Details

sample31.0ms

Algorithm

intervals

Results

13.0ms	284×	body	80	valid
3.0ms	95×	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: 24.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
6.7b	(* (* x y) z)
8.2b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
26.1b	(sqrt (- (* z z) (* t a)))

rewrite27.0ms

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

series192.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* z z) (* t a))
22.0ms	(* (* x y) z)
79.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
59.0ms	(sqrt (- (* z z) (* t a)))

simplify56.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (46.0ms)

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

prune270.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.4b	(- (* z z) (* t a))
3.5b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
26.1b	(sqrt (- (* z z) (* t a)))

rewrite36.0ms

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×	`expm1-log1p-u` `flip3--` `associate-/r/` `flip--` `log1p-expm1-u`
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` `fma-neg` `diff-log` `associate-r/` `associate-l` `prod-diff` `clear-num` `-commutative`

Counts

4 → 122

Calls

4 calls:

6.0ms	(/ z (sqrt (- (* z z) (* t a))))
3.0ms	(- (* z z) (* t a))
19.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series218.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(/ z (sqrt (- (* z z) (* t a))))
31.0ms	(- (* z z) (* t a))
79.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify62.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	453	1067
1	2239	963
2	5001	942

prune325.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.7b

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
3.5b	(* (* x y) (* (/ 1 (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
26.1b	(sqrt (- (* z z) (* t a)))
26.1b	(sqrt (- (* z z) (* t a)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
45×	`add-cbrt-cube`
43×	`prod-exp`
23×	`cbrt-unprod`
18×	`pow1`
16×	`div-exp`
8×	`cbrt-undiv` `add-sqr-sqrt` `pow-prod-down`
6×	`add-cube-cbrt` `*-un-lft-identity` `sqrt-prod` `add-log-exp`
4×	`expm1-log1p-u` `rec-exp` `sqrt-div` `1-exp` `associate-*r/` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `associate-r` `associate-l` `prod-diff` `associate-l/` `-commutative`

Counts

4 → 97

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
56.0ms	(* (* x y) (* (/ 1 (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
7.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series231.0ms

Counts

4 → 12

Calls

4 calls:

31.0ms	(- (* z z) (* t a))
80.0ms	(* (* x y) (* (/ 1 (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
59.0ms	(sqrt (- (* z z) (* t a)))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (50.0ms)

Iter	Nodes	Cost
0	507	1327
1	2360	994
2	5002	801

prune321.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.7b

localize17.0ms

Local error

Found 4 expressions with local error:

3.0b	(/ (* x (* y (/ z (sqrt (sqrt (- (* z z) (* t a))))))) (sqrt (sqrt (- (* z z) (* t a)))))
3.9b	(* x (* y (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
26.1b	(sqrt (- (* z z) (* t a)))
26.1b	(sqrt (- (* z z) (* t a)))

rewrite67.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 99

Calls

4 calls:

31.0ms	(/ (* x (* y (/ z (sqrt (sqrt (- (* z z) (* t a))))))) (sqrt (sqrt (- (* z z) (* t a)))))
25.0ms	(* x (* y (/ 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:

83.0ms	(/ (* x (* y (/ z (sqrt (sqrt (- (* z z) (* t a))))))) (sqrt (sqrt (- (* z z) (* t a)))))
111.0ms	(* x (* y (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
60.0ms	(sqrt (- (* z z) (* t a)))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	429	1296
1	1999	1070
2	5001	1056

prune303.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 4.7b

regimes332.0ms

Accuracy

79.8% (4.2b remaining)

Error of 7.6b against oracle of 3.4b and baseline of 24.0b

bsearch95.0ms

Steps

Iters	Range		Point
8	1.415354163576236e+117	8.302175042271763e+120	1.507591943378104e+117
8	-335813708160.4535	-59376144.544019125	-329128518468.4069

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	35	24
1	41	24
2	41	24

end0.0ms

sample798.0ms

Algorithm

intervals

Results

340.0ms	8874×	body	80	valid
101.0ms	2927×	body	80	nan