Details

sample115.0ms

Algorithm

intervals

Results

76.0ms

656×

body

valid

simplify93.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	47	14
1	110	13
2	335	13
3	1059	13
4	3442	13
5	5001	13

prune10.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 9.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (* c z) (* t i))
3.0b	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
4.0b	(* x (- (* y z) (* t a)))
4.5b	(* b (- (* c z) (* t i)))

rewrite25.0ms

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` `add-log-exp`
5×	`sub-neg` `prod-diff`
4×	`expm1-log1p-u` `associate-*r/` `log1p-expm1-u`
3×	`flip3--` `flip--`
2×	`pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`
1×	`fma-neg` `diff-log` `fma-udef`

Counts

4 → 82

Calls

4 calls:

3.0ms	(- (* c z) (* t i))
0.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
10.0ms	(* x (- (* y z) (* t a)))
10.0ms	(* b (- (* c z) (* t i)))

series754.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- (* c z) (* t i))
570.0ms	(fma (- (* c a) (* y i)) j (- (* x (- (* y z) (* t a))) (* b (- (* c z) (* t i)))))
66.0ms	(* x (- (* y z) (* t a)))
73.0ms	(* b (- (* c z) (* t i)))

simplify50.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	376	645
1	1499	568
2	5001	568

prune454.0ms

Pruning

14 alts after pruning (14 fresh and 0 done)

Merged error: 3.5b

localize23.0ms

Local error

Found 4 expressions with local error:

3.0b	(fma (- (* c a) (* y i)) j (- (+ (* x (* y z)) (* x (- (* t a)))) (* b (- (* c z) (* t i)))))
3.6b	(* x (- (* t a)))
4.5b	(* b (- (* c z) (* t i)))
6.0b	(* x (* y z))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

0.0ms	(fma (- (* c a) (* y i)) j (- (+ (* x (* y z)) (* x (- (* t a)))) (* b (- (* c z) (* t i)))))
4.0ms	(* x (- (* t a)))
9.0ms	(* b (- (* c z) (* t i)))
6.0ms	(* x (* y z))

series691.0ms

Counts

4 → 12

Calls

4 calls:

565.0ms	(fma (- (* c a) (* y i)) j (- (+ (* x (* y z)) (* x (- (* t a)))) (* b (- (* c z) (* t i)))))
32.0ms	(* x (- (* t a)))
66.0ms	(* b (- (* c z) (* t i)))
28.0ms	(* x (* y z))

simplify64.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	381	576
1	1754	498
2	5002	497

prune445.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.0b

localize31.0ms

Local error

Found 4 expressions with local error:

4.5b	(* b (- (* c z) (* t i)))
5.7b	(cbrt (- (* y z) (* t a)))
5.7b	(cbrt (- (* y z) (* t a)))
5.7b	(cbrt (- (* y z) (* t a)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 73

Calls

4 calls:

9.0ms	(* b (- (* c z) (* t i)))
2.0ms	(cbrt (- (* y z) (* t a)))
2.0ms	(cbrt (- (* y z) (* t a)))
2.0ms	(cbrt (- (* y z) (* t a)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(* b (- (* c z) (* t i)))
117.0ms	(cbrt (- (* y z) (* t a)))
113.0ms	(cbrt (- (* y z) (* t a)))
113.0ms	(cbrt (- (* y z) (* t a)))

simplify112.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	335	646
1	1158	598
2	4180	580
3	5001	580

prune705.0ms

Pruning

12 alts after pruning (12 fresh and 0 done)

Merged error: 3.0b

localize28.0ms

Local error

Found 4 expressions with local error:

4.5b	(* b (- (* c z) (* t i)))
4.5b	(* b (- (* c z) (* t i)))
4.5b	(* b (- (* c z) (* t i)))
6.0b	(* x (* y z))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 104

Calls

4 calls:

10.0ms	(* b (- (* c z) (* t i)))
10.0ms	(* b (- (* c z) (* t i)))
9.0ms	(* b (- (* c z) (* t i)))
6.0ms	(* x (* y z))

series232.0ms

Counts

4 → 12

Calls

4 calls:

68.0ms	(* b (- (* c z) (* t i)))
69.0ms	(* b (- (* c z) (* t i)))
66.0ms	(* b (- (* c z) (* t i)))
28.0ms	(* x (* y z))

simplify110.0ms

Algorithm

egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 1 (9.0ms)

Iter	Nodes	Cost
0	248	627
1	984	549
2	3962	549
3	5002	549

prune511.0ms

Pruning

13 alts after pruning (12 fresh and 1 done)

Merged error: 3.0b

regimes772.0ms

Accuracy

14.2% (7.0b remaining)

Error of 10.9b against oracle of 3.9b and baseline of 12.1b

bsearch207.0ms

Steps

Iters	Range		Point
6	4.0955264881084335e-05	0.00017903544813856285	0.00011914660913943379
8	-2.5606417028189997e-45	-1.936649753981274e-49	-1.0716846611179825e-48

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	63	30
1	76	30
2	80	30
3	80	30

end0.0ms

sample3.1s

Algorithm

intervals

Results

2.2s

19216×

body

valid