Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	280×	body	80	valid
4.0ms	97×	body	80	nan

simplify11.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	7
1	45	7
2	67	7
3	94	7
4	115	7
5	115	7

prune3.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 23.8b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
4.2b	(* (* x y) z)
8.1b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
22.2b	(sqrt (- (* z z) (* t a)))

rewrite25.0ms

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×	`sqrt-div`
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` `diff-log` `associate-l` `clear-num` `-commutative` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
10.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series204.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* z z) (* t a))
27.0ms	(* (* x y) z)
81.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
63.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

88 → 88

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	346	584
1	1863	515
2	5002	510

prune235.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 2.3b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.6b	(- (* z z) (* t a))
2.9b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
22.2b	(sqrt (- (* z z) (* t a)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
4.0ms	(- (* z z) (* t a))
12.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ z (sqrt (- (* z z) (* t a))))
32.0ms	(- (* z z) (* t a))
84.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
64.0ms	(sqrt (- (* z z) (* t a)))

simplify69.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	431	1015
1	2166	912
2	5002	893

prune308.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 1.8b

localize10.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
1.4b	(* y (/ z (sqrt (- (* z z) (* t a)))))
2.5b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
22.2b	(sqrt (- (* z z) (* t a)))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`add-cube-cbrt` `*-un-lft-identity` `times-frac`
18×	`add-exp-log` `add-cbrt-cube`
13×	`sqrt-prod`
12×	`pow1`
7×	`prod-exp` `cbrt-unprod`
6×	`associate-l` `add-log-exp`
4×	`sqrt-div` `pow-prod-down`
3×	`flip3--` `associate-*r/` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `associate-/r/` `*-commutative`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

4.0ms	(- (* z z) (* t a))
17.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
11.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* z z) (* t a))
59.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
87.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
59.0ms	(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	403	775
1	1781	676
2	5001	667

prune266.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 1.8b

localize17.0ms

Local error

Found 4 expressions with local error:

0.7b	(* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
2.5b	(* x (* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
22.2b	(sqrt (- (* z z) (* t a)))
22.2b	(sqrt (- (* z z) (* t a)))

rewrite75.0ms

Algorithm

rewrite-expression-head

Rules

78×	`add-exp-log`
62×	`add-cbrt-cube`
61×	`associate-r`
60×	`sqrt-prod`
54×	`times-frac`
46×	`add-sqr-sqrt`
44×	`add-cube-cbrt` `*-un-lft-identity`
41×	`prod-exp` `cbrt-unprod`
27×	`cbrt-prod`
20×	`pow1`
16×	`cbrt-undiv` `div-exp`
9×	`associate-*r/` `pow-prod-down`
8×	`sqrt-div`
4×	`associate-l` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `associate-/r/` `-commutative`
1×	`div-inv`

Counts

4 → 156

Calls

4 calls:

33.0ms	(* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
26.0ms	(* x (* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series314.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a))))))
113.0ms	(* x (* (* y (/ (* (cbrt z) (cbrt z)) (sqrt (sqrt (- (* z z) (* t a)))))) (/ (cbrt z) (sqrt (sqrt (- (* z z) (* t a)))))))
58.0ms	(sqrt (- (* z z) (* t a)))
67.0ms	(sqrt (- (* z z) (* t a)))

simplify125.0ms

Algorithm

egg-herbie

Counts

168 → 168

Iterations

Useful iterations: 2 (98.0ms)

Iter	Nodes	Cost
0	833	3166
1	4761	2602
2	5001	2550

prune712.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 1.8b

regimes446.0ms

Accuracy

80.1% (3.9b remaining)

Error of 7.3b against oracle of 3.4b and baseline of 23.0b

bsearch102.0ms

Steps

Iters	Range		Point
10	5.865088562177004e+136	3.2532963586704995e+147	6.27117431119542e+136
10	-2.8752459029099972e+78	-3.342866317005328e+63	-6.705006932778813e+76

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	11
1	32	11
2	38	11
3	38	11

end0.0ms

sample790.0ms

Algorithm

intervals

Results

344.0ms	8797×	body	80	valid
104.0ms	2959×	body	80	nan