expm1-udef`

Counts

4 → 144

Calls

4 calls:

20.0ms	(/ 1 (/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
0.0ms	(expm1 (/ 1 (/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))))
8.0ms	(- (* x x) (* (* y 4.0) y))
15.0ms	(/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

series268.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(/ 1 (/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y))))
95.0ms	(expm1 (/ 1 (/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))))
40.0ms	(- (* x x) (* (* y 4.0) y))
67.0ms	(/ (fma x x (* (* y 4.0) y)) (- (* x x) (* (* y 4.0) y)))

simplify78.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	462	2130
1	2211	1937
2	5002	1786

prune377.0ms

Pruning

4 alts after pruning (1 fresh and 3 done)

Merged error: 0.3b

regimes126.0ms

Accuracy

56.1% (13.7b remaining)

Error of 14.1b against oracle of 0.4b and baseline of 31.7b

bsearch207.0ms

Steps

Iters	Range		Point
10	3.0077710628296854e+26	3.687524441071998e+41	4.9502099980031536e+39
10	1.6096776765761708e-79	1.523631617599454e-63	1.366181191701136e-63
6	1.2160611135694172e-190	9.2571818059411e-190	9.050450195175466e-190
9	-3.7102722866200435e-146	-3.1945726965174795e-152	-2.9463808085280802e-149
9	-5.28789737177076e+121	-3.898811697184426e+115	-5.810291952691062e+115

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	24
1	36	24

end0.0ms

sample385.0ms

Algorithm

intervals

Results

217.0ms

8000×

body

valid