Details

sample43.0ms

Algorithm

intervals

Results

30.0ms

425×

body

valid

simplify65.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	23	7
1	59	6
2	111	6
3	204	6
4	369	6
5	839	6
6	2168	6
7	5001	6

prune6.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 27.2b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma x x (- (* y y) (* z z)))
3.5b	(- (* y y) (* z z))
25.2b	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

75×	`times-frac`
45×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
13×	`associate-/l*`
8×	`add-exp-log` `add-cbrt-cube`
5×	`div-inv` `add-log-exp`
3×	`pow1` `cbrt-undiv` `expm1-log1p-u` `div-exp` `associate-/r*` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `frac-2neg` `fma-neg` `diff-log` `prod-diff` `clear-num` `flip--` `fma-udef` `associate-/l/` `difference-of-squares`

Counts

3 → 99

Calls

3 calls:

0.0ms	(fma x x (- (* y y) (* z z)))
3.0ms	(- (* y y) (* z z))
6.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

series184.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(fma x x (- (* y y) (* z z)))
33.0ms	(- (* y y) (* z z))
99.0ms	(/ (/ (fma x x (- (* y y) (* z z))) 2.0) y)

simplify59.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (44.0ms)

Iter	Nodes	Cost
0	466	1096
1	1881	1029
2	5001	1026

prune334.0ms

Pruning

6 alts after pruning (6 fresh and 0 done)

Merged error: 10.8b

localize15.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
0.0b	(+ y (/ (pow x 2) y))
8.7b	(/ (pow z 2) y)
10.3b	(/ (pow x 2) y)

rewrite186.0ms

Algorithm

rewrite-expression-head

Rules

193×	`*-un-lft-identity`
148×	`times-frac`
140×	`add-sqr-sqrt`
128×	`add-cube-cbrt`
112×	`prod-diff`
61×	`unpow-prod-down`
31×	`distribute-lft-out`
21×	`unpow2` `sqr-pow`
16×	`associate-/l*`
14×	`add-exp-log`
11×	`add-log-exp`
8×	`add-cbrt-cube`
6×	`div-exp` `associate-/r*` `div-inv`
5×	`difference-of-squares`
4×	`pow1` `expm1-log1p-u` `fma-neg` `log1p-expm1-u`
3×	`fma-def`
2×	`cbrt-undiv` `pow-to-exp` `frac-2neg` `flip3-+` `diff-log` `pow-exp` `clear-num` `sum-log` `frac-sub` `flip-+` `distribute-lft-out--`
1×	`+-commutative` `sub-neg` `flip3--` `associate--l+` `flip--`

Counts

4 → 260

Calls

4 calls:

152.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
12.0ms	(+ y (/ (pow x 2) y))
4.0ms	(/ (pow z 2) y)
4.0ms	(/ (pow x 2) y)

series122.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- (+ y (/ (pow x 2) y)) (/ (pow z 2) y))
29.0ms	(+ y (/ (pow x 2) y))
20.0ms	(/ (pow z 2) y)
25.0ms	(/ (pow x 2) y)

simplify114.0ms

Algorithm

egg-herbie

Counts

272 → 272

Iterations

Useful iterations: 2 (80.0ms)

Iter	Nodes	Cost
0	966	4460
1	3272	3145
2	5001	2950

prune489.0ms

Pruning

8 alts after pruning (8 fresh and 0 done)

Merged error: 1.0b

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (+ y (* x (/ x y))) (/ (pow z 2) y))
0.0b	(+ y (* x (/ x y)))
0.2b	(* x (/ x y))
8.7b	(/ (pow z 2) y)

rewrite52.0ms

Algorithm

rewrite-expression-head

Rules

121×	`add-sqr-sqrt`
110×	`times-frac`
106×	`*-un-lft-identity`
104×	`add-cube-cbrt`
84×	`prod-diff`
40×	`unpow-prod-down`
14×	`add-exp-log` `unpow2` `sqr-pow`
13×	`associate-r`
11×	`add-cbrt-cube` `add-log-exp`
8×	`associate-/l*`
6×	`pow1`
5×	`div-inv` `difference-of-squares`
4×	`expm1-log1p-u` `div-exp` `log1p-expm1-u`
3×	`fma-def` `fma-neg` `associate-l` `associate-/r*`
2×	`cbrt-undiv` `flip3-+` `diff-log` `prod-exp` `sum-log` `frac-sub` `cbrt-unprod` `flip-+` `unswap-sqr`
1×	`+-commutative` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `associate-r/` `pow-prod-down` `pow-exp` `associate--l+` `clear-num` `-commutative` `flip--` `distribute-lft-out--`

Counts

4 → 212

Calls

4 calls:

28.0ms	(- (+ y (* x (/ x y))) (/ (pow z 2) y))
2.0ms	(+ y (* x (/ x y)))
7.0ms	(* x (/ x y))
4.0ms	(/ (pow z 2) y)

series125.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- (+ y (* x (/ x y))) (/ (pow z 2) y))
30.0ms	(+ y (* x (/ x y)))
21.0ms	(* x (/ x y))
26.0ms	(/ (pow z 2) y)

simplify119.0ms

Algorithm

egg-herbie

Counts

224 → 224

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	994	3551
1	3667	2455
2	5001	2446

prune458.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 0.0b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (fma x (/ x y) y) (/ (pow z 2) y))
0.1b	(fma x (/ x y) y)
8.7b	(/ (pow z 2) y)

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

106×	`add-sqr-sqrt`
100×	`times-frac`
96×	`*-un-lft-identity`
94×	`add-cube-cbrt`
84×	`prod-diff`
40×	`unpow-prod-down`
14×	`unpow2` `sqr-pow`
8×	`add-exp-log` `associate-/l*`
5×	`add-cbrt-cube` `add-log-exp` `difference-of-squares`
4×	`div-inv`
3×	`pow1` `expm1-log1p-u` `fma-neg` `div-exp` `associate-/r*` `log1p-expm1-u`
2×	`fma-udef`
1×	`cbrt-undiv` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `diff-log` `pow-exp` `associate--l+` `clear-num` `flip--` `distribute-lft-out--`

Counts

3 → 169

Calls

3 calls:

16.0ms	(- (fma x (/ x y) y) (/ (pow z 2) y))
0.0ms	(fma x (/ x y) y)
4.0ms	(/ (pow z 2) y)

series113.0ms

Counts

3 → 9

Calls

3 calls:

52.0ms	(- (fma x (/ x y) y) (/ (pow z 2) y))
36.0ms	(fma x (/ x y) y)
25.0ms	(/ (pow z 2) y)

simplify91.0ms

Algorithm

egg-herbie

Counts

178 → 178

Iterations

Useful iterations: 2 (63.0ms)

Iter	Nodes	Cost
0	786	3123
1	2585	2147
2	5001	2004

prune308.0ms

Pruning

7 alts after pruning (6 fresh and 1 done)

Merged error: 0.0b

regimes184.0ms

Accuracy

68.1% (2.0b remaining)

Error of 2.6b against oracle of 0.6b and baseline of 6.8b

bsearch176.0ms

Steps

Iters	Range		Point
9	4.5499695502683e+145	3.561053502382892e+154	1.3231454384958713e+154
10	-7.806677322421866e+160	-2.4992896547478044e+150	-1.3464060117545458e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	50	34
1	54	34
2	54	34

end0.0ms

sample1.3s

Algorithm

intervals

Results

966.0ms

13493×

body

valid