Details

sample31.0ms

Algorithm

intervals

Results

11.0ms	286×	body	80	valid
4.0ms	111×	body	80	nan

simplify11.0ms

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: 24.9b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
4.2b	(* (* x y) z)
8.7b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.1b	(sqrt (- (* z z) (* t a)))

rewrite24.0ms

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:

4.0ms	(- (* z z) (* t a))
5.0ms	(* (* x y) z)
9.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
4.0ms	(sqrt (- (* z z) (* t a)))

series199.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* z z) (* t a))
23.0ms	(* (* x y) z)
80.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
61.0ms	(sqrt (- (* z z) (* t a)))

simplify54.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (47.0ms)

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

prune269.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.5b

localize10.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.2b	(- (* z z) (* t a))
3.9b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.1b	(sqrt (- (* z z) (* t a)))

rewrite29.0ms

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

series227.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(/ z (sqrt (- (* z z) (* t a))))
33.0ms	(- (* z z) (* t a))
82.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
63.0ms	(sqrt (- (* z z) (* t a)))

simplify60.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (50.0ms)

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

prune321.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.2b

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
1.2b	(* y (/ z (sqrt (- (* z z) (* t a)))))
2.4b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
23.1b	(sqrt (- (* z z) (* t a)))

rewrite34.0ms

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:

4.0ms	(- (* z z) (* t a))
14.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
10.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
4.0ms	(sqrt (- (* z z) (* t a)))

series228.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* z z) (* t a))
55.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
81.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
58.0ms	(sqrt (- (* z z) (* t a)))

simplify58.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (47.0ms)

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

prune275.0ms

Pruning

10 alts after pruning (10 fresh and 0 done)

Merged error: 4.2b

localize13.0ms

Local error

Found 4 expressions with local error:

1.2b	(* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
2.4b	(* x (* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
23.1b	(sqrt (- (* z z) (* t a)))
23.1b	(sqrt (- (* z z) (* t a)))

rewrite49.0ms

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:

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

series261.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a)))))))
83.0ms	(* x (* y (/ z (* (sqrt (sqrt (- (* z z) (* t a)))) (sqrt (sqrt (- (* z z) (* t a))))))))
62.0ms	(sqrt (- (* z z) (* t a)))
64.0ms	(sqrt (- (* z z) (* t a)))

simplify51.0ms

Algorithm

egg-herbie

Counts

109 → 109

Iterations

Useful iterations: 2 (41.0ms)

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

prune304.0ms

Pruning

10 alts after pruning (9 fresh and 1 done)

Merged error: 4.2b

regimes337.0ms

Accuracy

81% (3.7b remaining)

Error of 7.2b against oracle of 3.5b and baseline of 22.8b

bsearch91.0ms

Steps

Iters	Range		Point
6	6.533440019736163e+126	9.198944834822479e+127	8.001380975877731e+126
10	-1.5217146184155857e+89	-7.696003816443151e+76	-1.1055887578016406e+87

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	34	22
1	35	22
2	38	22
3	38	22

end0.0ms

sample796.0ms

Algorithm

intervals

Results

342.0ms	8853×	body	80	valid
109.0ms	3007×	body	80	nan