Details

sample54.0ms

Algorithm

intervals

Results

22.0ms	285×	body	80	valid
6.0ms	82×	body	80	nan

simplify108.0ms

Counts

1 → 1

Iterations

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

prune11.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.3b

localize33.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
5.0b	(* (* x y) z)
8.3b	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
25.4b	(sqrt (- (* z z) (* t a)))

rewrite98.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-cbrt-cube` `add-exp-log`
11×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cube-cbrt`
9×	`sqrt-prod`
6×	`associate-/r*` `times-frac` `prod-exp` `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×	`rem-sqrt-square` `clear-num` `sub-neg` `frac-2neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `-commutative` `div-inv` `associate-/l`

Counts

4 → 86

Calls

4 calls:

14.0ms	(- (* z z) (* t a))
26.0ms	(* (* x y) z)
44.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
10.0ms	(sqrt (- (* z z) (* t a)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* z z) (* t a))
45.0ms	(* (* x y) z)
114.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
95.0ms	(sqrt (- (* z z) (* t a)))

simplify1.7s

Counts

98 → 98

Iterations

Iter	Nodes
done	5000
2	2299
1	385
0	146

prune800.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 2.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ z (sqrt (- (* z z) (* t a))))
0.8b	(- (* z z) (* t a))
2.2b	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
25.4b	(sqrt (- (* z z) (* t a)))

rewrite85.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 122

Calls

4 calls:

21.0ms	(/ z (sqrt (- (* z z) (* t a))))
6.0ms	(- (* z z) (* t a))
35.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
15.0ms	(sqrt (- (* z z) (* t a)))

series398.0ms

Counts

4 → 12

Calls

4 calls:

76.0ms	(/ z (sqrt (- (* z z) (* t a))))
62.0ms	(- (* z z) (* t a))
143.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
116.0ms	(sqrt (- (* z z) (* t a)))

simplify2.7s

Counts

134 → 134

Iterations

Iter	Nodes
done	5001
2	3165
1	496
0	179

prune858.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.7b

localize22.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
0.8b	(* x (/ z (sqrt (- (* z z) (* t a)))))
1.6b	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
25.4b	(sqrt (- (* z z) (* t a)))

rewrite102.0ms

Algorithm

rewrite-expression-head

Rules

29×	`add-sqr-sqrt`
25×	`associate-r`
20×	`*-un-lft-identity` `times-frac` `add-cube-cbrt`
18×	`add-cbrt-cube` `add-exp-log`
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×	`rem-sqrt-square` `sub-neg` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff` `div-inv`

Counts

4 → 102

Calls

4 calls:

6.0ms	(- (* z z) (* t a))
35.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
45.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
13.0ms	(sqrt (- (* z z) (* t a)))

series340.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* z z) (* t a))
78.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
129.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
80.0ms	(sqrt (- (* z z) (* t a)))

simplify1.4s

Counts

114 → 114

Iterations

Iter	Nodes
done	5001
2	1910
1	457
0	174

prune744.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.7b

localize62.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
2.2b	(* (* y x) (* (/ 1 (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
26.3b	(cbrt (- (* z z) (* t a)))
26.3b	(cbrt (- (* z z) (* t a)))

rewrite140.0ms

Algorithm

rewrite-expression-head

Rules

77×	`add-exp-log`
45×	`add-cbrt-cube`
43×	`prod-exp`
23×	`cbrt-unprod`
16×	`pow1` `div-exp`
8×	`cbrt-undiv` `pow-prod-down`
6×	`cbrt-prod` `add-sqr-sqrt` `*-un-lft-identity` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `rec-exp` `cbrt-div` `1-exp` `associate-*r/` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`pow1/3`
1×	`frac-times` `sub-neg` `fma-neg` `diff-log` `associate-r` `associate-l` `prod-diff` `associate-l/` `-commutative`

Counts

4 → 93

Calls

4 calls:

13.0ms	(- (* z z) (* t a))
110.0ms	(* (* y x) (* (/ 1 (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
4.0ms	(cbrt (- (* z z) (* t a)))
5.0ms	(cbrt (- (* z z) (* t a)))

series531.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* z z) (* t a))
249.0ms	(* (* y x) (* (/ 1 (fabs (cbrt (- (* z z) (* t a))))) (/ z (sqrt (cbrt (- (* z z) (* t a)))))))
124.0ms	(cbrt (- (* z z) (* t a)))
115.0ms	(cbrt (- (* z z) (* t a)))

simplify2.5s

Counts

105 → 105

Iterations

Iter	Nodes
done	5000
2	3400
1	620
0	200

prune769.0ms

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 2.7b

regimes1.1s

Accuracy

77.7% (4.4b remaining)

Error of 7.7b against oracle of 3.3b and baseline of 22.8b

bsearch137.0ms

Steps

Iters	Range		Point
8	6.89875157706557e+88	4.6365785633703446e+92	5.930939844067446e+90
9	-6.325039929345352e+73	-7.299257252973953e+68	-2.8854075548046605e+71

simplify6.0ms

Iterations

Iter	Nodes
done	37
2	37
1	35
0	26

end0.0ms

sample2.1s

Algorithm

intervals

Results

822.0ms	8854×	body	80	valid
670.0ms	2985×	body	80	nan