Details

sample22.0ms

Algorithm

intervals

Results

6.0ms	54×	body	1280	valid
4.0ms	40×	body	640	valid
3.0ms	128×	body	80	valid
2.0ms	26×	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: 30.7b

Counts

2 → 1

localize6.0ms

Local error

Found 3 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.6b	(cbrt x)
3.3b	(- (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))

series418.0ms

Counts

3 → 9

Calls

3 calls:

87.0ms	(cbrt (+ x 1.0))
181.0ms	(cbrt x)
150.0ms	(- (cbrt (+ x 1.0)) (cbrt x))

simplify56.0ms

Algorithm

egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 2 (44.0ms)

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

prune223.0ms

Filtered

108 candidates to 69 candidates (63.9%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	98	10	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	99	10	109

Merged error: 19.3b

Counts

109 → 10

localize12.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.6b	(cbrt x)
30.8b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

31×	`cbrt-prod`
30×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
14×	`add-cube-cbrt` `cbrt-div`
11×	`pow1`
9×	`swap-sqr`
8×	`pow1/3`
7×	`flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
6×	`add-exp-log`
4×	`expm1-log1p-u` `frac-times` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp` `unswap-sqr`
2×	`associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

4 → 94

Calls

4 calls:

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

series619.0ms

Counts

4 → 12

Calls

4 calls:

89.0ms	(cbrt (+ x 1.0))
102.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
178.0ms	(cbrt x)
249.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify53.0ms

Algorithm

egg-herbie

Counts

106 → 106

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	479	846
1	1610	782
2	5001	727

prune340.0ms

Filtered

106 candidates to 78 candidates (73.6%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	96	10	106
Fresh	2	7	9
Picked	1	0	1
Done	0	0	0
Total	99	17	116

Merged error: 19.3b

Counts

116 → 17

localize18.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.3b	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
0.6b	(cbrt x)
30.8b	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

51×	`cbrt-prod`
49×	`*-un-lft-identity`
37×	`add-sqr-sqrt`
24×	`cbrt-div`
21×	`add-cube-cbrt`
18×	`pow1` `swap-sqr`
14×	`associate-r` `associate-l`
13×	`pow1/3`
12×	`flip3-+` `flip-+` `distribute-lft-out`
8×	`add-exp-log` `frac-times` `unswap-sqr`
4×	`expm1-log1p-u` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod`
1×	`fma-udef`

Counts

4 → 133

Calls

4 calls:

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

series642.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
103.0ms	(* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))
176.0ms	(cbrt x)
253.0ms	(fma (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (* (cbrt (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0)))) (cbrt (cbrt (+ x 1.0))))) (- (cbrt x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 2 (40.0ms)

Iter	Nodes	Cost
0	423	1264
1	1407	1167
2	5002	1078

prune456.0ms

Filtered

145 candidates to 97 candidates (66.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	0	16	16
Picked	1	0	1
Done	0	0	0
Total	145	17	162

Merged error: 19.3b

Counts

162 → 17

localize15.0ms

Local error

Found 4 expressions with local error:

0.3b	(cbrt (+ x 1.0))
0.5b	(pow (cbrt (cbrt (+ x 1.0))) 4)
0.6b	(cbrt x)
30.6b	(fma (cbrt (* (pow (cbrt (cbrt (+ x 1.0))) 4) (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

rewrite12.0ms

Algorithm

rewrite-expression-head

Rules

18×	`cbrt-prod`
14×	`*-un-lft-identity`
10×	`add-sqr-sqrt` `add-cube-cbrt` `unpow-prod-down`
5×	`pow1` `add-exp-log`
4×	`expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`cbrt-div` `pow-pow` `distribute-lft-out`
1×	`pow-to-exp` `flip3-+` `pow-exp` `flip-+` `fma-udef` `sqr-pow`

Counts

4 → 66

Calls

4 calls:

3.0ms	(cbrt (+ x 1.0))
6.0ms	(pow (cbrt (cbrt (+ x 1.0))) 4)
1.0ms	(cbrt x)
1.0ms	(fma (cbrt (* (pow (cbrt (cbrt (+ x 1.0))) 4) (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

series678.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(cbrt (+ x 1.0))
154.0ms	(pow (cbrt (cbrt (+ x 1.0))) 4)
179.0ms	(cbrt x)
253.0ms	(fma (cbrt (* (pow (cbrt (cbrt (+ x 1.0))) 4) (* (cbrt (cbrt (+ x 1.0))) (cbrt (cbrt (+ x 1.0)))))) (cbrt (cbrt (+ x 1.0))) (- (cbrt x)))

simplify54.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 2 (45.0ms)

Iter	Nodes	Cost
0	523	737
1	1777	671
2	5002	630

prune270.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

19 alts after pruning (19 fresh and 0 done)

	Pruned	Kept	Total
New	74	4	78
Fresh	1	15	16
Picked	1	0	1
Done	0	0	0
Total	76	19	95

Merged error: 19.2b

Counts

95 → 19

regimes106.0ms

Accuracy

98.2% (0.2b remaining)

Error of 18.9b against oracle of 18.7b and baseline of 29.9b

bsearch112.0ms

Steps

Iters	Range		Point
10	0.005370866090842012	4.21737757242384e+15	3946.0010950283613
10	-7.754703851107508e+72	-6.681514996074174e+59	-4.499110118396043e+61

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	53	32
1	57	32
2	57	32

end0.0ms

sample603.0ms

Algorithm

intervals

Results

218.0ms	1726×	body	1280	valid
122.0ms	1230×	body	640	valid
104.0ms	4098×	body	80	valid
44.0ms	632×	body	320	valid
14.0ms	314×	body	160	valid