Details

sample27.0ms

Algorithm

intervals

Results

15.0ms

263×

body

valid

simplify53.0ms

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

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 9.0b

Counts

2 → 1

localize11.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (/ (- (* y z) x) (- (* t z) x)))
0.2b	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
10.8b	(/ (- (* y z) x) (- (* t z) x))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 95

Calls

3 calls:

11.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
15.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
9.0ms	(/ (- (* y z) x) (- (* t z) x))

series273.0ms

Counts

3 → 9

Calls

3 calls:

86.0ms	(+ x (/ (- (* y z) x) (- (* t z) x)))
122.0ms	(/ (+ x (/ (- (* y z) x) (- (* t z) x))) (+ x 1.0))
64.0ms	(/ (- (* y z) x) (- (* t z) x))

simplify49.0ms

Algorithm

egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	398	994
1	1427	934
2	5001	932

prune267.0ms

Filtered

104 candidates to 79 candidates (76.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	99	5	104
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	100	5	105

Merged error: 0.3b

Counts

105 → 5

localize12.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))) (+ x 1.0))
1.7b	(/ x (- (* t z) x))
2.3b	(fma (/ y (- (* t z) x)) z x)
2.4b	(/ y (- (* t z) x))

rewrite33.0ms

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:

17.0ms	(/ (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))) (+ x 1.0))
6.0ms	(/ x (- (* t z) x))
1.0ms	(fma (/ y (- (* t z) x)) z x)
6.0ms	(/ y (- (* t z) x))

series259.0ms

Counts

4 → 12

Calls

4 calls:

115.0ms	(/ (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))) (+ x 1.0))
60.0ms	(/ x (- (* t z) x))
55.0ms	(fma (/ y (- (* t z) x)) z x)
29.0ms	(/ y (- (* t z) x))

simplify55.0ms

Algorithm

egg-herbie

Counts

137 → 137

Iterations

Useful iterations: 2 (40.0ms)

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

prune382.0ms

Filtered

137 candidates to 105 candidates (76.6%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	133	4	137
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	135	7	142

Merged error: 0b

Counts

142 → 7

localize14.0ms

Local error

Found 4 expressions with local error:

0.3b	(/ (+ x 1.0) (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))))
1.7b	(/ x (- (* t z) x))
2.3b	(fma (/ y (- (* t z) x)) z x)
2.4b	(/ y (- (* t z) x))

rewrite31.0ms

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:

14.0ms	(/ (+ x 1.0) (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))))
6.0ms	(/ x (- (* t z) x))
1.0ms	(fma (/ y (- (* t z) x)) z x)
6.0ms	(/ y (- (* t z) x))

series262.0ms

Counts

4 → 12

Calls

4 calls:

117.0ms	(/ (+ x 1.0) (- (fma (/ y (- (* t z) x)) z x) (/ x (- (* t z) x))))
60.0ms	(/ x (- (* t z) x))
55.0ms	(fma (/ y (- (* t z) x)) z x)
30.0ms	(/ y (- (* t z) x))

simplify69.0ms

Algorithm

egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 1 (19.0ms)

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

prune342.0ms

Filtered

136 candidates to 103 candidates (75.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	136	0	136
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	136	7	143

Merged error: 0b

Counts

143 → 7

localize19.0ms

Local error

Found 4 expressions with local error:

1.0b	(* (* (cbrt y) (cbrt y)) (/ (cbrt y) (- (* t z) x)))
1.7b	(/ (cbrt y) (- (* t z) x))
1.7b	(/ x (- (* t z) x))
2.3b	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (- (* t z) x))) z x)

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

47×	`times-frac`
45×	`add-sqr-sqrt`
40×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate-r`
22×	`cbrt-prod`
20×	`add-exp-log`
13×	`add-cbrt-cube`
9×	`pow1` `associate-/l*`
6×	`prod-exp` `associate-/r*` `associate-/r/` `cbrt-unprod`
4×	`cbrt-undiv` `expm1-log1p-u` `div-exp` `log1p-expm1-u` `add-log-exp`
3×	`flip3--` `pow-prod-down` `flip--` `div-inv` `unswap-sqr`
2×	`frac-2neg` `clear-num`
1×	`associate-r/` `associate-l` `-commutative` `fma-udef`

Counts

4 → 133

Calls

4 calls:

15.0ms	(* (* (cbrt y) (cbrt y)) (/ (cbrt y) (- (* t z) x)))
7.0ms	(/ (cbrt y) (- (* t z) x))
5.0ms	(/ x (- (* t z) x))
1.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (- (* t z) x))) z x)

series293.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(* (* (cbrt y) (cbrt y)) (/ (cbrt y) (- (* t z) x)))
101.0ms	(/ (cbrt y) (- (* t z) x))
60.0ms	(/ x (- (* t z) x))
82.0ms	(fma (* (* (cbrt y) (cbrt y)) (/ (cbrt y) (- (* t z) x))) z x)

simplify67.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	472	1215
1	2303	1092
2	5001	1048

prune431.0ms

Filtered

145 candidates to 111 candidates (76.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	145	0	145
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	145	7	152

Merged error: 0b

Counts

152 → 7

regimes163.0ms

Accuracy

18% (3.6b remaining)

Error of 3.7b against oracle of 0.2b and baseline of 4.5b

bsearch125.0ms

Steps

Iters	Range		Point
8	1.0781451912101374e-112	3.558568062587178e-108	3.938006923925878e-109
9	1.899229458690153e-308	8.009123962750566e-303	1.2889474225732965e-305

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample634.0ms

Algorithm

intervals

Results

406.0ms

8339×

body

valid