Details

sample108.0ms

Algorithm

intervals

Results

59.0ms

565×

body

valid

simplify1.9s

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	23	569
1	43	569
2	96	569
3	290	569
4	953	569
done	5000	569

prune8.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 12.7b

localize44.0ms

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)))

rewrite79.0ms

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:

6.0ms	(- (* c z) (* t i))
21.0ms	(* b (- (* c z) (* t i)))
22.0ms	(* j (- (* c a) (* y i)))
28.0ms	(* x (- (* y z) (* t a)))

series308.0ms

Counts

4 → 12

Calls

4 calls:

42.0ms	(- (* c z) (* t i))
73.0ms	(* b (- (* c z) (* t i)))
97.0ms	(* j (- (* c a) (* y i)))
96.0ms	(* x (- (* y z) (* t a)))

simplify1.4s

Counts

96 → 96

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	166	21661
1	456	20174
2	1781	20014
done	5001	19694

prune1.1s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.6b

localize145.0ms

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))))

rewrite56.0ms

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:

21.0ms	(* x (- (* y z) (* t a)))
9.0ms	(cbrt (* j (- (* c a) (* y i))))
9.0ms	(cbrt (* j (- (* c a) (* y i))))
16.0ms	(cbrt (* j (- (* c a) (* y i))))

series669.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(* x (- (* y z) (* t a)))
196.0ms	(cbrt (* j (- (* c a) (* y i))))
167.0ms	(cbrt (* j (- (* c a) (* y i))))
196.0ms	(cbrt (* j (- (* c a) (* y i))))

simplify2.6s

Counts

69 → 69

Iterations

Useful iterations: 3 (1.5s)

Iter	Nodes	Cost
0	123	23385
1	323	22107
2	1093	21827
3	4558	21227
done	5000	21227

prune984.0ms

Pruning

22 alts after pruning (22 fresh and 0 done)

Merged error: 8.6b

localize153.0ms

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))))

rewrite90.0ms

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:

9.0ms	(cbrt (- (* c a) (* y i)))
45.0ms	(* x (- (* y z) (* t a)))
16.0ms	(cbrt (* j (- (* c a) (* y i))))
17.0ms	(cbrt (* j (- (* c a) (* y i))))

series672.0ms

Counts

4 → 12

Calls

4 calls:

164.0ms	(cbrt (- (* c a) (* y i)))
100.0ms	(* x (- (* y z) (* t a)))
204.0ms	(cbrt (* j (- (* c a) (* y i))))
203.0ms	(cbrt (* j (- (* c a) (* y i))))

simplify1.4s

Counts

71 → 71

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	156	24012
1	397	22614
2	1275	22374
done	5001	21774

prune1.3s

Pruning

24 alts after pruning (24 fresh and 0 done)

Merged error: 8.6b

localize153.0ms

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))))

rewrite75.0ms

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:

9.0ms	(cbrt (- (* c a) (* y i)))
42.0ms	(* x (- (* y z) (* t a)))
13.0ms	(cbrt (* j (- (* c a) (* y i))))
9.0ms	(cbrt (* j (- (* c a) (* y i))))

series683.0ms

Counts

4 → 12

Calls

4 calls:

169.0ms	(cbrt (- (* c a) (* y i)))
99.0ms	(* x (- (* y z) (* t a)))
204.0ms	(cbrt (* j (- (* c a) (* y i))))
210.0ms	(cbrt (* j (- (* c a) (* y i))))

simplify1.4s

Counts

71 → 71

Iterations

Useful iterations: done (1.4s)

Iter	Nodes	Cost
0	156	24012
1	397	22614
2	1275	22374
done	5001	21774

prune1.0s

Pruning

25 alts after pruning (24 fresh and 1 done)

Merged error: 8.6b

regimes3.5s

Accuracy

-8.4% (4.3b remaining)

Error of 12.9b against oracle of 8.6b and baseline of 12.6b

bsearch335.0ms

Steps

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

simplify50.0ms

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	43	1472
1	61	1471
2	67	1471
done	67	1471

end0.0ms

sample4.5s

Algorithm

intervals

Results

2.9s

19345×

body

valid