Details

sample83.0ms

Algorithm

intervals

Results

16.0ms	33×	body	2560	valid
14.0ms	181×	body	80	valid
14.0ms	27×	body	1280	valid
8.0ms	101×	body	80	nan
6.0ms	22×	body	640	valid
3.0ms	5×	body	5120	valid
1.0ms	5×	body	320	valid
0.0ms	3×	body	160	valid

simplify17.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	22	9
1	43	9
2	83	9
3	110	9
4	118	9
5	118	9

prune3.0ms

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: 35.6b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* 3.0 a) c)
0.4b	(- (* b b) (* (* 3.0 a) c))
1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite25.0ms

Algorithm

rewrite-expression-head

Rules

13×	`*-un-lft-identity`
10×	`pow1` `add-sqr-sqrt` `fma-def` `add-log-exp`
9×	`add-exp-log` `add-cube-cbrt` `add-cbrt-cube`
4×	`expm1-log1p-u` `distribute-rgt-neg-in` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `associate-r` `pow-prod-down` `prod-exp` `sqrt-prod` `cbrt-unprod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `fma-neg` `diff-log` `associate-l` `prod-diff` `neg-log` `*-commutative` `flip-+`

Counts

4 → 80

Calls

4 calls:

5.0ms	(* (* 3.0 a) c)
4.0ms	(- (* b b) (* (* 3.0 a) c))
9.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
5.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series220.0ms

Counts

4 → 12

Calls

4 calls:

23.0ms	(* (* 3.0 a) c)
45.0ms	(- (* b b) (* (* 3.0 a) c))
79.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
73.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (39.0ms)

Iter	Nodes	Cost
0	337	530
1	1440	479
2	5002	467

prune238.0ms

Filtered

92 candidates to 71 candidates (77.2%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	80	12	92
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	81	12	93

Merged error: 14.2b

Counts

93 → 12

localize13.0ms

Local error

Found 4 expressions with local error:

14.7b	(cbrt (* (* 3.0 a) c))
14.7b	(cbrt (* (* 3.0 a) c))
14.7b	(cbrt (* (* 3.0 a) c))
24.4b	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

6×	`add-sqr-sqrt`
5×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`cbrt-prod` `pow1/3` `sqrt-prod`
2×	`sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 50

Calls

4 calls:

4.0ms	(cbrt (* (* 3.0 a) c))
4.0ms	(cbrt (* (* 3.0 a) c))
4.0ms	(cbrt (* (* 3.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

series453.0ms

Counts

4 → 12

Calls

4 calls:

121.0ms	(cbrt (* (* 3.0 a) c))
110.0ms	(cbrt (* (* 3.0 a) c))
97.0ms	(cbrt (* (* 3.0 a) c))
124.0ms	(sqrt (- (* b b) (* (* (cbrt (* (* 3.0 a) c)) (cbrt (* (* 3.0 a) c))) (cbrt (* (* 3.0 a) c)))))

simplify66.0ms

Algorithm

egg-herbie

Counts

62 → 62

Iterations

Useful iterations: 3 (59.0ms)

Iter	Nodes	Cost
0	217	582
1	616	541
2	2127	513
3	5001	511

prune202.0ms

Filtered

62 candidates to 56 candidates (90.3%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	62	0	62
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	62	12	74

Merged error: 14.2b

Counts

74 → 12

localize19.0ms

Local error

Found 4 expressions with local error:

1.1b	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

14×	`*-un-lft-identity`
13×	`add-sqr-sqrt`
10×	`add-cube-cbrt` `fma-def`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `distribute-rgt-neg-in` `add-cbrt-cube` `log1p-expm1-u`
3×	`distribute-lft-neg-in` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
2×	`sum-log` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `neg-mul-1` `flip3-+` `neg-log` `flip-+`

Counts

4 → 78

Calls

4 calls:

8.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series283.0ms

Counts

4 → 12

Calls

4 calls:

78.0ms	(+ (- b) (sqrt (- (* b b) (* (* 3.0 a) c))))
69.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify106.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (99.0ms)

Iter	Nodes	Cost
0	234	620
1	888	589
2	3709	574
3	5001	572

prune317.0ms

Filtered

90 candidates to 80 candidates (88.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	90	12	102

Merged error: 14.2b

Counts

102 → 12

localize26.0ms

Local error

Found 4 expressions with local error:

22.8b	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (sqrt (- (* b b) (* (* 3.0 a) c))))
24.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))
24.4b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-sqr-sqrt`
9×	`sqrt-prod`
7×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
6×	`sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
3×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`
1×	`fma-udef`

Counts

4 → 61

Calls

4 calls:

1.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (sqrt (- (* b b) (* (* 3.0 a) c))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series357.0ms

Counts

4 → 12

Calls

4 calls:

151.0ms	(fma (- (* (cbrt b) (cbrt b))) (cbrt b) (sqrt (- (* b b) (* (* 3.0 a) c))))
70.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
65.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify81.0ms

Algorithm

egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 3 (73.0ms)

Iter	Nodes	Cost
0	181	607
1	594	569
2	2447	561
3	5001	553

prune302.0ms

Filtered

73 candidates to 64 candidates (87.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	71	2	73
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	72	13	85

Merged error: 14.2b

Counts

85 → 13

regimes360.0ms

Accuracy

86.7% (2.9b remaining)

Error of 15.6b against oracle of 12.7b and baseline of 34.5b

bsearch140.0ms

Steps

Iters	Range		Point
10	9.238381642553218e-43	2.4366564965413383e-29	1.4283457991144297e-30
11	-4.6778596556519216e+169	-3.105074477202361e+149	-6.248166611508614e+151

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	38	29
1	38	29

end0.0ms

sample1.3s

Algorithm

intervals

Results

286.0ms	1054×	body	2560	valid
283.0ms	5873×	body	80	valid
201.0ms	902×	body	1280	valid
136.0ms	2916×	body	80	nan
74.0ms	428×	body	640	valid
37.0ms	101×	body	5120	valid
31.0ms	241×	body	320	valid
9.0ms	107×	body	160	valid