Details

sample213.0ms

Algorithm

intervals

Results

109.0ms

642×

body

valid

simplify2.7s

Counts

1 → 1

Iterations

Useful iterations: 4 (347.0ms)

Iter	Nodes	Cost
0	23	29
1	47	29
2	110	28
3	333	28
4	1229	27
done	5000	27

prune24.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 11.4b

localize73.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i))))
4.1b	(* j (- (* c a) (* y i)))
5.6b	(* b (- (* c z) (* t i)))
6.7b	(* x (- (* y z) (* t a)))

rewrite331.0ms

Algorithm

rewrite-expression-head

Rules

34×	`associate-*r/`
19×	`flip3--` `flip--`
17×	`add-sqr-sqrt`
15×	`distribute-rgt-in` `distribute-lft-in`
12×	`frac-add`
11×	`add-cube-cbrt` `sub-neg` `*-un-lft-identity` `prod-diff`
10×	`pow1` `add-exp-log` `add-cbrt-cube`
9×	`associate-+l+` `associate-r` `associate-l` `add-log-exp`
8×	`frac-sub`
6×	`associate-+r+` `associate--l+`
4×	`expm1-log1p-u` `log1p-expm1-u`
3×	`fma-def` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
2×	`sum-log`
1×	`+-commutative` `associate-+l-` `flip3-+` `diff-log` `flip-+`

Counts

4 → 129

Calls

4 calls:

158.0ms	(+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i))))
49.0ms	(* j (- (* c a) (* y i)))
60.0ms	(* b (- (* c z) (* t i)))
55.0ms	(* x (- (* y z) (* t a)))

series1.3s

Counts

4 → 12

Calls

4 calls:

967.0ms	(+ (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))) (* j (- (* c a) (* y i))))
120.0ms	(* j (- (* c a) (* y i)))
121.0ms	(* b (- (* c z) (* t i)))
120.0ms	(* x (- (* y z) (* t a)))

simplify869.0ms

Counts

141 → 141

Iterations

Useful iterations: done (861.0ms)

Iter	Nodes	Cost
0	319	4255
1	1139	3841
done	5000	3690

prune2.2s

Pruning

17 alts after pruning (17 fresh and 0 done)

Merged error: 3.4b

localize97.0ms

Local error

Found 4 expressions with local error:

3.9b	(fma j (fma c a (- (* i y))) (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
5.6b	(* b (- (* c z) (* t i)))
6.7b	(* x (- (* y z) (* t a)))
51.1b	(fma (- i) y (* i y))

rewrite132.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 76

Calls

4 calls:

1.0ms	(fma j (fma c a (- (* i y))) (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
69.0ms	(* b (- (* c z) (* t i)))
58.0ms	(* x (- (* y z) (* t a)))
1.0ms	(fma (- i) y (* i y))

series1.4s

Counts

4 → 12

Calls

4 calls:

1.1s	(fma j (fma c a (- (* i y))) (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
140.0ms	(* b (- (* c z) (* t i)))
145.0ms	(* x (- (* y z) (* t a)))
50.0ms	(fma (- i) y (* i y))

simplify1.5s

Counts

88 → 88

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	160	1265
1	393	1257
2	1522	1099
done	5001	1089

prune1.5s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.4b

localize132.0ms

Local error

Found 4 expressions with local error:

5.6b	(* b (- (* c z) (* t i)))
5.6b	(* b (- (* c z) (* t i)))
6.7b	(* x (- (* y z) (* t a)))
51.1b	(fma (- i) y (* i y))

rewrite183.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 94

Calls

4 calls:

57.0ms	(* b (- (* c z) (* t i)))
61.0ms	(* b (- (* c z) (* t i)))
59.0ms	(* x (- (* y z) (* t a)))
1.0ms	(fma (- i) y (* i y))

series456.0ms

Counts

4 → 12

Calls

4 calls:

132.0ms	(* b (- (* c z) (* t i)))
137.0ms	(* b (- (* c z) (* t i)))
133.0ms	(* x (- (* y z) (* t a)))
53.0ms	(fma (- i) y (* i y))

simplify1.5s

Counts

106 → 106

Iterations

Useful iterations: done (1.5s)

Iter	Nodes	Cost
0	141	1258
1	354	1249
2	1397	1110
done	5000	1096

prune1.9s

Pruning

18 alts after pruning (18 fresh and 0 done)

Merged error: 3.4b

localize172.0ms

Local error

Found 4 expressions with local error:

7.0b	(cbrt (- (* c z) (* t i)))
7.0b	(cbrt (- (* c z) (* t i)))
7.0b	(cbrt (- (* c z) (* t i)))
51.1b	(fma (- i) y (* i y))

rewrite50.0ms

Algorithm

rewrite-expression-head

Rules

9×	`cbrt-prod`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`cbrt-div`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow1/3` `flip--`
1×	`fma-udef`

Counts

4 → 55

Calls

4 calls:

12.0ms	(cbrt (- (* c z) (* t i)))
23.0ms	(cbrt (- (* c z) (* t i)))
12.0ms	(cbrt (- (* c z) (* t i)))
1.0ms	(fma (- i) y (* i y))

series723.0ms

Counts

4 → 12

Calls

4 calls:

234.0ms	(cbrt (- (* c z) (* t i)))
214.0ms	(cbrt (- (* c z) (* t i)))
222.0ms	(cbrt (- (* c z) (* t i)))
52.0ms	(fma (- i) y (* i y))

simplify1.9s

Counts

67 → 67

Iterations

Useful iterations: done (1.9s)

Iter	Nodes	Cost
0	87	943
1	211	904
2	582	829
3	1867	805
done	5002	712

prune1.3s

Pruning

18 alts after pruning (17 fresh and 1 done)

Merged error: 3.4b

regimes3.8s

Accuracy

28.3% (7.2b remaining)

Error of 9.5b against oracle of 2.3b and baseline of 12.4b

bsearch359.0ms

Steps

Iters	Range		Point
9	1.3487116192662349e+17	1.200780111094521e+23	3.7534315229604977e+18
5	-7.773010243359408e-70	-3.514066727872466e-70	-7.670814752764665e-70

simplify21.0ms

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	58	150
1	84	150
2	86	150
done	86	150

end0.0ms

sample5.9s

Algorithm

intervals

Results

3.7s

18945×

body

valid