Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify36.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	27	8
1	63	8
2	149	8
3	358	8
4	840	8
5	5001	8

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 14.0b

localize14.0ms

Local error

Found 2 expressions with local error:

1.4b	(- (* (* z 2.0) z) (* y t))
21.0b	(/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

2 → 43

Calls

2 calls:

7.0ms	(- (* (* z 2.0) z) (* y t))
17.0ms	(/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))

series226.0ms

Counts

2 → 6

Calls

2 calls:

40.0ms	(- (* (* z 2.0) z) (* y t))
186.0ms	(/ (* (* y 2.0) z) (- (* (* z 2.0) z) (* y t)))

simplify44.0ms

Algorithm

egg-herbie

Counts

49 → 49

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	281	415
1	1422	344
2	5002	344

prune132.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize15.0ms

Local error

Found 4 expressions with local error:

5.7b	(/ (* y 2.0) (* (cbrt (- (* (* z 2.0) z) (* y t))) (cbrt (- (* (* z 2.0) z) (* y t)))))
23.6b	(cbrt (- (* (* z 2.0) z) (* y t)))
23.6b	(cbrt (- (* (* z 2.0) z) (* y t)))
23.6b	(cbrt (- (* (* z 2.0) z) (* y t)))

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

23.0ms	(/ (* y 2.0) (* (cbrt (- (* (* z 2.0) z) (* y t))) (cbrt (- (* (* z 2.0) z) (* y t)))))
6.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))
6.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))
10.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))

series625.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(/ (* y 2.0) (* (cbrt (- (* (* z 2.0) z) (* y t))) (cbrt (- (* (* z 2.0) z) (* y t)))))
125.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))
131.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))
126.0ms	(cbrt (- (* (* z 2.0) z) (* y t)))

simplify51.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	448	1102
1	1520	984
2	5002	964

prune361.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 5.4b

localize10.0ms

Local error

Found 3 expressions with local error:

1.4b	(- (* (* z 2.0) z) (* y t))
4.4b	(/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z))
17.2b	(/ (- (* (* z 2.0) z) (* y t)) z)

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 96

Calls

3 calls:

10.0ms	(- (* (* z 2.0) z) (* y t))
14.0ms	(/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z))
18.0ms	(/ (- (* (* z 2.0) z) (* y t)) z)

series289.0ms

Counts

3 → 9

Calls

3 calls:

43.0ms	(- (* (* z 2.0) z) (* y t))
193.0ms	(/ (* y 2.0) (/ (- (* (* z 2.0) z) (* y t)) z))
52.0ms	(/ (- (* (* z 2.0) z) (* y t)) z)

simplify63.0ms

Algorithm

egg-herbie

Counts

105 → 105

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	438	968
1	2164	856
2	5002	849

prune281.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 2.8b

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* 2.0 z) (/ (* t y) z))
4.4b	(/ y (/ (- (* 2.0 z) (/ (* t y) z)) 2.0))
5.9b	(/ (* t y) z)

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 117

Calls

3 calls:

5.0ms	(- (* 2.0 z) (/ (* t y) z))
9.0ms	(/ y (/ (- (* 2.0 z) (/ (* t y) z)) 2.0))
3.0ms	(/ (* t y) z)

series244.0ms

Counts

3 → 9

Calls

3 calls:

45.0ms	(- (* 2.0 z) (/ (* t y) z))
180.0ms	(/ y (/ (- (* 2.0 z) (/ (* t y) z)) 2.0))
19.0ms	(/ (* t y) z)

simplify77.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	595	1235
1	2754	1123
2	5002	1123

prune353.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 1.2b

regimes105.0ms

Accuracy

22.2% (1.4b remaining)

Error of 1.9b against oracle of 0.5b and baseline of 2.3b

bsearch100.0ms

Steps

Iters	Range		Point
8	1.1383016666528867e-247	2.6764326084756853e-244	2.572601767425259e-247
8	-1.1538838554921166e-125	-9.294658666337375e-130	-2.17270890305481e-126

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	30
1	37	30

end0.0ms

sample523.0ms

Algorithm

intervals

Results

308.0ms

8000×

body

valid