Details

sample16.0ms

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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 33.6b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
5.1b	(- (* x x) (* (* y 4.0) y))
33.1b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite50.0ms

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:

12.0ms	(+ (* x x) (* (* y 4.0) y))
9.0ms	(- (* x x) (* (* y 4.0) y))
28.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series150.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(+ (* x x) (* (* y 4.0) y))
46.0ms	(- (* x x) (* (* y 4.0) y))
64.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify44.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (36.0ms)

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

prune192.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 0.4b

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

prune11.0ms

Pruning

6 alts after pruning (5 fresh and 1 done)

Merged error: 0.4b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
0.4b	(expm1 (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
5.1b	(- (* x x) (* (* y 4.0) y))
33.1b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite40.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
0.0ms	(expm1 (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
10.0ms	(- (* x x) (* (* y 4.0) y))
28.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

118.0ms	(log1p (expm1 (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))))
98.0ms	(expm1 (/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y))))
45.0ms	(- (* x x) (* (* y 4.0) y))
69.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify46.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	267	889
1	1159	798
2	5001	787

prune240.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(log1p (expm1 (/ (fma x x (- (* (* y 4.0) y))) (+ (* x x) (* (* y 4.0) y)))))
0.4b	(expm1 (/ (fma x x (- (* (* y 4.0) y))) (+ (* x x) (* (* y 4.0) y))))
2.3b	(fma x x (- (* (* y 4.0) y)))
33.1b	(/ (fma x x (- (* (* y 4.0) y))) (+ (* x x) (* (* y 4.0) y)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

12×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
9×	`times-frac`
6×	`add-exp-log` `add-cbrt-cube`
5×	`log1p-expm1-u`
4×	`pow1` `expm1-log1p-u` `add-log-exp`
3×	`associate-/r` `associate-/l`
2×	`associate-/r/`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `frac-2neg` `flip3-+` `log1p-expm1` `div-exp` `clear-num` `flip-+` `fma-udef` `div-inv` `expm1-udef`

Counts

4 → 63

Calls

4 calls:

0.0ms	(log1p (expm1 (/ (fma x x (- (* (* y 4.0) y))) (+ (* x x) (* (* y 4.0) y)))))
0.0ms	(expm1 (/ (fma x x (- (* (* y 4.0) y))) (+ (* x x) (* (* y 4.0) y))))
0.0ms	(fma x x (- (* (* y 4.0) y)))
15.0ms	(/ (fma x x (- (* (* y 4.0) y))) (+ (* x x) (* (* y 4.0) y)))

series356.0ms

Counts

4 → 12

Calls

4 calls:

125.0ms	(log1p (expm1 (/ (fma x x (- (* (* y 4.0) y))) (+ (* x x) (* (* y 4.0) y)))))
103.0ms	(expm1 (/ (fma x x (- (* (* y 4.0) y))) (+ (* x x) (* (* y 4.0) y))))
56.0ms	(fma x x (- (* (* y 4.0) y)))
72.0ms	(/ (fma x x (- (* (* y 4.0) y))) (+ (* x x) (* (* y 4.0) y)))

simplify101.0ms

Algorithm

egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 3 (92.0ms)

Iter	Nodes	Cost
0	202	804
1	690	721
2	3077	719
3	5001	718

prune215.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.4b

regimes186.0ms

Accuracy

57.4% (13.3b remaining)

Error of 13.6b against oracle of 0.3b and baseline of 31.5b

bsearch65.0ms

Steps

Iters	Range		Point
8	2.119475714373064e+145	1.347487559726603e+150	3.3035750639902758e+146
7	1.767858896017963e+23	3.3826691965461095e+25	3.466117516972679e+23
6	2.3084783150670496e-30	2.3342772887013993e-29	6.796343694084571e-30
0	1.353739869605e-321	6.9752187879867e-320	3.5552963874736e-320

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	41	32
1	48	32
2	48	32

end0.0ms

sample396.0ms

Algorithm

intervals

Results

221.0ms

8000×

body

valid