Details

sample28.0ms

Algorithm

intervals

Results

10.0ms	280×	body	80	valid
3.0ms	85×	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

prune2.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 24.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
5.3b	(* (* x y) z)
9.1b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.4b	(sqrt (- (* z z) (* t a)))

rewrite29.0ms

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))
9.0ms	(* (* x y) z)
11.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series194.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* z z) (* t a))
22.0ms	(* (* x y) z)
81.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
56.0ms	(sqrt (- (* z z) (* t a)))

simplify52.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (45.0ms)

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

prune293.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.0b

localize11.0ms

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)))))
25.4b	(sqrt (- (* z z) (* t a)))

rewrite38.0ms

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))))
6.0ms	(- (* z z) (* t a))
18.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
4.0ms	(sqrt (- (* z z) (* t a)))

series219.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(/ z (sqrt (- (* z z) (* t a))))
35.0ms	(- (* z z) (* t a))
82.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
56.0ms	(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (50.0ms)

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

prune340.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 3.7b

localize10.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* z z) (* t a))
0.8b	(* y (/ z (sqrt (- (* z z) (* t a)))))
1.1b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
25.4b	(sqrt (- (* z z) (* t a)))

rewrite47.0ms

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×	`expm1-log1p-u` `sqrt-div` `pow-prod-down` `log1p-expm1-u`
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` `fma-neg` `diff-log` `prod-diff` `div-inv`

Counts

4 → 102

Calls

4 calls:

3.0ms	(- (* z z) (* t a))
18.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
19.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series230.0ms

Counts

4 → 12

Calls

4 calls:

38.0ms	(- (* z z) (* t a))
52.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
81.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
59.0ms	(sqrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (48.0ms)

Iter	Nodes	Cost
0	425	829
1	1848	729
2	5001	717

prune296.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 3.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.8b	(* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
1.1b	(* x (* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
25.4b	(sqrt (- (* z z) (* t a)))
25.4b	(sqrt (- (* z z) (* t a)))

rewrite164.0ms

Algorithm

rewrite-expression-head

Rules

28×	`sqrt-div`
27×	`add-exp-log` `add-cbrt-cube`
16×	`add-sqr-sqrt` `associate-r`
13×	`pow1`
12×	`prod-exp` `cbrt-unprod`
10×	`add-cube-cbrt` `*-un-lft-identity`
8×	`flip3--` `associate-/r/` `flip--`
6×	`associate-l` `sqrt-prod`
5×	`associate-*r/`
4×	`cbrt-undiv` `expm1-log1p-u` `frac-times` `times-frac` `div-exp` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l/` `-commutative` `unswap-sqr`
1×	`div-inv`

Counts

4 → 97

Calls

4 calls:

50.0ms	(* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
102.0ms	(* x (* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
4.0ms	(sqrt (- (* z z) (* t a)))
4.0ms	(sqrt (- (* z z) (* t a)))

series253.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
82.0ms	(* x (* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
60.0ms	(sqrt (- (* z z) (* t a)))
59.0ms	(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	427	1197
1	1744	935
2	5002	908

prune323.0ms

Pruning

9 alts after pruning (6 fresh and 3 done)

Merged error: 3.7b

regimes362.0ms

Accuracy

85.8% (2.7b remaining)

Error of 5.8b against oracle of 3.1b and baseline of 22.3b

bsearch79.0ms

Steps

Iters	Range		Point
8	2.961003054450564e+80	3.580192485387106e+83	3.43469549411493e+83
8	-2.9116578623443026e+156	-9.998794794503373e+152	-1.0932223177976295e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	10
1	30	10
2	33	10
3	33	10

end0.0ms

sample788.0ms

Algorithm

intervals

Results

338.0ms	8884×	body	80	valid
103.0ms	2952×	body	80	nan