Details

sample65.0ms

Algorithm

intervals

Results

11.0ms	212×	body	80	valid
6.0ms	20×	body	2560	valid
5.0ms	23×	body	1280	valid
4.0ms	87×	body	80	nan
3.0ms	14×	body	640	valid
1.0ms	6×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	24	9
1	45	9
2	79	9
3	97	9
4	105	9
5	105	9

prune4.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 31.1b

Counts

2 → 1

localize16.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.7b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.0b	(- (* b b) (* (* 4.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

11.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

29.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	396	773
1	1550	683
2	5001	673

prune157.0ms

Filtered

82 candidates to 63 candidates (23.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	8	83

Merged error: 7.2b

Counts

83 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 4.0 a) c))
1.0b	(- (* b b) (* (* 4.0 a) c))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite15.0ms

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` `flip3--` `sqrt-div` `add-cbrt-cube` `flip--`
2×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 54

Calls

4 calls:

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

series47.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 4.0 a) c))
8.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify88.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (82.0ms)

Iter	Nodes	Cost
0	147	474
1	570	446
2	2550	444
3	5001	442

prune143.0ms

Filtered

66 candidates to 50 candidates (24.2%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	66	8	74

Merged error: 7.2b

Counts

74 → 8

localize17.0ms

Local error

Found 4 expressions with local error:

1.4b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
2.0b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.4b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

90×	`times-frac`
84×	`add-sqr-sqrt`
83×	`*-un-lft-identity`
39×	`add-cube-cbrt`
30×	`associate-/l*`
22×	`distribute-lft-out--` `difference-of-squares`
18×	`add-exp-log` `add-cbrt-cube`
14×	`sqrt-prod`
11×	`distribute-rgt-neg-in`
8×	`associate-/r*` `add-log-exp`
7×	`cbrt-undiv` `div-exp`
6×	`associate-/r/`
5×	`pow1` `flip3--` `flip--`
4×	`div-inv`
3×	`associate-/l/`
2×	`frac-2neg` `sqrt-div` `diff-log` `prod-exp` `clear-num` `cbrt-unprod`
1×	`associate--l-` `neg-sub0` `sub-neg` `rem-sqrt-square` `sqrt-pow1` `flip3-+` `pow1/2` `neg-log` `flip-+`

Counts

4 → 154

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
16.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
12.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series132.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
44.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
56.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
17.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify116.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (92.0ms)

Iter	Nodes	Cost
0	646	2693
1	3163	2447
2	5003	2434

prune278.0ms

Filtered

166 candidates to 111 candidates (33.1%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	163	3	166
Fresh	1	4	5
Picked	0	1	1
Done	0	2	2
Total	164	10	174

Merged error: 7.1b

Counts

174 → 10

localize25.0ms

Local error

Found 4 expressions with local error:

15.6b	(cbrt (+ 0 (* 4.0 (* a c))))
15.6b	(cbrt (+ 0 (* 4.0 (* a c))))
15.6b	(cbrt (+ 0 (* 4.0 (* a c))))
22.7b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite11.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 54

Calls

4 calls:

2.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
2.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
2.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series66.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
17.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
18.0ms	(cbrt (+ 0 (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 2 (54.0ms)

Iter	Nodes	Cost
0	257	548
1	1011	508
2	5001	492

prune184.0ms

Filtered

66 candidates to 61 candidates (7.6%)

Pruning

10 alts after pruning (6 fresh and 4 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	6	6
Picked	0	1	1
Done	0	3	3
Total	66	10	76

Merged error: 7.1b

Counts

76 → 10

regimes410.0ms

Accuracy

89.3% (2.9b remaining)

Error of 8.8b against oracle of 5.9b and baseline of 32.6b

bsearch119.0ms

Steps

Iters	Range	Point
10	5.5981910563155256e+85	9.646889156889423e+104	9.075371034647116e+86
11	5.161507994152902e-229	1.548877845421406e-196	1.1260596000274454e-196
5	-4.3562246007774435e+118	-1.8745594453170666e+118	-3.926021394052593e+118

Iters

Range

Point

5.5981910563155256e+85

9.646889156889423e+104

9.075371034647116e+86

5.161507994152902e-229

1.548877845421406e-196

1.1260596000274454e-196

-4.3562246007774435e+118

-1.8745594453170666e+118

-3.926021394052593e+118

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	46	28
1	48	28
2	48	28

end0.0ms

sample1.4s

Algorithm

intervals

Results

336.0ms	6323×	body	80	valid
249.0ms	839×	body	2560	valid
184.0ms	755×	body	1280	valid
124.0ms	2492×	body	80	nan
73.0ms	368×	body	640	valid
27.0ms	76×	body	5120	valid
26.0ms	167×	body	320	valid
9.0ms	96×	body	160	valid

Details

sample65.0ms

simplify13.0ms

prune4.0ms

localize16.0ms

rewrite27.0ms

series66.0ms

simplify50.0ms

prune157.0ms

localize15.0ms

rewrite15.0ms

series47.0ms

simplify88.0ms

prune143.0ms

localize17.0ms

rewrite45.0ms

series132.0ms

simplify116.0ms

prune278.0ms

localize25.0ms

rewrite11.0ms

series66.0ms

simplify63.0ms

prune184.0ms

regimes410.0ms

bsearch119.0ms

simplify2.0ms

end0.0ms

sample1.4s

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