Details

sample30.0ms

Algorithm

intervals

Results

11.0ms	277×	body	80	valid
4.0ms	101×	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 21.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
4.8b	(* (* x y) z)
8.9b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite30.0ms

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)
14.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series205.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* z z) (* t a))
24.0ms	(* (* x y) z)
86.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (50.0ms)

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

prune274.0ms

Filtered

98 candidates to 71 candidates (72.4%)

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 3.3b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.2b	(- (* z z) (* t a))
2.3b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite39.0ms

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))
22.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(/ z (sqrt (- (* z z) (* t a))))
39.0ms	(- (* z z) (* t a))
84.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify66.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (55.0ms)

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

prune333.0ms

Filtered

134 candidates to 93 candidates (69.4%)

Pruning

9 alts after pruning (9 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)
0.2b	(- (* z z) (* t a))
2.4b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
23.4b	(sqrt (- (* z z) (* t a)))

rewrite29.0ms

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)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (sqrt (- (* z z) (* t a))) z)
32.0ms	(- (* z z) (* t a))
81.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify65.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (51.0ms)

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

prune408.0ms

Filtered

154 candidates to 110 candidates (71.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 3.3b

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (* 1 (- (* z z) (* t a)))) z)
0.2b	(- (* z z) (* t a))
2.4b	(/ (* x y) (/ (sqrt (* 1 (- (* z z) (* t a)))) z))
23.4b	(sqrt (* 1 (- (* z z) (* t a))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 120

Calls

4 calls:

6.0ms	(/ (sqrt (* 1 (- (* z z) (* t a)))) z)
3.0ms	(- (* z z) (* t a))
8.0ms	(/ (* x y) (/ (sqrt (* 1 (- (* z z) (* t a)))) z))
6.0ms	(sqrt (* 1 (- (* z z) (* t a))))

series250.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(/ (sqrt (* 1 (- (* z z) (* t a)))) z)
32.0ms	(- (* z z) (* t a))
83.0ms	(/ (* x y) (/ (sqrt (* 1 (- (* z z) (* t a)))) z))
63.0ms	(sqrt (* 1 (- (* z z) (* t a))))

simplify63.0ms

Algorithm

egg-herbie

Counts

132 → 132

Iterations

Useful iterations: 2 (51.0ms)

Iter	Nodes	Cost
0	521	1220
1	2430	1102
2	5001	1075

prune350.0ms

Filtered

132 candidates to 102 candidates (77.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.3b

regimes390.0ms

Accuracy

84.8% (3.0b remaining)

Error of 6.2b against oracle of 3.2b and baseline of 22.6b

bsearch66.0ms

Steps

Iters	Range		Point
3	4.1175183293486755e+113	5.454825581884215e+113	4.368263439199089e+113
9	-7.721518663878112e+154	-1.486644691915056e+146	-1.3273676981364367e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	12
1	49	12
2	49	12

end0.0ms

sample1.0s

Algorithm

intervals

Results

537.0ms	8868×	body	80	valid
107.0ms	2917×	body	80	nan