Details

sample168.0ms

Algorithm

intervals

Results

83.0ms

565×

body

valid

simplify1.8s

Counts

1 → 1

Iterations

Iter	Nodes
done	5000
4	953
3	290
2	96
1	43
0	23

prune9.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize64.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* c z) (* t i))
4.1b	(* b (- (* c z) (* t i)))
4.5b	(* j (- (* c a) (* y i)))
6.6b	(* x (- (* y z) (* t a)))

rewrite113.0ms

Algorithm

rewrite-expression-head

Rules

16×	`add-sqr-sqrt`
10×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt`
9×	`associate-r` `associate-l`
7×	`sub-neg`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-*r/` `add-log-exp`
4×	`flip3--` `flip--`
3×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`diff-log`

Counts

4 → 84

Calls

4 calls:

8.0ms	(- (* c z) (* t i))
34.0ms	(* b (- (* c z) (* t i)))
32.0ms	(* j (- (* c a) (* y i)))
36.0ms	(* x (- (* y z) (* t a)))

series354.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(- (* c z) (* t i))
88.0ms	(* b (- (* c z) (* t i)))
99.0ms	(* j (- (* c a) (* y i)))
100.0ms	(* x (- (* y z) (* t a)))

simplify1.3s

Counts

96 → 96

Iterations

Iter	Nodes
done	5001
2	1781
1	456
0	166

prune1.2s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.6b

localize107.0ms

Local error

Found 4 expressions with local error:

6.6b	(* x (- (* y z) (* t a)))
8.4b	(cbrt (* j (- (* c a) (* y i))))
8.4b	(cbrt (* j (- (* c a) (* y i))))
8.4b	(cbrt (* j (- (* c a) (* y i))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 57

Calls

4 calls:

26.0ms	(* x (- (* y z) (* t a)))
8.0ms	(cbrt (* j (- (* c a) (* y i))))
15.0ms	(cbrt (* j (- (* c a) (* y i))))
17.0ms	(cbrt (* j (- (* c a) (* y i))))

series709.0ms

Counts

4 → 12

Calls

4 calls:

119.0ms	(* x (- (* y z) (* t a)))
194.0ms	(cbrt (* j (- (* c a) (* y i))))
195.0ms	(cbrt (* j (- (* c a) (* y i))))
201.0ms	(cbrt (* j (- (* c a) (* y i))))

simplify2.9s

Counts

69 → 69

Iterations

Iter	Nodes
done	5000
3	4558
2	1093
1	323
0	123

prune1.2s

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 8.6b

localize132.0ms

Local error

Found 4 expressions with local error:

6.3b	(cbrt (- (* c a) (* y i)))
6.6b	(* x (- (* y z) (* t a)))
8.4b	(cbrt (* j (- (* c a) (* y i))))
8.4b	(cbrt (* j (- (* c a) (* y i))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `cbrt-div` `add-cbrt-cube` `associate-*r/` `add-exp-log`
5×	`cbrt-prod`
4×	`flip3--` `flip--` `add-log-exp`
3×	`pow1/3` `associate-r` `associate-l`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

11.0ms	(cbrt (- (* c a) (* y i)))
36.0ms	(* x (- (* y z) (* t a)))
8.0ms	(cbrt (* j (- (* c a) (* y i))))
8.0ms	(cbrt (* j (- (* c a) (* y i))))

series700.0ms

Counts

4 → 12

Calls

4 calls:

154.0ms	(cbrt (- (* c a) (* y i)))
92.0ms	(* x (- (* y z) (* t a)))
217.0ms	(cbrt (* j (- (* c a) (* y i))))
237.0ms	(cbrt (* j (- (* c a) (* y i))))

simplify1.5s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
2	1275
1	397
0	156

prune1.3s

Pruning

23 alts after pruning (23 fresh and 0 done)

Merged error: 8.6b

localize186.0ms

Local error

Found 4 expressions with local error:

6.3b	(cbrt (- (* c a) (* y i)))
6.6b	(* x (- (* y z) (* t a)))
8.4b	(cbrt (* j (- (* c a) (* y i))))
8.4b	(cbrt (* j (- (* c a) (* y i))))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

9×	`add-sqr-sqrt`
7×	`*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `cbrt-div` `add-cbrt-cube` `associate-*r/` `add-exp-log`
5×	`cbrt-prod`
4×	`flip3--` `flip--` `add-log-exp`
3×	`pow1/3` `associate-r` `associate-l`
2×	`distribute-rgt-in` `sub-neg` `distribute-lft-in`
1×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 59

Calls

4 calls:

5.0ms	(cbrt (- (* c a) (* y i)))
24.0ms	(* x (- (* y z) (* t a)))
18.0ms	(cbrt (* j (- (* c a) (* y i))))
20.0ms	(cbrt (* j (- (* c a) (* y i))))

series697.0ms

Counts

4 → 12

Calls

4 calls:

184.0ms	(cbrt (- (* c a) (* y i)))
79.0ms	(* x (- (* y z) (* t a)))
222.0ms	(cbrt (* j (- (* c a) (* y i))))
212.0ms	(cbrt (* j (- (* c a) (* y i))))

simplify1.2s

Counts

71 → 71

Iterations

Iter	Nodes
done	5001
2	1275
1	397
0	156

prune979.0ms

Pruning

24 alts after pruning (23 fresh and 1 done)

Merged error: 8.6b

regimes3.4s

Accuracy

-8.5% (4.3b remaining)

Error of 12.9b against oracle of 8.7b and baseline of 12.6b

bsearch274.0ms

Steps

Iters	Range		Point
7	8.215161490639778e-161	9.057925172271956e-159	1.0618402080152867e-159
9	-2.1716537244083813e-76	-2.6314939040449578e-82	-2.6778192819212064e-82

simplify18.0ms

Iterations

Iter	Nodes
done	67
2	67
1	61
0	43

end0.0ms

sample5.6s

Algorithm

intervals

Results

3.5s

19345×

body

valid