Details

sample38.0ms

Algorithm

intervals

Results

19.0ms

498×

body

valid

simplify4.2s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
7	4088
6	1776
5	748
4	361
3	169
2	51
1	21
0	11

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.8b

localize24.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
0.0b	(- (* z z) t)
7.3b	(* (* y 4.0) (- (* z z) t))

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

16×	`prod-diff`
11×	`add-sqr-sqrt`
10×	`distribute-rgt-in` `distribute-lft-in` `associate--r+`
9×	`*-un-lft-identity` `add-cube-cbrt`
8×	`pow1` `add-cbrt-cube` `add-exp-log`
7×	`add-log-exp`
6×	`sub-neg`
4×	`associate-r`
3×	`expm1-log1p-u` `flip3--` `pow-prod-down` `prod-exp` `cbrt-unprod` `log1p-expm1-u` `flip--`
2×	`fma-neg` `diff-log` `associate-*r/` `difference-of-squares`
1×	`associate-l` `*-commutative`

Counts

3 → 78

Calls

3 calls:

13.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
9.0ms	(- (* z z) t)
47.0ms	(* (* y 4.0) (- (* z z) t))

series217.0ms

Counts

3 → 9

Calls

3 calls:

113.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
24.0ms	(- (* z z) t)
80.0ms	(* (* y 4.0) (- (* z z) t))

simplify1.1s

Counts

87 → 87

Iterations

Iter	Nodes
done	5001
2	1309
1	441
0	148

prune452.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 4.7b

localize31.0ms

Local error

Found 4 expressions with local error:

2.2b	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
2.2b	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
7.3b	(* (* y 4.0) (- (* z z) t))
7.3b	(* (* y 4.0) (- (* z z) t))

rewrite81.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt` `pow1`
14×	`add-cbrt-cube` `add-exp-log`
12×	`*-un-lft-identity` `prod-diff` `add-cube-cbrt`
10×	`distribute-rgt-in` `distribute-lft-in`
8×	`associate-r`
6×	`pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `flip3--` `sqrt-div` `associate-*r/` `log1p-expm1-u` `flip--` `add-log-exp`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `*-commutative` `difference-of-squares`

Counts

4 → 100

Calls

4 calls:

9.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
9.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
32.0ms	(* (* y 4.0) (- (* z z) t))
29.0ms	(* (* y 4.0) (- (* z z) t))

series464.0ms

Counts

4 → 12

Calls

4 calls:

161.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
155.0ms	(sqrt (- (* x x) (* (* y 4.0) (- (* z z) t))))
74.0ms	(* (* y 4.0) (- (* z z) t))
73.0ms	(* (* y 4.0) (- (* z z) t))

simplify2.7s

Counts

112 → 112

Iterations

Iter	Nodes
done	5000
3	4825
2	1125
1	381
0	133

prune650.0ms

Pruning

7 alts after pruning (5 fresh and 2 done)

Merged error: 4.7b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* z z) t)
0.1b	(* (+ (* z z) t) (- (* z z) t))
6.7b	(* (* y 4.0) (* (+ (* z z) t) (- (* z z) t)))
21.2b	(/ (* (* y 4.0) (* (+ (* z z) t) (- (* z z) t))) (+ (* z z) t))

rewrite269.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-cbrt-cube` `add-exp-log`
25×	`distribute-rgt-in` `distribute-lft-in`
22×	`associate-*r/`
21×	`prod-diff`
19×	`add-sqr-sqrt`
18×	`pow1`
17×	`prod-exp` `cbrt-unprod`
15×	`*-un-lft-identity` `add-cube-cbrt`
12×	`frac-times`
10×	`flip3-+` `flip3--` `flip-+` `flip--`
9×	`pow-prod-down`
8×	`associate-/l/`
7×	`sub-neg`
6×	`associate-*l/` `add-log-exp`
5×	`cbrt-undiv` `div-exp` `associate-r`
4×	`expm1-log1p-u` `associate-l` `log1p-expm1-u`
3×	`associate-/r*` `times-frac`
2×	`associate-/r/` `*-commutative` `difference-of-squares`
1×	`clear-num` `frac-2neg` `fma-neg` `diff-log` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 149

Calls

4 calls:

7.0ms	(- (* z z) t)
57.0ms	(* (+ (* z z) t) (- (* z z) t))
94.0ms	(* (* y 4.0) (* (+ (* z z) t) (- (* z z) t)))
106.0ms	(/ (* (* y 4.0) (* (+ (* z z) t) (- (* z z) t))) (+ (* z z) t))

series340.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(- (* z z) t)
71.0ms	(* (+ (* z z) t) (- (* z z) t))
164.0ms	(* (* y 4.0) (* (+ (* z z) t) (- (* z z) t)))
76.0ms	(/ (* (* y 4.0) (* (+ (* z z) t) (- (* z z) t))) (+ (* z z) t))

simplify2.4s

Counts

161 → 161

Iterations

Iter	Nodes
done	5012
2	3462
1	848
0	238

prune855.0ms

Pruning

7 alts after pruning (4 fresh and 3 done)

Merged error: 4.7b

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (* y 4.0) (sqrt (- (* z z) t)))
0.1b	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
7.3b	(sqrt (- (* z z) t))
7.3b	(sqrt (- (* z z) t))

rewrite177.0ms

Algorithm

rewrite-expression-head

Rules

20×	`pow1`
18×	`add-cbrt-cube` `sqrt-div` `add-exp-log`
16×	`add-sqr-sqrt` `sqrt-prod`
14×	`associate-r`
10×	`-un-lft-identity` `associate-r/` `add-cube-cbrt`
9×	`flip3--` `pow-prod-down` `prod-exp` `cbrt-unprod` `flip--`
4×	`expm1-log1p-u` `frac-times` `log1p-expm1-u` `add-log-exp` `difference-of-squares`
2×	`rem-sqrt-square` `sqrt-pow1` `pow1/2` `associate-l` `associate-l/` `-commutative`

Counts

4 → 97

Calls

4 calls:

48.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
100.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
14.0ms	(sqrt (- (* z z) t))
10.0ms	(sqrt (- (* z z) t))

series310.0ms

Counts

4 → 12

Calls

4 calls:

107.0ms	(* (* y 4.0) (sqrt (- (* z z) t)))
83.0ms	(* (* (* y 4.0) (sqrt (- (* z z) t))) (sqrt (- (* z z) t)))
61.0ms	(sqrt (- (* z z) t))
58.0ms	(sqrt (- (* z z) t))

simplify1.5s

Counts

109 → 109

Iterations

Iter	Nodes
done	5001
2	1444
1	398
0	142

prune533.0ms

Pruning

7 alts after pruning (3 fresh and 4 done)

Merged error: 4.7b

regimes1.1s

Accuracy

85.3% (0.5b remaining)

Error of 3.0b against oracle of 2.6b and baseline of 5.7b

bsearch1.0ms

simplify3.0ms

Iterations

Iter	Nodes
done	25
1	25
0	20

end0.0ms

sample1.8s

Algorithm

intervals

Results

1.2s

15951×

body

valid