Details

sample142.0ms

Algorithm

intervals

Results

81.0ms

674×

body

valid

simplify4.0s

Counts

1 → 1

Iterations

Useful iterations: 5 (1.8s)

Iter	Nodes	Cost
0	23	569
1	47	569
2	110	544
3	333	544
4	907	544
5	2724	519
done	5000	519

prune49.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 11.8b

localize64.0ms

Local error

Found 4 expressions with local error:

0.4b	(- (* c z) (* i a))
5.1b	(* j (- (* c t) (* i y)))
5.5b	(* x (- (* y z) (* t a)))
6.1b	(* b (- (* c z) (* i a)))

rewrite146.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 100

Calls

4 calls:

14.0ms	(- (* c z) (* i a))
41.0ms	(* j (- (* c t) (* i y)))
41.0ms	(* x (- (* y z) (* t a)))
47.0ms	(* b (- (* c z) (* i a)))

series368.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- (* c z) (* i a))
113.0ms	(* j (- (* c t) (* i y)))
114.0ms	(* x (- (* y z) (* t a)))
87.0ms	(* b (- (* c z) (* i a)))

simplify1.9s

Counts

112 → 112

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	200	26045
1	526	24473
2	1625	24233
done	5000	23978

prune1.3s

Pruning

20 alts after pruning (20 fresh and 0 done)

Merged error: 8.6b

localize59.0ms

Local error

Found 4 expressions with local error:

4.9b	(* (* c t) j)
5.5b	(* x (- (* y z) (* t a)))
5.7b	(* (- (* i y)) j)
6.1b	(* b (- (* c z) (* i a)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
15×	`pow1` `add-cbrt-cube` `add-exp-log`
13×	`associate-l`
12×	`associate-r`
11×	`*-un-lft-identity` `add-cube-cbrt`
6×	`distribute-rgt-in` `distribute-lft-in` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`expm1-log1p-u` `sub-neg` `prod-diff` `associate-r/` `-commutative` `log1p-expm1-u` `add-log-exp`
3×	`unswap-sqr`
2×	`flip3--` `flip--`
1×	`distribute-lft-neg-out` `distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in`

Counts

4 → 100

Calls

4 calls:

28.0ms	(* (* c t) j)
22.0ms	(* x (- (* y z) (* t a)))
8.0ms	(* (- (* i y)) j)
33.0ms	(* b (- (* c z) (* i a)))

series274.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(* (* c t) j)
101.0ms	(* x (- (* y z) (* t a)))
35.0ms	(* (- (* i y)) j)
102.0ms	(* b (- (* c z) (* i a)))

simplify2.0s

Counts

112 → 112

Iterations

Useful iterations: done (2.0s)

Iter	Nodes	Cost
0	200	22390
1	528	21242
2	1781	20842
done	5003	20562

prune1.2s

Pruning

19 alts after pruning (19 fresh and 0 done)

Merged error: 6.4b

localize40.0ms

Local error

Found 4 expressions with local error:

0.5b	(- (* i a) (* c z))
4.9b	(fma b (- (* i a) (* c z)) (* j (- (* c t) (* i y))))
5.1b	(* j (- (* c t) (* i y)))
5.1b	(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (* j (- (* c t) (* i y)))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt`
6×	`pow1` `*-un-lft-identity` `add-cbrt-cube` `add-exp-log` `add-cube-cbrt` `add-log-exp`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`distribute-rgt-in` `sub-neg` `distribute-lft-in` `associate-r` `associate-l` `prod-diff`
2×	`flip3--` `associate-*r/` `fma-udef` `flip--`
1×	`fma-neg` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 64

Calls

4 calls:

7.0ms	(- (* i a) (* c z))
0.0ms	(fma b (- (* i a) (* c z)) (* j (- (* c t) (* i y))))
20.0ms	(* j (- (* c t) (* i y)))
0.0ms	(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (* j (- (* c t) (* i y)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

63.0ms	(- (* i a) (* c z))
298.0ms	(fma b (- (* i a) (* c z)) (* j (- (* c t) (* i y))))
117.0ms	(* j (- (* c t) (* i y)))
757.0ms	(fma (- (* y z) (* t a)) x (fma b (- (* i a) (* c z)) (* j (- (* c t) (* i y)))))

simplify2.7s

Counts

76 → 76

Iterations

Useful iterations: 3 (1.1s)

Iter	Nodes	Cost
0	137	22045
1	332	21117
2	942	20977
3	3251	20897
done	5001	20897

prune885.0ms

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 4.4b

localize78.0ms

Local error

Found 4 expressions with local error:

5.7b	(* (- (* i y)) j)
7.4b	(cbrt (- (* c z) (* i a)))
7.4b	(cbrt (- (* c z) (* i a)))
7.4b	(cbrt (- (* c z) (* i a)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`cbrt-prod` `*-un-lft-identity` `add-cube-cbrt`
6×	`pow1` `cbrt-div` `add-cbrt-cube` `associate-l` `add-exp-log`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `associate-r` `flip--`
1×	`distribute-lft-neg-out` `distribute-lft-neg-in` `neg-mul-1` `distribute-rgt-neg-in` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 69

Calls

4 calls:

8.0ms	(* (- (* i y)) j)
4.0ms	(cbrt (- (* c z) (* i a)))
5.0ms	(cbrt (- (* c z) (* i a)))
7.0ms	(cbrt (- (* c z) (* i a)))

series457.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(* (- (* i y)) j)
125.0ms	(cbrt (- (* c z) (* i a)))
140.0ms	(cbrt (- (* c z) (* i a)))
163.0ms	(cbrt (- (* c z) (* i a)))

simplify2.9s

Counts

81 → 81

Iterations

Useful iterations: done (2.9s)

Iter	Nodes	Cost
0	113	25216
1	292	23687
2	897	23487
3	3570	22860
done	5004	22665

prune855.0ms

Pruning

19 alts after pruning (18 fresh and 1 done)

Merged error: 4.4b

regimes2.5s

Accuracy

7.8% (7.1b remaining)

Error of 12.0b against oracle of 4.9b and baseline of 12.6b

bsearch261.0ms

Steps

Iters	Range		Point
5	2.746211025770307e-261	7.7318060463821265e-261	3.1894835506665283e-261
9	-1.629619105604237e-140	-4.496833981351579e-146	-2.7345770242756358e-142

simplify25.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	42	1351
1	71	1351
2	84	1351
3	88	1351
done	88	1351

end0.0ms

sample4.7s

Algorithm

intervals

Results

3.4s

19044×

body

valid