Details

sample31.0ms

Algorithm

intervals

Results

11.0ms	282×	body	80	valid
4.0ms	103×	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

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.0b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
2.9b	(* (* x y) z)
11.4b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
23.6b	(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))
7.0ms	(* (* x y) z)
12.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
5.0ms	(sqrt (- (* z z) (* t a)))

series213.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(- (* z z) (* t a))
24.0ms	(* (* x y) z)
89.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
67.0ms	(sqrt (- (* z z) (* t a)))

simplify55.0ms

Algorithm

egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 2 (47.0ms)

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

prune291.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 4.4b

localize14.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.6b	(- (* z z) (* t a))
2.5b	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite37.0ms

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

series234.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ z (sqrt (- (* z z) (* t a))))
33.0ms	(- (* z z) (* t a))
85.0ms	(* (* x y) (/ z (sqrt (- (* z z) (* t a)))))
65.0ms	(sqrt (- (* z z) (* t a)))

simplify61.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (51.0ms)

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

prune352.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 4.2b

localize11.0ms

Local error

Found 4 expressions with local error:

0.6b	(- (* z z) (* t a))
0.9b	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
2.0b	(* y (/ z (sqrt (- (* z z) (* t a)))))
23.6b	(sqrt (- (* z z) (* t a)))

rewrite54.0ms

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))
23.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
20.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
5.0ms	(sqrt (- (* z z) (* t a)))

series240.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(- (* z z) (* t a))
87.0ms	(* x (* y (/ z (sqrt (- (* z z) (* t a))))))
60.0ms	(* y (/ z (sqrt (- (* z z) (* t a)))))
60.0ms	(sqrt (- (* z z) (* t a)))

simplify53.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 2 (44.0ms)

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

prune320.0ms

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 4.1b

localize14.0ms

Local error

Found 4 expressions with local error:

0.9b	(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
4.1b	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
24.3b	(cbrt (- (* z z) (* t a)))
24.3b	(cbrt (- (* z z) (* t a)))

rewrite74.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
46×	`times-frac`
34×	`add-exp-log` `associate-r` `add-cbrt-cube`
33×	`add-cube-cbrt` `*-un-lft-identity`
22×	`sqrt-prod`
17×	`cbrt-prod`
16×	`associate-l`
13×	`prod-exp` `cbrt-unprod`
11×	`pow1`
8×	`cbrt-undiv` `div-exp` `unswap-sqr`
6×	`cbrt-div`
5×	`associate-*r/`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `flip--`
2×	`frac-times` `pow1/3` `sqrt-div` `associate-l/` `associate-/r/` `-commutative` `div-inv`

Counts

4 → 135

Calls

4 calls:

28.0ms	(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
36.0ms	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
2.0ms	(cbrt (- (* z z) (* t a)))
2.0ms	(cbrt (- (* z z) (* t a)))

series546.0ms

Counts

4 → 12

Calls

4 calls:

217.0ms	(* x (* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
152.0ms	(* (/ y (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a))))))
87.0ms	(cbrt (- (* z z) (* t a)))
89.0ms	(cbrt (- (* z z) (* t a)))

simplify83.0ms

Algorithm

egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 2 (66.0ms)

Iter	Nodes	Cost
0	756	2247
1	3399	1947
2	5002	1937

prune517.0ms

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 4.1b

regimes477.0ms

Accuracy

84.6% (2.9b remaining)

Error of 6.6b against oracle of 3.7b and baseline of 22.6b

bsearch99.0ms

Steps

Iters	Range		Point
9	1.1514081473628363e+89	6.147715137559524e+97	8.840009572039548e+95
10	-2.167781788999652e+162	-1.4102566258715918e+152	-1.2137296334810365e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	11
1	48	11
2	48	11

end0.0ms

sample835.0ms

Algorithm

intervals

Results

349.0ms	8878×	body	80	valid
100.0ms	2953×	body	80	nan