Details

sample21.0ms

Algorithm

intervals

Results

10.0ms

266×

body

valid

simplify59.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	8
1	39	8
2	64	8
3	115	8
4	207	8
5	465	8
6	1337	8
7	5001	8

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.9b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(- (* t z) x)
0.0b	(+ x (/ (- (* y z) x) (- (* t z) x)))
0.5b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
11.1b	(/ (- (* y z) x) (- (* t z) x))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

46×	`*-un-lft-identity`
25×	`times-frac`
24×	`add-sqr-sqrt` `add-cube-cbrt`
11×	`distribute-lft-out`
8×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
7×	`associate-/r` `associate-/l`
4×	`pow1` `expm1-log1p-u` `div-sub` `associate-/r/` `log1p-expm1-u` `associate-/l/`
3×	`flip3--` `fma-def` `flip3-+` `prod-diff` `flip--` `flip-+`
2×	`cbrt-undiv` `associate-+r-` `frac-2neg` `div-exp` `clear-num` `div-inv`
1×	`+-commutative` `sub-neg` `fma-neg` `diff-log` `sum-log`

Counts

4 → 113

Calls

4 calls:

5.0ms	(- (* t z) x)
11.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
15.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
13.0ms	(/ (- (* y z) x) (- (* t z) x))

series280.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(- (* t z) x)
81.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
115.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
60.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify68.0ms

Algorithm

egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	453	1085
1	1987	1003
2	5001	1002

prune350.0ms

Filtered

125 candidates to 93 candidates (74.4%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))) (+ x 1.0))
1.8b	(/ y (- (* t z) x))
2.2b	(fma (/ y (- (* t z) x)) z x)
4.1b	(/ x (- (* t z) x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
47×	`times-frac`
32×	`add-cube-cbrt`
12×	`associate-/l*`
10×	`add-exp-log` `associate-/r*` `add-cbrt-cube` `difference-of-squares`
7×	`distribute-lft-out`
6×	`associate-/r/`
5×	`distribute-lft-out--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`associate-/l/`
1×	`flip3-+` `div-sub` `flip-+` `fma-udef`

Counts

4 → 125

Calls

4 calls:

18.0ms	(/ (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))) (+ x 1.0))
9.0ms	(/ y (- (* t z) x))
1.0ms	(fma (/ y (- (* t z) x)) z x)
6.0ms	(/ x (- (* t z) x))

series267.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(/ (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))) (+ x 1.0))
28.0ms	(/ y (- (* t z) x))
57.0ms	(fma (/ y (- (* t z) x)) z x)
61.0ms	(/ x (- (* t z) x))

simplify56.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	488	1388
1	1679	1305
2	5002	1301

prune417.0ms

Filtered

137 candidates to 105 candidates (76.6%)

Pruning

9 alts after pruning (9 fresh and 0 done)

Merged error: 0.5b

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(/ (+ x 1.0) (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))))
1.8b	(/ y (- (* t z) x))
2.2b	(fma (/ y (- (* t z) x)) z x)
4.1b	(/ x (- (* t z) x))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

57×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
47×	`times-frac`
32×	`add-cube-cbrt`
12×	`associate-/r*`
10×	`add-exp-log` `add-cbrt-cube` `associate-/l*` `difference-of-squares`
7×	`distribute-lft-out`
6×	`associate-/r/`
5×	`distribute-lft-out--`
4×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `flip--` `div-inv`
2×	`associate-/l/`
1×	`flip3-+` `flip-+` `fma-udef`

Counts

4 → 124

Calls

4 calls:

18.0ms	(/ (+ x 1.0) (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))))
6.0ms	(/ y (- (* t z) x))
1.0ms	(fma (/ y (- (* t z) x)) z x)
6.0ms	(/ x (- (* t z) x))

series269.0ms

Counts

4 → 12

Calls

4 calls:

124.0ms	(/ (+ x 1.0) (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))))
28.0ms	(/ y (- (* t z) x))
57.0ms	(fma (/ y (- (* t z) x)) z x)
60.0ms	(/ x (- (* t z) x))

simplify51.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (12.0ms)

Iter	Nodes	Cost
0	424	1343
1	1484	1277
2	5002	1277

prune431.0ms

Filtered

136 candidates to 103 candidates (75.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (* (- (* y z) x) (/ 1 (- (* t z) x))))
0.2b	(/ 1 (- (* t z) x))
0.5b	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
11.0b	(* (- (* y z) x) (/ 1 (- (* t z) x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

39×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
32×	`times-frac`
30×	`add-cube-cbrt`
19×	`add-exp-log`
15×	`associate-r`
13×	`add-cbrt-cube`
7×	`pow1` `associate-/r*`
6×	`associate-/r/` `associate-/l*` `add-log-exp`
5×	`div-exp`
4×	`expm1-log1p-u` `flip3--` `prod-exp` `flip--` `log1p-expm1-u` `distribute-lft-out`
3×	`cbrt-undiv` `fma-def` `flip3-+` `associate-l` `flip-+` `div-inv` `unswap-sqr`
2×	`frac-times` `rec-exp` `frac-2neg` `1-exp` `associate-*l/` `clear-num` `cbrt-unprod` `associate-/l/`
1×	`+-commutative` `pow-flip` `associate-r/` `pow-prod-down` `sum-log` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 132

Calls

4 calls:

3.0ms	(+ x (* (- (* y z) x) (/ 1 (- (* t z) x))))
10.0ms	(/ 1 (- (* t z) x))
7.0ms	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
13.0ms	(* (- (* y z) x) (/ 1 (- (* t z) x)))

series302.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(+ x (* (- (* y z) x) (/ 1 (- (* t z) x))))
32.0ms	(/ 1 (- (* t z) x))
124.0ms	(/ (+ x (* (- (* y z) x) (/ 1 (- (* t z) x)))) (+ x 1.0))
57.0ms	(* (- (* y z) x) (/ 1 (- (* t z) x)))

simplify69.0ms

Algorithm

egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	489	1257
1	2101	1127
2	5001	1095

prune607.0ms

Filtered

144 candidates to 101 candidates (70.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

Merged error: 0.5b

regimes158.0ms

Accuracy

34.3% (2.9b remaining)

Error of 3.1b against oracle of 0.3b and baseline of 4.6b

bsearch91.0ms

Steps

Iters	Range		Point
7	1.4411111155905935e-45	1.5655308314484462e-43	6.761309753126492e-45
9	-2.666222699328035e+140	-2.784784425602926e+135	-4.5810378724450705e+135

simplify5.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	24
1	38	24

end0.0ms

sample527.0ms

Algorithm

intervals

Results

317.0ms

8322×

body

valid