Details

sample21.0ms

Algorithm

intervals

Results

7.0ms	256×	body	80	valid
5.0ms	229×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	21	7
1	41	6
2	69	6
3	95	6
4	125	6
5	140	6
6	142	6
7	142	6

prune5.0ms

Filtered

1 candidates to 1 candidates (100.0%)

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: 0.0b

Counts

2 → 2

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (sqrt x) 4.0 (+ x 1.0))
0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
0.0b	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

128×	`times-frac`
95×	`add-sqr-sqrt` `*-un-lft-identity`
67×	`add-cube-cbrt`
16×	`associate-/r*`
14×	`distribute-lft-out--` `difference-of-squares`
10×	`add-exp-log` `add-cbrt-cube`
8×	`div-inv` `associate-/l*`
4×	`cbrt-undiv` `div-exp`
3×	`pow1` `expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
2×	`frac-2neg` `clear-num` `associate-/l/`
1×	`flip3--` `div-sub` `associate-/r/` `flip--` `fma-udef`

Counts

3 → 142

Calls

3 calls:

1.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
3.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
9.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

series165.0ms

Counts

3 → 9

Calls

3 calls:

39.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
44.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
82.0ms	(/ (- x 1.0) (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0))

simplify69.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	627	1691
1	2379	1609
2	5002	1609

prune328.0ms

Filtered

151 candidates to 117 candidates (77.5%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	146	5	151
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	148	5	153

Merged error: 0b

Counts

153 → 5

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma (sqrt x) 4.0 (+ x 1.0))
0.0b	(* (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)
0.0b	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

42×	`add-sqr-sqrt`
37×	`*-un-lft-identity`
31×	`times-frac`
23×	`add-cube-cbrt`
19×	`associate-l`
10×	`add-exp-log` `add-cbrt-cube`
7×	`distribute-lft-out--` `difference-of-squares`
5×	`pow1` `associate-/l*`
3×	`expm1-log1p-u` `associate-r` `associate-/r*` `log1p-expm1-u` `add-log-exp`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`flip3--` `frac-2neg` `div-sub` `pow-prod-down` `associate-l/` `clear-num` `-commutative` `flip--` `fma-udef`

Counts

3 → 90

Calls

3 calls:

1.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
9.0ms	(* (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)
7.0ms	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

series186.0ms

Counts

3 → 9

Calls

3 calls:

35.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
80.0ms	(* (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))) 6.0)
72.0ms	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))

simplify46.0ms

Algorithm

egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	357	827
1	1182	752
2	5001	738

prune220.0ms

Filtered

99 candidates to 77 candidates (77.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	98	1	99
Fresh	1	3	4
Picked	1	0	1
Done	0	0	0
Total	100	4	104

Merged error: 0b

Counts

104 → 4

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (log1p (expm1 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))) 6.0)
0.0b	(log1p (expm1 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))))
0.0b	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))
0.5b	(expm1 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-sqr-sqrt`
24×	`*-un-lft-identity`
16×	`add-cube-cbrt`
15×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
6×	`pow1`
5×	`log1p-expm1-u` `associate-/l*`
4×	`expm1-log1p-u` `distribute-lft-out--` `add-log-exp` `difference-of-squares`
3×	`associate-r` `associate-l` `associate-/r*`
2×	`associate-/l/`
1×	`cbrt-undiv` `log1p-udef` `expm1-log1p` `flip3--` `frac-2neg` `div-sub` `log1p-expm1` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `div-inv` `expm1-udef` `unswap-sqr`

Counts

4 → 82

Calls

4 calls:

3.0ms	(* (log1p (expm1 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))) 6.0)
1.0ms	(log1p (expm1 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))))
6.0ms	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))
1.0ms	(expm1 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))

series544.0ms

Counts

4 → 12

Calls

4 calls:

190.0ms	(* (log1p (expm1 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))) 6.0)
174.0ms	(log1p (expm1 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))))
72.0ms	(/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0)))
107.0ms	(expm1 (/ (- x 1.0) (fma (sqrt x) 4.0 (+ x 1.0))))

simplify42.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (32.0ms)

Iter	Nodes	Cost
0	342	847
1	1085	756
2	5001	737

prune238.0ms

Filtered

94 candidates to 75 candidates (79.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	0	94
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	94	4	98

Merged error: 0b

Counts

98 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (sqrt x) 4.0 (+ x 1.0))
0.0b	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
0.0b	(/ 1 (/ (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0) (- x 1.0)))
0.2b	(/ (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0) (- x 1.0))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

781×	`times-frac`
468×	`add-sqr-sqrt` `*-un-lft-identity`
336×	`add-cube-cbrt`
79×	`associate-/r*`
66×	`distribute-lft-out--` `difference-of-squares`
33×	`div-inv`
32×	`add-exp-log`
20×	`add-cbrt-cube`
19×	`div-exp` `associate-/l*`
11×	`associate-/r/`
10×	`cbrt-undiv`
5×	`pow1` `flip3--` `flip--`
4×	`expm1-log1p-u` `log1p-expm1-u` `add-log-exp`
3×	`rec-exp` `frac-2neg` `1-exp` `clear-num`
1×	`pow-flip` `fma-udef` `associate-/l/` `inv-pow`

Counts

4 → 455

Calls

4 calls:

1.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
3.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
18.0ms	(/ 1 (/ (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0) (- x 1.0)))
9.0ms	(/ (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0) (- x 1.0))

series234.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(fma (sqrt x) 4.0 (+ x 1.0))
48.0ms	(/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0)
72.0ms	(/ 1 (/ (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0) (- x 1.0)))
79.0ms	(/ (/ (fma (sqrt x) 4.0 (+ x 1.0)) 6.0) (- x 1.0))

simplify96.0ms

Algorithm

egg-herbie

Counts

467 → 467

Iterations

Useful iterations: 1 (31.0ms)

Iter	Nodes	Cost
0	1455	6777
1	5001	6250

prune894.0ms

Filtered

467 candidates to 290 candidates (62.1%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	467	0	467
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	467	4	471

Merged error: 0b

Counts

471 → 4

regimes15.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	8
1	14	8

end0.0ms

sample579.0ms

Algorithm

intervals

Results

216.0ms	8000×	body	80	valid
191.0ms	7833×	body	80	nan