Details

sample18.0ms

Algorithm

intervals

Results

5.0ms	49×	body	1280	valid
4.0ms	48×	body	640	valid
3.0ms	130×	body	80	valid
1.0ms	21×	body	320	valid
0.0ms	8×	body	160	valid

simplify5.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	9	4
1	10	4
2	10	4

prune2.0ms

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: 29.8b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
2.4b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite19.0ms

Algorithm

rewrite-expression-head

Rules

64×	`cbrt-prod`
56×	`*-un-lft-identity`
42×	`prod-diff`
41×	`add-sqr-sqrt`
33×	`add-cube-cbrt`
9×	`distribute-lft-out`
7×	`fma-neg`
5×	`add-log-exp`
4×	`difference-of-squares`
3×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
2×	`cbrt-div` `pow1/3`
1×	`sub-neg` `flip3--` `flip3-+` `diff-log` `flip--` `flip-+`

Counts

3 → 99

Calls

3 calls:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
10.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series427.0ms

Counts

3 → 9

Calls

3 calls:

94.0ms	(cbrt (+ x 1.0))
179.0ms	(cbrt x)
153.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify54.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	428	1315
1	1366	1045
2	5002	1031

prune233.0ms

Filtered

108 candidates to 78 candidates (72.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	96	12	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	97	12	109

Merged error: 17.6b

Counts

109 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
0.6b	(cbrt x)
2.3b	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

1321×	`cbrt-prod`
1261×	`add-sqr-sqrt`
976×	`*-un-lft-identity`
864×	`prod-diff`
547×	`add-cube-cbrt`
490×	`swap-sqr`
396×	`associate-l`
388×	`associate-r`
312×	`unswap-sqr`
173×	`distribute-lft-out`
81×	`difference-of-squares`
78×	`*-commutative`
32×	`fma-neg`
11×	`distribute-lft-out--`
6×	`add-log-exp`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow1/3`
1×	`sub-neg` `flip3--` `diff-log` `flip--`

Counts

4 → 1041

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
1.0ms	(cbrt x)
79.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

series744.0ms

Counts

4 → 12

Calls

4 calls:

181.0ms	(cbrt x)
180.0ms	(cbrt x)
184.0ms	(cbrt x)
197.0ms	(- (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt x)))

simplify329.0ms

Algorithm

egg-herbie

Counts

1053 → 1053

Iterations

Useful iterations: 2 (116.0ms)

Iter	Nodes	Cost
0	1827	31215
1	4147	21496
2	5001	21128

prune706.0ms

Filtered

1053 candidates to 193 candidates (18.3%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	1047	6	1053
Fresh	8	3	11
Picked	0	1	1
Done	0	0	0
Total	1055	10	1065

Merged error: 11.4b

Counts

1065 → 10

localize27.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (cbrt x))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
30.2b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (* (cbrt (cbrt (+ x 1.0))) (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt x)) (cbrt (* (cbrt x) (cbrt x))))))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

95×	`cbrt-prod`
40×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
12×	`swap-sqr` `associate-r` `associate-l`
8×	`unswap-sqr`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3`
2×	`*-commutative`
1×	`fma-udef`

Counts

4 → 100

Calls

4 calls:

2.0ms	(cbrt (cbrt x))
7.0ms	(cbrt (* (cbrt x) (cbrt x)))
11.0ms	(cbrt (* (cbrt x) (cbrt x)))
1.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (* (cbrt (cbrt (+ x 1.0))) (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt x)) (cbrt (* (cbrt x) (cbrt x))))))

series1.3s

Counts

4 → 12

Calls

4 calls:

254.0ms	(cbrt (cbrt x))
285.0ms	(cbrt (* (cbrt x) (cbrt x)))
282.0ms	(cbrt (* (cbrt x) (cbrt x)))
508.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (* (cbrt (cbrt (+ x 1.0))) (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt x)) (cbrt (* (cbrt x) (cbrt x))))))

simplify112.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	280	1041
1	875	967
2	3797	903
3	5001	902

prune524.0ms

Filtered

112 candidates to 85 candidates (75.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	107	5	112
Fresh	2	6	8
Picked	1	0	1
Done	0	1	1
Total	110	12	122

Merged error: 11.4b

Counts

122 → 12

localize38.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt (* (cbrt x) (cbrt x)))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
0.6b	(cbrt (* (cbrt x) (cbrt x)))
30.0b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (* (cbrt (cbrt (+ x 1.0))) (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt x)) (* (cbrt (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (* (cbrt x) (cbrt x))))) (cbrt (* (cbrt (cbrt x)) (cbrt (cbrt x))))))))

rewrite30.0ms

Algorithm

rewrite-expression-head

Rules

129×	`cbrt-prod`
55×	`add-sqr-sqrt`
31×	`add-cube-cbrt` `*-un-lft-identity`
18×	`swap-sqr` `associate-r` `associate-l`
12×	`unswap-sqr`
4×	`pow1` `add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow1/3` `*-commutative`
1×	`fma-udef`

Counts

4 → 121

Calls

4 calls:

10.0ms	(cbrt (* (cbrt x) (cbrt x)))
7.0ms	(cbrt (* (cbrt x) (cbrt x)))
7.0ms	(cbrt (* (cbrt x) (cbrt x)))
1.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (* (cbrt (cbrt (+ x 1.0))) (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt x)) (* (cbrt (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (* (cbrt x) (cbrt x))))) (cbrt (* (cbrt (cbrt x)) (cbrt (cbrt x))))))))

series1.1s

Counts

4 → 12

Calls

4 calls:

272.0ms	(cbrt (* (cbrt x) (cbrt x)))
282.0ms	(cbrt (* (cbrt x) (cbrt x)))
280.0ms	(cbrt (* (cbrt x) (cbrt x)))
300.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (* (cbrt (cbrt (+ x 1.0))) (cbrt (+ x 1.0))) (- (* (* (cbrt (cbrt x)) (cbrt x)) (* (cbrt (* (cbrt (* (cbrt x) (cbrt x))) (cbrt (* (cbrt x) (cbrt x))))) (cbrt (* (cbrt (cbrt x)) (cbrt (cbrt x))))))))

simplify121.0ms

Algorithm

egg-herbie

Counts

133 → 133

Iterations

Useful iterations: 3 (102.0ms)

Iter	Nodes	Cost
0	259	1422
1	842	1318
2	3878	1231
3	5001	1230

prune635.0ms

Filtered

133 candidates to 97 candidates (72.9%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	130	3	133
Fresh	2	8	10
Picked	0	1	1
Done	0	1	1
Total	132	13	145

Merged error: 11.4b

Counts

145 → 13

regimes110.0ms

Accuracy

99% (0.2b remaining)

Error of 11.6b against oracle of 11.4b and baseline of 29.0b

bsearch147.0ms

Steps

Iters	Range		Point
10	1.0482644148039984e-06	3857898261607.3584	3932.660291133761
9	-9.882636446590618e+66	-3.181364016106587e+61	-4.5086911354082924e+61

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	92	85
1	105	85
2	105	85

end0.0ms

sample486.0ms

Algorithm

intervals

Results

169.0ms	1663×	body	1280	valid
98.0ms	1193×	body	640	valid
82.0ms	4200×	body	80	valid
35.0ms	618×	body	320	valid
12.0ms	326×	body	160	valid