Details

sample50.0ms

Algorithm

intervals

Results

25.0ms

496×

body

valid

simplify4.5s

Counts

1 → 1

Iterations

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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.6b

localize21.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (* z z) t)
0.0b	(- (* x x) (* (* y 4.0) (- (* z z) t)))
6.2b	(* (* y 4.0) (- (* z z) t))

rewrite62.0ms

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:

11.0ms	(- (* z z) t)
11.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
37.0ms	(* (* y 4.0) (- (* z z) t))

series256.0ms

Counts

3 → 9

Calls

3 calls:

41.0ms	(- (* z z) t)
128.0ms	(- (* x x) (* (* y 4.0) (- (* z z) t)))
87.0ms	(* (* y 4.0) (- (* z z) t))

simplify1.3s

Counts

87 → 87

Iterations

Iter	Nodes
done	5003
2	1308
1	441
0	148

prune469.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.6b

localize56.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma x x (- (* (- (* z z) t) (* y 4.0))))
6.2b	(* (- (* z z) t) (* y 4.0))
6.2b	(* (- (* z z) t) (* y 4.0))
56.9b	(fma (- (- (* z z) t)) (* y 4.0) (* (- (* z z) t) (* y 4.0)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1` `add-cbrt-cube` `add-exp-log`
8×	`add-sqr-sqrt` `associate-l`
6×	`*-un-lft-identity` `pow-prod-down` `prod-exp` `add-cube-cbrt` `cbrt-unprod`
4×	`expm1-log1p-u` `associate-*l/` `log1p-expm1-u` `add-log-exp`
2×	`flip3--` `associate-r` `*-commutative` `fma-udef` `flip--` `difference-of-squares`

Counts

4 → 66

Calls

4 calls:

0.0ms	(fma x x (- (* (- (* z z) t) (* y 4.0))))
40.0ms	(* (- (* z z) t) (* y 4.0))
43.0ms	(* (- (* z z) t) (* y 4.0))
1.0ms	(fma (- (- (* z z) t)) (* y 4.0) (* (- (* z z) t) (* y 4.0)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(fma x x (- (* (- (* z z) t) (* y 4.0))))
68.0ms	(* (- (* z z) t) (* y 4.0))
76.0ms	(* (- (* z z) t) (* y 4.0))
102.0ms	(fma (- (- (* z z) t)) (* y 4.0) (* (- (* z z) t) (* y 4.0)))

simplify2.2s

Counts

78 → 78

Iterations

Iter	Nodes
done	5001
3	2574
2	623
1	206
0	88

prune598.0ms

Pruning

8 alts after pruning (7 fresh and 1 done)

Merged error: 3.5b

localize37.0ms

Local error

Found 4 expressions with local error:

4.3b	(cbrt (* (* y 4.0) (- (* z z) t)))
6.2b	(* (* y 4.0) (- (* z z) t))
6.2b	(* (* y 4.0) (- (* z z) t))
6.2b	(* (* y 4.0) (- (* z z) t))

rewrite160.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 112

Calls

4 calls:

24.0ms	(cbrt (* (* y 4.0) (- (* z z) t)))
51.0ms	(* (* y 4.0) (- (* z z) t))
46.0ms	(* (* y 4.0) (- (* z z) t))
36.0ms	(* (* y 4.0) (- (* z z) t))

series495.0ms

Counts

4 → 12

Calls

4 calls:

196.0ms	(cbrt (* (* y 4.0) (- (* z z) t)))
109.0ms	(* (* y 4.0) (- (* z z) t))
101.0ms	(* (* y 4.0) (- (* z z) t))
89.0ms	(* (* y 4.0) (- (* z z) t))

simplify2.8s

Counts

124 → 124

Iterations

Iter	Nodes
done	5000
3	4558
2	1120
1	395
0	144

prune658.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.5b

localize38.0ms

Local error

Found 4 expressions with local error:

6.2b	(* (* y 4.0) (* (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t))) (cbrt (- (* z z) t))))
6.8b	(cbrt (- (* z z) t))
6.8b	(cbrt (- (* z z) t))
6.8b	(cbrt (- (* z z) t))

rewrite307.0ms

Algorithm

rewrite-expression-head

Rules

60×	`cbrt-div`
34×	`associate-*r/`
30×	`flip3--` `flip--`
28×	`frac-times`
25×	`pow1` `add-exp-log`
17×	`add-cbrt-cube`
15×	`pow-prod-down` `prod-exp` `cbrt-unprod`
14×	`associate-*l/`
12×	`cbrt-prod`
10×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `difference-of-squares`
1×	`associate-r` `associate-l` `*-commutative`

Counts

4 → 104

Calls

4 calls:

274.0ms	(* (* y 4.0) (* (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t))) (cbrt (- (* z z) t))))
10.0ms	(cbrt (- (* z z) t))
10.0ms	(cbrt (- (* z z) t))
9.0ms	(cbrt (- (* z z) t))

series466.0ms

Counts

4 → 12

Calls

4 calls:

99.0ms	(* (* y 4.0) (* (* (cbrt (- (* z z) t)) (cbrt (- (* z z) t))) (cbrt (- (* z z) t))))
143.0ms	(cbrt (- (* z z) t))
121.0ms	(cbrt (- (* z z) t))
103.0ms	(cbrt (- (* z z) t))

simplify2.8s

Counts

116 → 116

Iterations

Iter	Nodes
done	5001
3	4271
2	1390
1	477
0	176

prune624.0ms

Pruning

8 alts after pruning (5 fresh and 3 done)

Merged error: 3.5b

regimes1.2s

Accuracy

85.1% (0.5b remaining)

Error of 3.0b against oracle of 2.5b and baseline of 6.0b

bsearch2.0ms

simplify13.0ms

Iterations

Iter	Nodes
done	41
2	41
1	33
0	24

end0.0ms

sample2.0s

Algorithm

intervals

Results

1.1s

15655×

body

valid