Details

sample16.0ms

Algorithm

intervals

Results

8.0ms

256×

body

valid

simplify21.0ms

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: 28.9b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ (* x x) (* (* y 4.0) y))
2.9b	(- (* x x) (* (* y 4.0) y))
28.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite17.0ms

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:

3.0ms	(+ (* x x) (* (* y 4.0) y))
3.0ms	(- (* x x) (* (* y 4.0) y))
10.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series146.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(+ (* x x) (* (* y 4.0) y))
42.0ms	(- (* x x) (* (* y 4.0) y))
65.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify46.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (37.0ms)

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

prune194.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(pow (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))) 3)
0.0b	(cbrt (pow (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))) 3))
2.9b	(- (* x x) (* (* y 4.0) y))
28.3b	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

45×	`times-frac`
42×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
32×	`cbrt-prod`
26×	`unpow-prod-down` `cube-prod`
9×	`add-exp-log` `add-cbrt-cube`
6×	`add-log-exp`
5×	`pow1` `div-inv`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`pow-unpow` `associate-/r` `associate-/l`
2×	`cbrt-undiv` `cube-div` `cube-mult` `flip3--` `unpow3` `div-exp` `pow-exp` `flip--` `associate-/l/` `rem-cube-cbrt` `sqr-pow`
1×	`pow-to-exp` `sub-neg` `cbrt-div` `pow-pow` `frac-2neg` `fma-neg` `pow1/3` `diff-log` `div-sub` `prod-diff` `clear-num` `rem-cbrt-cube`

Counts

4 → 140

Calls

4 calls:

6.0ms	(pow (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))) 3)
7.0ms	(cbrt (pow (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))) 3))
3.0ms	(- (* x x) (* (* y 4.0) y))
8.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

series265.0ms

Counts

4 → 12

Calls

4 calls:

80.0ms	(pow (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))) 3)
69.0ms	(cbrt (pow (/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y))) 3))
46.0ms	(- (* x x) (* (* y 4.0) y))
69.0ms	(/ (- (* x x) (* (* y 4.0) y)) (fma x x (* (* y 4.0) y)))

simplify79.0ms

Algorithm

egg-herbie

Counts

152 → 152

Iterations

Useful iterations: 2 (57.0ms)

Iter	Nodes	Cost
0	453	1951
1	2271	1831
2	5002	1815

prune343.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.2b

localize13.0ms

Local error

Found 4 expressions with local error:

2.9b	(- (* x x) (* (* y 4.0) y))
28.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
28.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
28.3b	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

rewrite41.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 118

Calls

4 calls:

3.0ms	(- (* x x) (* (* y 4.0) y))
14.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
10.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
11.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

series234.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* x x) (* (* y 4.0) y))
65.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
65.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))
61.0ms	(/ (- (* x x) (* (* y 4.0) y)) (+ (* x x) (* (* y 4.0) y)))

simplify51.0ms

Algorithm

egg-herbie

Counts

130 → 130

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	237	1605
1	1114	1473
2	5002	1451

prune474.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.2b

localize16.0ms

Local error

Found 4 expressions with local error:

27.9b	(cbrt (fma x x (* (* y 4.0) y)))
27.9b	(cbrt (fma x x (* (* y 4.0) y)))
27.9b	(cbrt (fma x x (* (* y 4.0) y)))
27.9b	(/ (- (* x x) (* (* y 4.0) y)) (* (cbrt (fma x x (* (* y 4.0) y))) (cbrt (fma x x (* (* y 4.0) y)))))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 65

Calls

4 calls:

0.0ms	(cbrt (fma x x (* (* y 4.0) y)))
0.0ms	(cbrt (fma x x (* (* y 4.0) y)))
0.0ms	(cbrt (fma x x (* (* y 4.0) y)))
10.0ms	(/ (- (* x x) (* (* y 4.0) y)) (* (cbrt (fma x x (* (* y 4.0) y))) (cbrt (fma x x (* (* y 4.0) y)))))

series580.0ms

Counts

4 → 12

Calls

4 calls:

122.0ms	(cbrt (fma x x (* (* y 4.0) y)))
118.0ms	(cbrt (fma x x (* (* y 4.0) y)))
123.0ms	(cbrt (fma x x (* (* y 4.0) y)))
216.0ms	(/ (- (* x x) (* (* y 4.0) y)) (* (cbrt (fma x x (* (* y 4.0) y))) (cbrt (fma x x (* (* y 4.0) y)))))

simplify103.0ms

Algorithm

egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 3 (94.0ms)

Iter	Nodes	Cost
0	293	841
1	992	743
2	3940	726
3	5001	709

prune314.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.2b

regimes223.0ms

Accuracy

58.6% (13.0b remaining)

Error of 13.4b against oracle of 0.4b and baseline of 31.8b

bsearch192.0ms

Steps

Iters	Range		Point
10	2.7192299414326856e+45	1.7413792139761589e+59	2.0459804393047752e+46
8	1.085653884907432e-19	1.091098110926274e-15	1.0681527009565245e-15
9	2.7896520524483803e-176	1.9938584051409808e-169	1.9644387956096076e-169
11	-9.977133551234359e-98	-7.915908561553019e-120	-8.011433477517387e-117
5	-2.408561575053933e+131	-6.201413291767227e+130	-1.4667592323261061e+131

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	66
1	38	66

end0.0ms

sample382.0ms

Algorithm

intervals

Results

244.0ms

8000×

body

valid