Details

sample54.0ms

Algorithm

intervals

Results

25.0ms	284×	body	80	valid
8.0ms	92×	body	80	nan

simplify15.0ms

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: 23.7b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* z z) (* t a))
6.2b	(* (* x y) z)
8.4b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite28.0ms

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)))

series238.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* z z) (* t a))
26.0ms	(* (* x y) z)
98.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
71.0ms	(sqrt (- (* z z) (* t a)))

simplify64.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (56.0ms)

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

prune312.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 3.1b

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (sqrt (- (* z z) (* t a))) z)
1.2b	(- (* z z) (* t a))
2.9b	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
24.5b	(sqrt (- (* z z) (* t a)))

rewrite30.0ms

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

series292.0ms

Counts

4 → 12

Calls

4 calls:

85.0ms	(/ (sqrt (- (* z z) (* t a))) z)
36.0ms	(- (* z z) (* t a))
98.0ms	(/ (* x y) (/ (sqrt (- (* z z) (* t a))) z))
73.0ms	(sqrt (- (* z z) (* t a)))

simplify77.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 2 (63.0ms)

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

prune471.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.1b

localize20.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* z z) (* t a))
24.5b	(sqrt (- (* z z) (* t a)))
24.5b	(sqrt (- (* z z) (* t a)))
24.5b	(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)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

43.0ms	(- (* z z) (* t a))
72.0ms	(sqrt (- (* z z) (* t a)))
65.0ms	(sqrt (- (* z z) (* t a)))
73.0ms	(sqrt (- (* z z) (* t a)))

simplify66.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 3 (58.0ms)

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

prune402.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.1b

localize11.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* z z) (* t a))
2.1b	(/ (* x y) (sqrt (- (* z z) (* t a))))
8.9b	(* (/ (* x y) (sqrt (- (* z z) (* t a)))) z)
24.5b	(sqrt (- (* z z) (* t a)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 98

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
7.0ms	(/ (* x y) (sqrt (- (* z z) (* t a))))
20.0ms	(* (/ (* x y) (sqrt (- (* z z) (* t a)))) z)
5.0ms	(sqrt (- (* z z) (* t a)))

series294.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(- (* z z) (* t a))
86.0ms	(/ (* x y) (sqrt (- (* z z) (* t a))))
99.0ms	(* (/ (* x y) (sqrt (- (* z z) (* t a)))) z)
72.0ms	(sqrt (- (* z z) (* t a)))

simplify57.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (47.0ms)

Iter	Nodes	Cost
0	386	818
1	1716	724
2	5001	714

prune322.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.1b

regimes668.0ms

Accuracy

88% (2.3b remaining)

Error of 5.6b against oracle of 3.3b and baseline of 22.2b

bsearch130.0ms

Steps

Iters	Range		Point
8	1.6906878989450038e+108	1.9687550893258914e+111	3.210515607801375e+110
9	-3.4624365171705646e+156	-2.2826144912851317e+150	-1.3632525312502413e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	28
1	38	28
2	38	28

end0.0ms

sample1.4s

Algorithm

intervals

Results

801.0ms	8873×	body	80	valid
250.0ms	2989×	body	80	nan