Details

sample45.0ms

Algorithm

intervals

Results

14.0ms	287×	body	80	valid
4.0ms	94×	body	80	nan

simplify91.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	118
5	118
4	97
3	72
2	46
1	22
0	12

prune21.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 21.6b

localize33.0ms

Local error

Found 4 expressions with local error:

0.3b	(fma z z (- (* a t)))
1.0b	(* (/ (* z y) (sqrt (fma z z (- (* a t))))) x)
8.7b	(/ (* z y) (sqrt (fma z z (- (* a t)))))
24.8b	(sqrt (fma z z (- (* a t))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 86

Calls

4 calls:

0.0ms	(fma z z (- (* a t)))
22.0ms	(* (/ (* z y) (sqrt (fma z z (- (* a t))))) x)
8.0ms	(/ (* z y) (sqrt (fma z z (- (* a t)))))
1.0ms	(sqrt (fma z z (- (* a t))))

series461.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(fma z z (- (* a t)))
173.0ms	(* (/ (* z y) (sqrt (fma z z (- (* a t))))) x)
116.0ms	(/ (* z y) (sqrt (fma z z (- (* a t)))))
96.0ms	(sqrt (fma z z (- (* a t))))

simplify1.2s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	1731
1	312
0	130

prune673.0ms

Pruning

11 alts after pruning (11 fresh and 0 done)

Merged error: 3.8b

localize31.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (/ z (fabs (cbrt (- (* z z) (* t a))))) (/ y (sqrt (cbrt (- (* z z) (* t a)))))) x)
3.6b	(* (/ z (fabs (cbrt (- (* z z) (* t a))))) (/ y (sqrt (cbrt (- (* z z) (* t a))))))
25.6b	(cbrt (- (* z z) (* t a)))
25.6b	(cbrt (- (* z z) (* t a)))

rewrite159.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 135

Calls

4 calls:

83.0ms	(* (* (/ z (fabs (cbrt (- (* z z) (* t a))))) (/ y (sqrt (cbrt (- (* z z) (* t a)))))) x)
57.0ms	(* (/ z (fabs (cbrt (- (* z z) (* t a))))) (/ y (sqrt (cbrt (- (* z z) (* t a))))))
5.0ms	(cbrt (- (* z z) (* t a)))
5.0ms	(cbrt (- (* z z) (* t a)))

series1.1s

Counts

4 → 12

Calls

4 calls:

498.0ms	(* (* (/ z (fabs (cbrt (- (* z z) (* t a))))) (/ y (sqrt (cbrt (- (* z z) (* t a)))))) x)
367.0ms	(* (/ z (fabs (cbrt (- (* z z) (* t a))))) (/ y (sqrt (cbrt (- (* z z) (* t a))))))
125.0ms	(cbrt (- (* z z) (* t a)))
156.0ms	(cbrt (- (* z z) (* t a)))

simplify2.4s

Counts

147 → 147

Iterations

Iter	Nodes
done	5000
2	4852
1	852
0	287

prune1.1s

Pruning

11 alts after pruning (10 fresh and 1 done)

Merged error: 3.8b

localize40.0ms

Local error

Found 4 expressions with local error:

3.6b	(* (/ z (fabs (* (sqrt (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a))))))) (/ y (sqrt (cbrt (- (* z z) (* t a))))))
25.6b	(cbrt (- (* z z) (* t a)))
25.6b	(cbrt (- (* z z) (* t a)))
25.6b	(cbrt (- (* z z) (* t a)))

rewrite103.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 121

Calls

4 calls:

68.0ms	(* (/ z (fabs (* (sqrt (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a))))))) (/ y (sqrt (cbrt (- (* z z) (* t a))))))
9.0ms	(cbrt (- (* z z) (* t a)))
13.0ms	(cbrt (- (* z z) (* t a)))
5.0ms	(cbrt (- (* z z) (* t a)))

series804.0ms

Counts

4 → 12

Calls

4 calls:

377.0ms	(* (/ z (fabs (* (sqrt (cbrt (- (* z z) (* t a)))) (sqrt (cbrt (- (* z z) (* t a))))))) (/ y (sqrt (cbrt (- (* z z) (* t a))))))
145.0ms	(cbrt (- (* z z) (* t a)))
144.0ms	(cbrt (- (* z z) (* t a)))
139.0ms	(cbrt (- (* z z) (* t a)))

simplify1.9s

Counts

133 → 133

Iterations

Iter	Nodes
done	5000
2	3788
1	712
0	241

prune1.3s

Pruning

11 alts after pruning (9 fresh and 2 done)

Merged error: 3.8b

localize36.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* z z) (* t a))
1.0b	(* (* (* z y) (/ 1 (sqrt (- (* z z) (* t a))))) x)
8.9b	(* (* z y) (/ 1 (sqrt (- (* z z) (* t a)))))
24.8b	(sqrt (- (* z z) (* t a)))

rewrite196.0ms

Algorithm

rewrite-expression-head

Rules

58×	`add-exp-log`
34×	`add-cbrt-cube`
33×	`prod-exp`
27×	`associate-r`
20×	`add-sqr-sqrt`
19×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
18×	`times-frac`
17×	`cbrt-unprod`
12×	`sqrt-prod`
9×	`pow-prod-down`
8×	`div-exp`
6×	`add-log-exp`
4×	`expm1-log1p-u` `cbrt-undiv` `rec-exp` `sqrt-div` `1-exp` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`associate-l` `associate-l/` `associate-r/` `associate-/r/` `un-div-inv` `*-commutative`
1×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `div-inv`

Counts

4 → 117

Calls

4 calls:

6.0ms	(- (* z z) (* t a))
122.0ms	(* (* (* z y) (/ 1 (sqrt (- (* z z) (* t a))))) x)
48.0ms	(* (* z y) (/ 1 (sqrt (- (* z z) (* t a)))))
16.0ms	(sqrt (- (* z z) (* t a)))

series365.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- (* z z) (* t a))
142.0ms	(* (* (* z y) (/ 1 (sqrt (- (* z z) (* t a))))) x)
97.0ms	(* (* z y) (/ 1 (sqrt (- (* z z) (* t a)))))
81.0ms	(sqrt (- (* z z) (* t a)))

simplify5.5s

Counts

129 → 129

Iterations

Iter	Nodes
done	5000
2	4329
1	593
0	197

prune664.0ms

Pruning

11 alts after pruning (8 fresh and 3 done)

Merged error: 3.8b

regimes1.3s

Accuracy

80.1% (4.0b remaining)

Error of 7.3b against oracle of 3.3b and baseline of 23.4b

bsearch107.0ms

Steps

Iters	Range		Point
6	4.392987423579743e+60	5.909848464129449e+61	1.1285411644606883e+61
8	-2.128153111494975e+100	-6.116329696038052e+95	-6.273512883606797e+95

simplify5.0ms

Iterations

Iter	Nodes
done	35
2	35
1	32
0	23

end0.0ms

sample1.9s

Algorithm

intervals

Results

807.0ms	8908×	body	80	valid
301.0ms	2898×	body	80	nan