Details

sample68.0ms

Algorithm

intervals

Results

11.0ms	212×	body	80	valid
7.0ms	20×	body	2560	valid
7.0ms	14×	body	640	valid
5.0ms	23×	body	1280	valid
4.0ms	87×	body	80	nan
1.0ms	6×	body	320	valid
0.0ms	1×	body	5120	valid
0.0ms	3×	body	160	valid

simplify12.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

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

prune3.0ms

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

localize11.0ms

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

series64.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c))))) (* 2.0 a))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* 4.0 (* a c)))))
11.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify45.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (36.0ms)

Iter	Nodes	Cost
0	394	773
1	1501	683
2	5002	673

prune156.0ms

Filtered

82 candidates to 63 candidates (23.2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	74	9	83

Merged error: 7.2b

Counts

83 → 9

localize14.0ms

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))))

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

series44.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
9.0ms	(- (* b b) (* 4.0 (* a c)))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))
14.0ms	(sqrt (- (* b b) (* 4.0 (* a c))))

simplify74.0ms

Algorithm

egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 3 (68.0ms)

Iter	Nodes	Cost
0	144	474
1	524	446
2	2276	444
3	5002	442

prune144.0ms

Filtered

66 candidates to 50 candidates (24.2%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	66	0	66
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	66	9	75

Merged error: 7.2b

Counts

75 → 9

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
8.1b	(+ (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
23.4b	(cbrt (- (* b b) (* 4.0 (* a c))))
23.4b	(cbrt (- (* b b) (* 4.0 (* a c))))

rewrite15.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

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

series89.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* 4.0 (* a c)))
31.0ms	(+ (neg b) (* (fabs (cbrt (- (* b b) (* 4.0 (* a c))))) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
26.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))

simplify41.0ms

Algorithm

egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 2 (33.0ms)

Iter	Nodes	Cost
0	349	804
1	1302	725
2	5001	702

prune172.0ms

Filtered

63 candidates to 56 candidates (11.1%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	1	5	6
Picked	0	1	1
Done	0	2	2
Total	63	9	72

Merged error: 7.2b

Counts

72 → 9

localize23.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* 4.0 (* a c)))
16.1b	(+ (neg b) (* (fabs (pow (- (* b b) (* 4.0 (* a c))) 1/3)) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
23.4b	(cbrt (- (* b b) (* 4.0 (* a c))))
26.1b	(pow (- (* b b) (* 4.0 (* a c))) 1/3)

rewrite16.0ms

Algorithm

rewrite-expression-head

Rules

10×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
5×	`pow1` `add-exp-log`
4×	`add-cbrt-cube`
3×	`cbrt-prod` `unpow-prod-down` `pow-unpow`
2×	`cbrt-div` `flip3--` `sum-log` `flip--`
1×	`+-commutative` `neg-sub0` `pow-to-exp` `associate-+l-` `sub-neg` `pow-pow` `flip3-+` `unpow1/3` `pow1/3` `diff-log` `neg-log` `pow-exp` `flip-+` `sqr-pow`

Counts

4 → 56

Calls

4 calls:

4.0ms	(- (* b b) (* 4.0 (* a c)))
4.0ms	(+ (neg b) (* (fabs (pow (- (* b b) (* 4.0 (* a c))) 1/3)) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
3.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
4.0ms	(pow (- (* b b) (* 4.0 (* a c))) 1/3)

series88.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* 4.0 (* a c)))
31.0ms	(+ (neg b) (* (fabs (pow (- (* b b) (* 4.0 (* a c))) 1/3)) (sqrt (cbrt (- (* b b) (* 4.0 (* a c)))))))
24.0ms	(cbrt (- (* b b) (* 4.0 (* a c))))
24.0ms	(pow (- (* b b) (* 4.0 (* a c))) 1/3)

simplify45.0ms

Algorithm

egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 2 (37.0ms)

Iter	Nodes	Cost
0	398	787
1	1524	700
2	5001	677

prune150.0ms

Filtered

68 candidates to 54 candidates (20.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	5	5
Picked	1	0	1
Done	0	3	3
Total	68	9	77

Merged error: 7.2b

Counts

77 → 9

regimes355.0ms

Accuracy

89.5% (2.8b remaining)

Error of 8.8b against oracle of 6.0b and baseline of 32.6b

bsearch116.0ms

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	42	28
1	44	28
2	44	28

end0.0ms

sample1.4s

Algorithm

intervals

Results

332.0ms	6323×	body	80	valid
245.0ms	839×	body	2560	valid
183.0ms	755×	body	1280	valid
125.0ms	2492×	body	80	nan
70.0ms	368×	body	640	valid
32.0ms	76×	body	5120	valid
24.0ms	167×	body	320	valid
9.0ms	96×	body	160	valid

Details

sample68.0ms

simplify12.0ms

prune3.0ms

localize11.0ms

rewrite27.0ms

series64.0ms

simplify45.0ms

prune156.0ms

localize14.0ms

rewrite17.0ms

series44.0ms

simplify74.0ms

prune144.0ms

localize15.0ms

rewrite15.0ms

series89.0ms

simplify41.0ms

prune172.0ms

localize23.0ms

rewrite16.0ms

series88.0ms

simplify45.0ms

prune150.0ms

regimes355.0ms

bsearch116.0ms

simplify2.0ms

end0.0ms

sample1.4s

Profiling