Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	48×	body	1280	valid
3.0ms	138×	body	80	valid
3.0ms	34×	body	640	valid
1.0ms	22×	body	320	valid
1.0ms	14×	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: 28.1b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite17.0ms

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)
9.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

series419.0ms

Counts

3 → 9

Calls

3 calls:

88.0ms	(cbrt (+ x 1.0))
177.0ms	(cbrt x)
154.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify61.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (49.0ms)

Iter	Nodes	Cost
0	430	1315
1	1394	1045
2	5001	981

prune219.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	97	11	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	11	109

Merged error: 17.2b

Counts

109 → 11

localize8.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.5b	(- (cbrt (+ x 1.0)) (cbrt x))
7.8b	(log (- (cbrt (+ x 1.0)) (cbrt x)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

72×	`cbrt-prod`
65×	`*-un-lft-identity`
51×	`add-sqr-sqrt`
42×	`prod-diff`
35×	`add-cube-cbrt`
10×	`log-prod` `distribute-lft-out`
8×	`difference-of-squares`
7×	`fma-neg`
6×	`distribute-lft-out--` `add-log-exp`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u`
2×	`log-div` `cbrt-div` `flip3--` `pow1/3` `flip--`
1×	`sub-neg` `flip3-+` `diff-log` `rem-log-exp` `log-pow` `flip-+`

Counts

4 → 122

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
1.0ms	(cbrt x)
9.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
10.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))

series642.0ms

Counts

4 → 12

Calls

4 calls:

92.0ms	(cbrt (+ x 1.0))
184.0ms	(cbrt x)
157.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
207.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))

simplify72.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (56.0ms)

Iter	Nodes	Cost
0	619	1676
1	2175	1385
2	5002	1322

prune333.0ms

Filtered

134 candidates to 88 candidates (65.7%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	128	6	134
Fresh	3	7	10
Picked	0	1	1
Done	0	0	0
Total	131	14	145

Merged error: 11.1b

Counts

145 → 14

localize21.0ms

Local error

Found 4 expressions with local error:

0.8b	(pow (cbrt x) 3)
2.4b	(- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3))
5.8b	(log (- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3)))
7.8b	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

rewrite135.0ms

Algorithm

rewrite-expression-head

Rules

360×	`prod-diff`
358×	`cbrt-prod`
342×	`*-un-lft-identity`
331×	`unpow-prod-down` `cube-prod`
326×	`add-sqr-sqrt`
206×	`add-cube-cbrt`
72×	`difference-of-squares`
64×	`sqr-pow`
56×	`log-prod`
46×	`distribute-lft-out`
40×	`cube-mult` `unpow3`
26×	`distribute-lft-out--`
24×	`cbrt-div`
21×	`flip3-+` `flip-+`
20×	`log-div` `fma-neg`
16×	`frac-add`
8×	`frac-times`
7×	`pow1` `add-exp-log`
6×	`add-log-exp`
4×	`expm1-log1p-u` `associate-r/` `associate-l/` `add-cbrt-cube` `log1p-expm1-u`
3×	`pow-unpow`
2×	`difference-cubes` `flip3--` `pow-pow` `rem-log-exp` `log-pow` `flip--`
1×	`pow-to-exp` `sub-neg` `pow1/3` `diff-log` `pow-exp` `rem-cube-cbrt`

Counts

4 → 574

Calls

4 calls:

3.0ms	(pow (cbrt x) 3)
35.0ms	(- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3))
43.0ms	(log (- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3)))
14.0ms	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

series817.0ms

Counts

4 → 12

Calls

4 calls:

224.0ms	(pow (cbrt x) 3)
58.0ms	(- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3))
188.0ms	(log (- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3)))
348.0ms	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

simplify130.0ms

Algorithm

egg-herbie

Counts

586 → 586

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1680	9752
1	5001	4965

prune579.0ms

Filtered

586 candidates to 108 candidates (18.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	584	2	586
Fresh	9	3	12
Picked	1	0	1
Done	1	0	1
Total	595	5	600

Merged error: 2.3b

Counts

600 → 5

localize16.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.4b	(exp (- (log 1.0) (log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))))
7.8b	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

rewrite37.0ms

Algorithm

rewrite-expression-head

Rules

48×	`cbrt-div`
42×	`flip3-+` `flip-+`
39×	`exp-sum`
36×	`log-div`
32×	`frac-add`
21×	`*-un-lft-identity`
19×	`add-sqr-sqrt`
18×	`associate--r-`
17×	`pow1` `add-cube-cbrt`
16×	`frac-times` `prod-diff`
13×	`log-pow`
8×	`exp-prod` `associate-r/` `associate-l/`
6×	`cbrt-prod` `log-prod`
5×	`add-exp-log` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `distribute-lft-out--`
3×	`associate--l+`
2×	`pow1/3` `rem-exp-log`
1×	`sub-neg` `exp-diff` `diff-log` `rem-log-exp` `difference-of-squares`

Counts

4 → 117

Calls

4 calls:

1.0ms	(cbrt x)
1.0ms	(cbrt x)
12.0ms	(exp (- (log 1.0) (log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))))
15.0ms	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

series1.2s

Counts

4 → 12

Calls

4 calls:

187.0ms	(cbrt x)
184.0ms	(cbrt x)
517.0ms	(exp (- (log 1.0) (log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))))
341.0ms	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

simplify75.0ms

Algorithm

egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 1 (32.0ms)

Iter	Nodes	Cost
0	1557	5860
1	5001	5088

prune487.0ms

Filtered

129 candidates to 90 candidates (69.8%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	120	9	129
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	121	13	134

Merged error: 0.4b

Counts

134 → 13

regimes89.0ms

Accuracy

0% (0.1b remaining)

Error of 0.5b against oracle of 0.5b and baseline of 0.5b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	15
1	15	15

end0.0ms

sample544.0ms

Algorithm

intervals

Results

189.0ms	1681×	body	1280	valid
116.0ms	1263×	body	640	valid
95.0ms	4095×	body	80	valid
40.0ms	640×	body	320	valid
14.0ms	321×	body	160	valid