Details

sample34.0ms

Algorithm

intervals

Results

14.0ms	276×	body	80	valid
4.0ms	85×	body	80	nan

simplify15.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	18
1	67	18
2	123	18
3	160	18
4	175	18
5	177	18
6	177	18

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: 21.0b

Counts

2 → 1

localize114.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (* b b) (* (* 4.0 a) c))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

8×	`add-sqr-sqrt` `add-log-exp`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity` `sqrt-prod`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--` `log1p-expm1-u`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `fma-neg` `diff-log` `prod-diff`

Counts

4 → 66

Calls

4 calls:

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

series237.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- (* b b) (* (* 4.0 a) c))
47.0ms	(- (* b b) (* (* 4.0 a) c))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
74.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify92.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (85.0ms)

Iter	Nodes	Cost
0	170	540
1	665	506
2	2968	498
3	5001	488

prune280.0ms

Filtered

78 candidates to 62 candidates (79.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	71	7	78
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	7	79

Merged error: 10.6b

Counts

79 → 7

localize117.0ms

Local error

Found 4 expressions with local error:

6.8b	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

17×	`add-sqr-sqrt`
13×	`add-cube-cbrt` `*-un-lft-identity`
10×	`fma-neg` `prod-diff`
9×	`sqrt-prod`
8×	`add-log-exp`
7×	`pow1`
6×	`distribute-lft-neg-in` `distribute-rgt-neg-in` `sqrt-div`
4×	`add-exp-log` `expm1-log1p-u` `flip3--` `add-cbrt-cube` `flip--` `log1p-expm1-u`
3×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`
2×	`neg-mul-1` `diff-log`
1×	`associate--l-` `neg-sub0` `sub-neg` `neg-log` `difference-of-squares`

Counts

4 → 88

Calls

4 calls:

5.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series289.0ms

Counts

4 → 12

Calls

4 calls:

74.0ms	(- (- b) (* (sqrt (sqrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (sqrt (- (* b b) (* (* 4.0 a) c))))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
73.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify184.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (31.0ms)

Iter	Nodes	Cost
0	283	1391
1	998	1121
2	4723	1013
3	5001	1013

prune376.0ms

Filtered

100 candidates to 83 candidates (83.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	3	3	6
Picked	0	1	1
Done	0	0	0
Total	101	6	107

Merged error: 10.6b

Counts

107 → 6

localize122.0ms

Local error

Found 4 expressions with local error:

9.9b	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

5.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series351.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(+ (- b) (* (fabs (cbrt (- (* b b) (* (* 4.0 a) c)))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
71.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
95.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
97.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	391	872
1	1588	795
2	5001	765

prune413.0ms

Filtered

84 candidates to 76 candidates (90.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	83	7	90

Merged error: 10.6b

Counts

90 → 7

localize125.0ms

Local error

Found 4 expressions with local error:

22.9b	(+ (- b) (* (fabs (exp (log (cbrt (- (* b b) (* (* 4.0 a) c)))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
23.1b	(sqrt (- (* b b) (* (* 4.0 a) c)))
24.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))
24.0b	(cbrt (- (* b b) (* (* 4.0 a) c)))

rewrite18.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 72

Calls

4 calls:

5.0ms	(+ (- b) (* (fabs (exp (log (cbrt (- (* b b) (* (* 4.0 a) c)))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
4.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

series384.0ms

Counts

4 → 12

Calls

4 calls:

98.0ms	(+ (- b) (* (fabs (exp (log (cbrt (- (* b b) (* (* 4.0 a) c)))))) (sqrt (cbrt (- (* b b) (* (* 4.0 a) c))))))
83.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
106.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))
96.0ms	(cbrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	393	914
1	1590	815
2	5002	782

prune436.0ms

Filtered

84 candidates to 76 candidates (90.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	83	1	84
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	84	7	91

Merged error: 10.6b

Counts

91 → 7

regimes166.0ms

Accuracy

93.3% (0.8b remaining)

Error of 8.6b against oracle of 7.8b and baseline of 19.8b

bsearch173.0ms

Steps

Iters	Range		Point
8	2.000287750443077e+147	1.6365741300291856e+150	1.091736019600057e+148
8	-7.940186999589029e+157	-2.4392292464634512e+153	-1.3442754169306616e+154

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	59
1	51	59

end0.0ms

sample827.0ms

Algorithm

intervals

Results

442.0ms	8710×	body	80	valid
132.0ms	2898×	body	80	nan