Details

sample89.0ms

Algorithm

intervals

Results

39.0ms

542×

body

valid

simplify1.8s

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	13
1	19	13
2	50	13
3	160	13
4	443	13
5	1442	13
done	5000	13

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 5.3b

localize27.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
5.0b	(* (* y 4.0) (- (* z z) t))

rewrite105.0ms

Algorithm

rewrite-expression-head

Rules

8×	`pow1` `add-exp-log` `add-cbrt-cube`
7×	`add-log-exp`
6×	`add-sqr-sqrt` `sub-neg`
4×	`distribute-rgt-in` `add-cube-cbrt` `-un-lft-identity` `distribute-lft-in` `associate-r*` `associate--r+`
3×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
2×	`diff-log` `associate-*r/` `difference-of-squares`
1×	`associate-l` `*-commutative`

Counts

3 → 54

Calls

3 calls:

14.0ms	(- (* z z) t)
16.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
72.0ms	(* (* y 4.0) (- (* z z) t))

series286.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(- (* z z) t)
144.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
104.0ms	(* (* y 4.0) (- (* z z) t))

simplify1.8s

Counts

63 → 63

Iterations

Useful iterations: 2 (373.0ms)

Iter	Nodes	Cost
0	103	843
1	327	802
2	1901	696
done	5001	696

prune371.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.7b

localize33.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (sqrt (- (* z z) t)) (* y 4.0))
0.1b	(* (* (sqrt (- (* z z) t)) (* y 4.0)) (sqrt (- (* z z) t)))
5.0b	(sqrt (- (* z z) t))
5.0b	(sqrt (- (* z z) t))

rewrite338.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-exp-log` `sqrt-div` `add-cbrt-cube`
16×	`add-sqr-sqrt` `sqrt-prod`
10×	`add-cube-cbrt` `-un-lft-identity` `associate-l/`
9×	`flip3--` `pow-prod-down` `prod-exp` `flip--` `cbrt-unprod`
8×	`associate-r` `associate-l`
4×	`frac-times` `add-log-exp` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-r/` `-commutative`

Counts

4 → 89

Calls

4 calls:

79.0ms	(* (sqrt (- (* z z) t)) (* y 4.0))
213.0ms	(* (* (sqrt (- (* z z) t)) (* y 4.0)) (sqrt (- (* z z) t)))
20.0ms	(sqrt (- (* z z) t))
19.0ms	(sqrt (- (* z z) t))

series411.0ms

Counts

4 → 12

Calls

4 calls:

138.0ms	(* (sqrt (- (* z z) t)) (* y 4.0))
84.0ms	(* (* (sqrt (- (* z z) t)) (* y 4.0)) (sqrt (- (* z z) t)))
100.0ms	(sqrt (- (* z z) t))
88.0ms	(sqrt (- (* z z) t))

simplify1.6s

Counts

101 → 101

Iterations

Useful iterations: done (1.6s)

Iter	Nodes	Cost
0	135	1676
1	358	1493
2	1733	1181
done	5001	1127

prune752.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.7b

localize45.0ms

Local error

Found 4 expressions with local error:

0.0b	(- z (sqrt t))
0.0b	(+ z (sqrt t))
0.1b	(* (+ z (sqrt t)) (* y 4.0))
0.1b	(* (* (+ z (sqrt t)) (* y 4.0)) (- z (sqrt t)))

rewrite270.0ms

Algorithm

rewrite-expression-head

Rules

18×	`pow1` `add-exp-log` `add-cbrt-cube`
14×	`add-sqr-sqrt` `*-un-lft-identity`
10×	`associate-*l/`
9×	`pow-prod-down` `prod-exp` `cbrt-unprod`
8×	`add-log-exp`
7×	`associate-r`
6×	`add-cube-cbrt`
5×	`flip3-+` `associate-l` `flip-+`
4×	`frac-times` `flip3--` `flip--` `difference-of-squares`
3×	`sub-neg`
2×	`distribute-rgt-in` `distribute-lft-in` `associate-r/` `sqrt-prod` `-commutative` `distribute-lft-out` `distribute-lft-out--`
1×	`+-commutative` `diff-log` `sum-log`

Counts

4 → 84

Calls

4 calls:

13.0ms	(- z (sqrt t))
12.0ms	(+ z (sqrt t))
71.0ms	(* (+ z (sqrt t)) (* y 4.0))
168.0ms	(* (* (+ z (sqrt t)) (* y 4.0)) (- z (sqrt t)))

series330.0ms

Counts

4 → 12

Calls

4 calls:

61.0ms	(- z (sqrt t))
40.0ms	(+ z (sqrt t))
75.0ms	(* (+ z (sqrt t)) (* y 4.0))
153.0ms	(* (* (+ z (sqrt t)) (* y 4.0)) (- z (sqrt t)))

simplify2.1s

Counts

96 → 96

Iterations

Useful iterations: done (2.1s)

Iter	Nodes	Cost
0	134	1351
1	405	1263
2	2325	1023
done	5000	1005

prune677.0ms

Pruning

6 alts after pruning (3 fresh and 3 done)

Merged error: 1.7b

localize64.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (- z (sqrt t)))
0.3b	(cbrt (- z (sqrt t)))
0.3b	(cbrt (- z (sqrt t)))
0.3b	(* (cbrt (- z (sqrt t))) (cbrt (- z (sqrt t))))

rewrite137.0ms

Algorithm

rewrite-expression-head

Rules

59×	`add-sqr-sqrt`
54×	`cbrt-prod`
35×	`*-un-lft-identity`
18×	`cbrt-div` `difference-of-squares`
15×	`add-cube-cbrt`
13×	`swap-sqr`
11×	`pow1`
9×	`flip3--` `pow1/3` `associate-r` `associate-l` `sqrt-prod` `flip--` `distribute-lft-out--`
6×	`add-exp-log`
4×	`frac-times` `add-cbrt-cube` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`

Counts

4 → 109

Calls

4 calls:

11.0ms	(cbrt (- z (sqrt t)))
10.0ms	(cbrt (- z (sqrt t)))
10.0ms	(cbrt (- z (sqrt t)))
97.0ms	(* (cbrt (- z (sqrt t))) (cbrt (- z (sqrt t))))

series634.0ms

Counts

4 → 12

Calls

4 calls:

147.0ms	(cbrt (- z (sqrt t)))
160.0ms	(cbrt (- z (sqrt t)))
154.0ms	(cbrt (- z (sqrt t)))
173.0ms	(* (cbrt (- z (sqrt t))) (cbrt (- z (sqrt t))))

simplify1.2s

Counts

121 → 121

Iterations

Useful iterations: done (1.2s)

Iter	Nodes	Cost
0	170	1963
1	421	1768
2	1516	1654
done	5000	1557

prune992.0ms

Pruning

6 alts after pruning (2 fresh and 4 done)

Merged error: 1.7b

regimes1.4s

Accuracy

87.1% (0.4b remaining)

Error of 3.0b against oracle of 2.6b and baseline of 6.1b

bsearch254.0ms

Steps

Iters	Range		Point
7	2.8887670795419047e+153	2.0288491840215392e+155	1.357517357166764e+154
9	-2.1403686743155935e+158	-6.9116960623280505e+149	-1.357021107064521e+154

simplify7.0ms

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	64
1	38	64
done	38	64

end0.0ms

sample3.0s

Algorithm

intervals

Results

1.9s

15725×

body

valid