Details

sample41.0ms

Algorithm

intervals

Results

19.0ms	287×	body	80	valid
6.0ms	95×	body	80	nan

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	7
1	46	7
2	72	7
3	99	7
4	120	7
5	120	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.0b

localize12.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
6.2b	(* (* x y) z)
8.2b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.1b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
7.0ms	(* (* x y) z)
11.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
5.0ms	(sqrt (- (* z z) (* t a)))

series206.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
24.0ms	(* (* x y) z)
85.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	368	630
1	1941	560
2	5001	551

prune264.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
0.8b	(- (* z z) (* t a))
3.1b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.1b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 142

Calls

4 calls:

7.0ms	(/ (sqrt (- (* z z) (* t a))) z)
3.0ms	(- (* z z) (* t a))
10.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
4.0ms	(sqrt (- (* z z) (* t a)))

series242.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(/ (sqrt (- (* z z) (* t a))) z)
35.0ms	(- (* z z) (* t a))
81.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify66.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	543	1379
1	2448	1281
2	5001	1260

prune392.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 3.3b

localize19.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
24.1b	(sqrt (- (* z z) (* t a)))
24.1b	(sqrt (- (* z z) (* t a)))
24.1b	(sqrt (- (* z z) (* t a)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div` `add-log-exp`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`sub-neg` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 67

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))
5.0ms	(sqrt (- (* z z) (* t a)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
58.0ms	(sqrt (- (* z z) (* t a)))
61.0ms	(sqrt (- (* z z) (* t a)))
64.0ms	(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (46.0ms)

Iter	Nodes	Cost
0	160	467
1	530	446
2	1714	437
3	5002	431

prune339.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
1.5b	(/ y (/ (sqrt (- (* z z) (* t a))) z))
2.0b	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
24.1b	(sqrt (- (* z z) (* t a)))

rewrite64.0ms

Algorithm

rewrite-expression-head

Rules

263×	`times-frac`
157×	`add-sqr-sqrt`
143×	`add-cube-cbrt` `*-un-lft-identity`
71×	`associate-r`
67×	`sqrt-prod`
22×	`associate-/r*`
18×	`add-exp-log` `add-cbrt-cube`
9×	`div-inv`
7×	`pow1`
6×	`cbrt-undiv` `div-exp` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `unswap-sqr`
3×	`associate-l` `prod-exp` `cbrt-unprod` `associate-/l*`
2×	`flip3--` `sqrt-div` `associate-/r/` `flip--`
1×	`sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-r/` `prod-diff` `pow-prod-down` `clear-num` `-commutative`

Counts

4 → 237

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
9.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
35.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
4.0ms	(sqrt (- (* z z) (* t a)))

series263.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* z z) (* t a))
77.0ms	(/ y (/ (sqrt (- (* z z) (* t a))) z))
81.0ms	(* x (/ y (/ (sqrt (- (* z z) (* t a))) z)))
62.0ms	(sqrt (- (* z z) (* t a)))

simplify97.0ms

Algorithm

egg-herbie

Counts

249 → 249

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	839	2556
1	4071	2400
2	5002	2396

prune617.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 3.3b

regimes351.0ms

Accuracy

82% (3.4b remaining)

Error of 6.6b against oracle of 3.2b and baseline of 22.2b

bsearch123.0ms

Steps

Iters	Range		Point
10	2.339439842960722e-20	2.380532195432991e-09	2.3472884937339154e-09
9	-2.848647277932525e+111	-5.3377324555457014e+104	-2.7962215868489545e+111

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	28
1	35	28
2	38	28
3	38	28

end0.0ms

sample1.2s

Algorithm

intervals

Results

608.0ms	8879×	body	80	valid
177.0ms	2916×	body	80	nan