Details

sample280.0ms

Algorithm

intervals

Results

8.0ms	194×	body	80	valid
7.0ms	35×	body	2560	valid
5.0ms	33×	body	1280	valid
3.0ms	97×	body	80	nan
1.0ms	9×	body	640	valid
1.0ms	6×	body	320	valid
1.0ms	2×	body	5120	valid
0.0ms	2×	body	160	valid

simplify16.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	14	7
1	22	7
2	25	7
3	27	7
4	29	7
5	29	7

prune4.0ms

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: 33.0b

Counts

2 → 1

localize11.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

35×	`*-un-lft-identity`
16×	`add-sqr-sqrt`
15×	`add-cube-cbrt` `times-frac`
10×	`distribute-lft-out` `add-log-exp`
6×	`add-exp-log` `add-cbrt-cube`
5×	`pow1` `distribute-rgt-neg-in` `associate-/l*`
3×	`associate-/r*` `sqrt-prod`
2×	`neg-sub0` `associate-+l-` `flip3--` `flip3-+` `sqrt-div` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `div-exp` `neg-log` `clear-num` `div-inv`

Counts

4 → 80

Calls

4 calls:

24.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
7.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
6.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series259.0ms

Counts

4 → 12

Calls

4 calls:

88.0ms	(/ (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) a)
66.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
37.0ms	(- (* b_2 b_2) (* a c))
67.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify46.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	358	790
1	1261	727
2	5001	705

prune227.0ms

Filtered

92 candidates to 69 candidates (75.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	85	7	92
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	85	8	93

Merged error: 5.8b

Counts

93 → 8

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity`
21×	`add-sqr-sqrt`
13×	`add-exp-log` `add-cube-cbrt` `associate-r`
11×	`times-frac`
10×	`add-log-exp`
9×	`add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`prod-exp` `distribute-lft-out`
3×	`flip3-+` `sqrt-prod` `flip-+` `unswap-sqr`
2×	`frac-times` `flip3--` `distribute-rgt-neg-in` `sqrt-div` `div-exp` `associate-*l/` `sum-log` `flip--` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `rec-exp` `sqrt-pow1` `pow1/2` `diff-log` `1-exp` `associate-r/` `pow-prod-down` `neg-log` `un-div-inv` `-commutative` `div-inv`

Counts

4 → 84

Calls

4 calls:

13.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
3.0ms	(- (* b_2 b_2) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series247.0ms

Counts

4 → 12

Calls

4 calls:

87.0ms	(* (+ (- b_2) (sqrt (- (* b_2 b_2) (* a c)))) (/ 1 a))
68.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
32.0ms	(- (* b_2 b_2) (* a c))
61.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 2 (46.0ms)

Iter	Nodes	Cost
0	448	823
1	1968	724
2	5003	682

prune229.0ms

Filtered

96 candidates to 71 candidates (74.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	93	3	96
Fresh	2	4	6
Picked	1	0	1
Done	0	1	1
Total	96	8	104

Merged error: 5.8b

Counts

104 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

0.6b	(cbrt a)
0.9b	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
1.0b	(- (* b_2 b_2) (* a c))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

10×	`*-un-lft-identity` `add-log-exp`
7×	`add-sqr-sqrt`
6×	`add-cube-cbrt`
5×	`pow1`
4×	`add-exp-log` `add-cbrt-cube`
3×	`cbrt-prod` `sqrt-prod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `distribute-lft-out`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `flip3-+` `pow1/2` `pow1/3` `diff-log` `neg-log` `flip-+`

Counts

4 → 53

Calls

4 calls:

1.0ms	(cbrt a)
8.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
4.0ms	(- (* b_2 b_2) (* a c))
7.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series335.0ms

Counts

4 → 12

Calls

4 calls:

174.0ms	(cbrt a)
70.0ms	(+ (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
35.0ms	(- (* b_2 b_2) (* a c))
56.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify92.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 3 (86.0ms)

Iter	Nodes	Cost
0	261	379
1	876	349
2	3154	335
3	5001	333

prune198.0ms

Filtered

65 candidates to 52 candidates (80.0%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	65	8	73

Merged error: 5.8b

Counts

73 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b_2 b_2) (* a c))
1.5b	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
15.0b	(* (/ 1 a) (* a c))
24.1b	(sqrt (- (* b_2 b_2) (* a c)))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

26×	`add-exp-log`
17×	`add-sqr-sqrt`
16×	`*-un-lft-identity` `add-cbrt-cube`
13×	`associate-l`
12×	`add-cube-cbrt` `prod-exp`
10×	`pow1` `add-log-exp`
9×	`times-frac`
6×	`cbrt-unprod`
4×	`div-exp` `sqrt-prod`
3×	`flip3--` `diff-log` `pow-prod-down` `flip--`
2×	`cbrt-undiv` `sub-neg` `rec-exp` `sqrt-div` `1-exp` `distribute-lft-out--` `difference-of-squares`
1×	`associate--l-` `neg-sub0` `rem-sqrt-square` `distribute-rgt-neg-in` `sqrt-pow1` `pow1/2` `associate-r` `neg-log` `associate-l/` `-commutative` `div-inv`

Counts

4 → 82

Calls

4 calls:

4.0ms	(- (* b_2 b_2) (* a c))
11.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
8.0ms	(* (/ 1 a) (* a c))
4.0ms	(sqrt (- (* b_2 b_2) (* a c)))

series167.0ms

Counts

4 → 12

Calls

4 calls:

32.0ms	(- (* b_2 b_2) (* a c))
71.0ms	(- (- b_2) (sqrt (- (* b_2 b_2) (* a c))))
6.0ms	(* (/ 1 a) (* a c))
58.0ms	(sqrt (- (* b_2 b_2) (* a c)))

simplify66.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	407	532
1	1938	427
2	5001	419

prune216.0ms

Filtered

94 candidates to 63 candidates (67.0%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	92	2	94
Fresh	2	3	5
Picked	1	0	1
Done	1	1	2
Total	96	6	102

Merged error: 5.7b

Counts

102 → 6

regimes174.0ms

Accuracy

96.3% (0.9b remaining)

Error of 6.3b against oracle of 5.4b and baseline of 29.3b

bsearch158.0ms

Steps

Iters	Range	Point
8	1.31764557419022e+108	4.7801703725873666e+111	5.8672354253329364e+110
10	-3.3872652091741538e-211	-3.093295365731255e-225	-8.781062788627254e-225
10	-3.0529494422842112e+156	-1.5054982703030158e+138	-2.7863758169125638e+138

Iters

Range

Point

1.31764557419022e+108

4.7801703725873666e+111

5.8672354253329364e+110

-3.3872652091741538e-211

-3.093295365731255e-225

-8.781062788627254e-225

-3.0529494422842112e+156

-1.5054982703030158e+138

-2.7863758169125638e+138

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	43	24
1	43	24

end0.0ms

sample1.0s

Algorithm

intervals

Results

222.0ms	1105×	body	2560	valid
201.0ms	5783×	body	80	valid
144.0ms	898×	body	1280	valid
90.0ms	2921×	body	80	nan
62.0ms	460×	body	640	valid
26.0ms	105×	body	5120	valid
21.0ms	226×	body	320	valid
8.0ms	124×	body	160	valid