Details

sample41.0ms

Algorithm

intervals

Results

21.0ms	281×	body	80	valid
5.0ms	63×	body	80	nan

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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: 26.0b

localize11.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* z z) (* t a))
4.3b	(* (* x y) z)
8.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.5b	(sqrt (- (* z z) (* t a)))

rewrite32.0ms

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))
10.0ms	(* (* x y) z)
12.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
5.0ms	(sqrt (- (* z z) (* t a)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
81.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (48.0ms)

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

prune263.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.9b

localize14.0ms

Local error

Found 4 expressions with local error:

3.5b	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
5.3b	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
26.4b	(cbrt (- (* z z) (* t a)))
26.4b	(cbrt (- (* z z) (* t a)))

rewrite77.0ms

Algorithm

rewrite-expression-head

Rules

189×	`times-frac`
147×	`add-sqr-sqrt`
102×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l`
33×	`associate-r`
30×	`add-exp-log` `add-cbrt-cube`
24×	`sqrt-prod`
18×	`cbrt-prod`
13×	`associate-/r*`
12×	`cbrt-undiv` `div-exp` `unswap-sqr`
10×	`div-inv`
6×	`pow1` `cbrt-div` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--` `associate-/l*`
2×	`pow1/3` `sqrt-div`
1×	`frac-times` `frac-2neg` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative`

Counts

4 → 217

Calls

4 calls:

5.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
57.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
2.0ms	(cbrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))

series534.0ms

Counts

4 → 12

Calls

4 calls:

54.0ms	(/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y))
311.0ms	(* (/ x (/ (fabs (cbrt (- (* z z) (* t a)))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
83.0ms	(cbrt (- (* z z) (* t a)))
86.0ms	(cbrt (- (* z z) (* t a)))

simplify59.0ms

Algorithm

egg-herbie

Counts

229 → 229

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1093	3523
1	5001	3265

prune862.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 2.9b

localize15.0ms

Local error

Found 4 expressions with local error:

3.2b	(* x (/ 1 (/ (fabs (cbrt (- (* z z) (* t a)))) y)))
5.3b	(* (* x (/ 1 (/ (fabs (cbrt (- (* z z) (* t a)))) y))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
26.4b	(cbrt (- (* z z) (* t a)))
26.4b	(cbrt (- (* z z) (* t a)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

99×	`times-frac`
87×	`add-exp-log`
77×	`associate-r`
75×	`add-sqr-sqrt`
63×	`*-un-lft-identity`
61×	`add-cube-cbrt`
45×	`add-cbrt-cube`
37×	`prod-exp`
29×	`div-exp`
18×	`sqrt-prod`
17×	`cbrt-unprod`
15×	`cbrt-prod`
13×	`cbrt-undiv`
11×	`pow1`
6×	`rec-exp` `cbrt-div` `1-exp`
5×	`div-inv` `unswap-sqr`
4×	`expm1-log1p-u` `associate-r/` `associate-l*` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `associate-/r/` `un-div-inv` `flip--`
2×	`frac-times` `pow1/3` `sqrt-div` `associate-l/` `-commutative`

Counts

4 → 180

Calls

4 calls:

21.0ms	(* x (/ 1 (/ (fabs (cbrt (- (* z z) (* t a)))) y)))
48.0ms	(* (* x (/ 1 (/ (fabs (cbrt (- (* z z) (* t a)))) y))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
2.0ms	(cbrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))

series539.0ms

Counts

4 → 12

Calls

4 calls:

55.0ms	(* x (/ 1 (/ (fabs (cbrt (- (* z z) (* t a)))) y)))
316.0ms	(* (* x (/ 1 (/ (fabs (cbrt (- (* z z) (* t a)))) y))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
86.0ms	(cbrt (- (* z z) (* t a)))
81.0ms	(cbrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

192 → 192

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1049	2560
1	5001	2173

prune627.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 2.9b

localize19.0ms

Local error

Found 4 expressions with local error:

5.3b	(* (/ x (/ (fabs (* (sqrt (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
26.4b	(cbrt (- (* z z) (* t a)))
26.4b	(cbrt (- (* z z) (* t a)))
26.4b	(cbrt (- (* z z) (* t a)))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

114×	`times-frac`
106×	`add-sqr-sqrt`
61×	`add-cube-cbrt` `*-un-lft-identity`
44×	`associate-l`
33×	`associate-r`
25×	`add-exp-log` `add-cbrt-cube`
24×	`sqrt-prod`
21×	`cbrt-prod`
12×	`unswap-sqr`
9×	`cbrt-undiv` `div-exp`
8×	`cbrt-div`
6×	`pow1` `prod-exp` `cbrt-unprod`
5×	`div-inv`
4×	`expm1-log1p-u` `flip3--` `flip--` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `associate-/r/`
2×	`sqrt-div`
1×	`frac-times` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative`

Counts

4 → 160

Calls

4 calls:

57.0ms	(* (/ x (/ (fabs (* (sqrt (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
3.0ms	(cbrt (- (* z z) (* t a)))
2.0ms	(cbrt (- (* z z) (* t a)))
3.0ms	(cbrt (- (* z z) (* t a)))

series571.0ms

Counts

4 → 12

Calls

4 calls:

315.0ms	(* (/ x (/ (fabs (* (sqrt (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a)))))) y)) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
83.0ms	(cbrt (- (* z z) (* t a)))
85.0ms	(cbrt (- (* z z) (* t a)))
87.0ms	(cbrt (- (* z z) (* t a)))

simplify104.0ms

Algorithm

egg-herbie

Counts

172 → 172

Iterations

Useful iterations: 2 (79.0ms)

Iter	Nodes	Cost
0	940	3559
1	4269	2828
2	5001	2802

prune740.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 2.9b

regimes559.0ms

Accuracy

80.6% (4.2b remaining)

Error of 7.5b against oracle of 3.3b and baseline of 24.8b

bsearch102.0ms

Steps

Iters	Range		Point
8	2.0803801984952915e+82	5.581089211160368e+85	3.9023810506562994e+82
6	-9.287529331322677e+113	-1.109941606813071e+113	-1.1652473300983582e+113

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	31
1	46	31
2	46	31

end0.0ms

sample1.3s

Algorithm

intervals

Results

671.0ms	8863×	body	80	valid
215.0ms	2803×	body	80	nan