Details

sample66.0ms

Algorithm

intervals

Results

26.0ms	285×	body	80	valid
7.0ms	82×	body	80	nan

simplify101.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	114
5	114
4	93
3	68
2	45
1	21
0	12

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 25.3b

localize28.0ms

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)))

rewrite83.0ms

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×	`sqrt-div`
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` `diff-log` `associate-l` `-commutative` `div-inv` `associate-/l`

Counts

4 → 76

Calls

4 calls:

12.0ms	(- (* z z) (* t a))
18.0ms	(* (* x y) z)
29.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
20.0ms	(sqrt (- (* z z) (* t a)))

series422.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (* z z) (* t a))
45.0ms	(* (* x y) z)
161.0ms	(/ (* (* x y) z) (sqrt (- (* z z) (* t a))))
144.0ms	(sqrt (- (* z z) (* t a)))

simplify1.6s

Counts

88 → 88

Iterations

Iter	Nodes
done	5001
2	2365
1	368
0	134

prune657.0ms

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 2.8b

localize47.0ms

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)))

rewrite105.0ms

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×	`flip3--` `associate-/r/` `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` `diff-log` `associate-l` `associate-r/` `-commutative`

Counts

4 → 112

Calls

4 calls:

26.0ms	(/ z (sqrt (- (* z z) (* t a))))
13.0ms	(- (* z z) (* t a))
49.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
9.0ms	(sqrt (- (* z z) (* t a)))

series415.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(/ z (sqrt (- (* z z) (* t a))))
58.0ms	(- (* z z) (* t a))
153.0ms	(* (* y x) (/ z (sqrt (- (* z z) (* t a)))))
100.0ms	(sqrt (- (* z z) (* t a)))

simplify2.1s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
2	2925
1	474
0	167

prune806.0ms

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 2.8b

localize30.0ms

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)))

rewrite98.0ms

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×	`sqrt-div` `pow-prod-down`
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` `diff-log` `div-inv`

Counts

4 → 92

Calls

4 calls:

7.0ms	(- (* z z) (* t a))
39.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
39.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
8.0ms	(sqrt (- (* z z) (* t a)))

series405.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- (* z z) (* t a))
107.0ms	(* x (/ z (sqrt (- (* z z) (* t a)))))
137.0ms	(* y (* x (/ z (sqrt (- (* z z) (* t a))))))
110.0ms	(sqrt (- (* z z) (* t a)))

simplify1.5s

Counts

104 → 104

Iterations

Iter	Nodes
done	5000
2	1914
1	439
0	162

prune782.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 2.8b

localize53.0ms

Local error

Found 4 expressions with local error:

0.8b	(- (* z z) (* t a))
2.2b	(* (* y x) (* (/ 1 (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
25.4b	(sqrt (- (* z z) (* t a)))
25.4b	(sqrt (- (* z z) (* t a)))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 87

Calls

4 calls:

6.0ms	(- (* z z) (* t a))
114.0ms	(* (* y x) (* (/ 1 (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
7.0ms	(sqrt (- (* z z) (* t a)))
11.0ms	(sqrt (- (* z z) (* t a)))

series407.0ms

Counts

4 → 12

Calls

4 calls:

64.0ms	(- (* z z) (* t a))
142.0ms	(* (* y x) (* (/ 1 (sqrt (sqrt (- (* z z) (* t a))))) (/ z (sqrt (sqrt (- (* z z) (* t a)))))))
109.0ms	(sqrt (- (* z z) (* t a)))
91.0ms	(sqrt (- (* z z) (* t a)))

simplify2.4s

Counts

99 → 99

Iterations

Iter	Nodes
done	5000
2	3369
1	524
0	159

prune699.0ms

Pruning

10 alts after pruning (7 fresh and 3 done)

Merged error: 2.8b

regimes1.2s

Accuracy

77.5% (4.4b remaining)

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

bsearch181.0ms

Steps

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

simplify12.0ms

Iterations

Iter	Nodes
done	30
2	30
1	28
0	21

end0.0ms

sample2.2s

Algorithm

intervals

Results

1.3s	8854×	body	80	valid
236.0ms	2985×	body	80	nan