Details

sample19.0ms

Algorithm

intervals

Results

5.0ms	52×	body	1280	valid
4.0ms	45×	body	640	valid
3.0ms	132×	body	80	valid
1.0ms	16×	body	320	valid
0.0ms	11×	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: 29.7b

Counts

2 → 1

localize5.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.2b	(- (cbrt (+ x 1.0)) (cbrt x))

rewrite18.0ms

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))

series430.0ms

Counts

3 → 9

Calls

3 calls:

91.0ms	(cbrt (+ x 1.0))
185.0ms	(cbrt x)
154.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify60.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (43.0ms)

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

prune234.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

16 alts after pruning (16 fresh and 0 done)

	Pruned	Kept	Total
New	92	16	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	16	109

Merged error: 18.5b

Counts

109 → 16

localize9.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.2b	(- (cbrt (+ x 1.0)) (cbrt x))
9.5b	(log (- (cbrt (+ x 1.0)) (cbrt x)))

rewrite33.0ms

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)
13.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
10.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))

series618.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ x 1.0))
178.0ms	(cbrt x)
153.0ms	(- (cbrt (+ x 1.0)) (cbrt x))
196.0ms	(log (- (cbrt (+ x 1.0)) (cbrt x)))

simplify73.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (58.0ms)

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

prune558.0ms

Filtered

134 candidates to 88 candidates (65.7%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	124	10	134
Fresh	8	7	15
Picked	1	0	1
Done	0	0	0
Total	133	17	150

Merged error: 11.6b

Counts

150 → 17

localize22.0ms

Local error

Found 4 expressions with local error:

0.7b	(pow (cbrt x) 3)
2.4b	(- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3))
4.6b	(log (- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3)))
9.5b	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

rewrite145.0ms

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)
34.0ms	(- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3))
45.0ms	(log (- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3)))
15.0ms	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

series813.0ms

Counts

4 → 12

Calls

4 calls:

226.0ms	(pow (cbrt x) 3)
65.0ms	(- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3))
178.0ms	(log (- (pow (cbrt (+ x 1.0)) 3) (pow (cbrt x) 3)))
344.0ms	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

simplify128.0ms

Algorithm

egg-herbie

Counts

586 → 586

Iterations

Useful iterations: 1 (38.0ms)

Iter	Nodes	Cost
0	1680	9752
1	5001	4965

prune594.0ms

Filtered

586 candidates to 108 candidates (18.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	583	3	586
Fresh	13	3	16
Picked	1	0	1
Done	0	0	0
Total	597	6	603

Merged error: 2.6b

Counts

603 → 6

localize17.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt x)
0.6b	(cbrt x)
2.6b	(exp (- (log 1.0) (log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))))
9.5b	(log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))

rewrite39.0ms

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)
13.0ms	(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)
177.0ms	(cbrt x)
508.0ms	(exp (- (log 1.0) (log (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (+ (* (cbrt x) (cbrt x)) (* (cbrt (+ x 1.0)) (cbrt x)))))))
339.0ms	(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

prune495.0ms

Filtered

129 candidates to 90 candidates (69.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	125	4	129
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	128	7	135

Merged error: 0.5b

Counts

135 → 7

regimes44.0ms

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

sample495.0ms

Algorithm

intervals

Results

171.0ms	1676×	body	1280	valid
100.0ms	1236×	body	640	valid
83.0ms	4135×	body	80	valid
35.0ms	624×	body	320	valid
12.0ms	329×	body	160	valid