Details

sample33.0ms

Algorithm

intervals

Results

13.0ms

492×

body

valid

simplify87.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 9 (72.0ms)

Iter	Nodes	Cost
0	21	6
1	52	6
2	171	6
3	401	6
4	829	6
5	1090	6
6	1610	6
7	1956	6
8	2252	6
9	2367	5
10	2367	5

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.1b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(- t (* z z))
0.0b	(fma x x (* (* y 4.0) (- t (* z z))))
6.6b	(* (* y 4.0) (- t (* z z)))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 64

Calls

3 calls:

6.0ms	(- t (* z z))
0.0ms	(fma x x (* (* y 4.0) (- t (* z z))))
29.0ms	(* (* y 4.0) (- t (* z z)))

series189.0ms

Counts

3 → 9

Calls

3 calls:

37.0ms	(- t (* z z))
85.0ms	(fma x x (* (* y 4.0) (- t (* z z))))
67.0ms	(* (* y 4.0) (- t (* z z)))

simplify41.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 2 (35.0ms)

Iter	Nodes	Cost
0	279	440
1	1253	374
2	5002	367

prune178.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 3.7b

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(- t (* z z))
0.0b	(fma x x (+ (* (* y 4.0) (- t (* z z))) (* (* y 4.0) (fma (- z) z (* z z)))))
6.6b	(* (* y 4.0) (- t (* z z)))
42.0b	(fma (- z) z (* z z))

rewrite39.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 74

Calls

4 calls:

6.0ms	(- t (* z z))
0.0ms	(fma x x (+ (* (* y 4.0) (- t (* z z))) (* (* y 4.0) (fma (- z) z (* z z)))))
30.0ms	(* (* y 4.0) (- t (* z z)))
0.0ms	(fma (- z) z (* z z))

series1.7s

Counts

4 → 12

Calls

4 calls:

30.0ms	(- t (* z z))
1.6s	(fma x x (+ (* (* y 4.0) (- t (* z z))) (* (* y 4.0) (fma (- z) z (* z z)))))
74.0ms	(* (* y 4.0) (- t (* z z)))
47.0ms	(fma (- z) z (* z z))

simplify44.0ms

Algorithm

egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	293	562
1	1301	478
2	5001	467

prune247.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 3.7b

localize18.0ms

Local error

Found 4 expressions with local error:

7.2b	(cbrt (- t (* z z)))
7.2b	(cbrt (- t (* z z)))
7.2b	(cbrt (- t (* z z)))
42.0b	(fma (- z) z (* z z))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

12×	`cbrt-prod`
10×	`add-sqr-sqrt`
7×	`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--` `difference-of-squares`
1×	`fma-udef`

Counts

4 → 58

Calls

4 calls:

3.0ms	(cbrt (- t (* z z)))
3.0ms	(cbrt (- t (* z z)))
4.0ms	(cbrt (- t (* z z)))
0.0ms	(fma (- z) z (* z z))

series801.0ms

Counts

4 → 12

Calls

4 calls:

244.0ms	(cbrt (- t (* z z)))
253.0ms	(cbrt (- t (* z z)))
255.0ms	(cbrt (- t (* z z)))
48.0ms	(fma (- z) z (* z z))

simplify48.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (40.0ms)

Iter	Nodes	Cost
0	176	443
1	423	415
2	1390	406
3	5002	395

prune292.0ms

Pruning

8 alts after pruning (6 fresh and 2 done)

Merged error: 3.6b

localize5.0ms

Local error

Found 1 expressions with local error:

0.0b	(fma x x (* (* y 4.0) t))

rewrite1.0ms

Algorithm

rewrite-expression-head

Rules

1×	`pow1` `add-exp-log` `add-sqr-sqrt` `expm1-log1p-u` `add-cube-cbrt` `*-un-lft-identity` `add-cbrt-cube` `fma-udef` `log1p-expm1-u` `add-log-exp`

Counts

1 → 10

Calls

1 calls:

0.0ms

(fma x x (* (* y 4.0) t))

series36.0ms

Counts

1 → 3

Calls

1 calls:

36.0ms

(fma x x (* (* y 4.0) t))

simplify45.0ms

Algorithm

egg-herbie

Counts

13 → 13

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	35	61
1	71	51
2	257	51
3	1001	51
4	5001	51

prune31.0ms

Pruning

10 alts after pruning (8 fresh and 2 done)

Merged error: 3.6b

regimes309.0ms

Accuracy

82% (0.6b remaining)

Error of 3.1b against oracle of 2.5b and baseline of 5.9b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	30	20
1	30	20

end0.0ms

sample1.1s

Algorithm

intervals

Results

487.0ms

16137×

body

valid