Details

analyze464.0ms

Algorithm: search

sample47.0ms

Algorithm

intervals

Results

11.0ms	36×	body	2560	valid
9.0ms	165×	body	80	valid
7.0ms	27×	body	1280	valid
3.0ms	4×	body	5120	valid
3.0ms	14×	body	640	valid
1.0ms	29×	body	80	nan
1.0ms	8×	body	320	valid
1.0ms	22×	body	80	invalid
0.0ms	2×	body	160	valid

simplify10.0ms

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

prune4.0ms

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: 32.4b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.6b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
22.5b	(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)))

series67.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
18.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify44.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (35.0ms)

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

prune158.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

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: 6.6b

Counts

83 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

1.2b	(- (* b b) (* (* 4.0 a) c))
2.6b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.0b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
22.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite43.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 148

Calls

4 calls:

3.0ms	(- (* 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))
14.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series130.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* 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))
62.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify112.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (88.0ms)

Iter	Nodes	Cost
0	637	2580
1	3184	2341
2	5001	2328

prune290.0ms

Filtered

106 candidates to 160 candidates (-50.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	156	4	160
Fresh	1	5	6
Picked	1	0	1
Done	0	1	1
Total	158	10	168

Merged error: 6.5b

Counts

168 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

1.1b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
13.5b	(/ (* 2.0 a) (* 4.0 (* a c)))
22.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 70

Calls

4 calls:

8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series45.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
11.0ms	(- (* b b) (* (* 4.0 a) c))
2.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify63.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (55.0ms)

Iter	Nodes	Cost
0	426	636
1	2470	542
2	5003	534

prune129.0ms

Filtered

55 candidates to 82 candidates (-49.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	81	1	82
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	83	9	92

Merged error: 6.5b

Counts

92 → 9

localize13.0ms

Local error

Found 4 expressions with local error:

0.5b	(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
1.1b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
22.5b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 82

Calls

4 calls:

14.0ms	(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms	(- (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)))

series91.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify50.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	439	925
1	1879	796
2	5003	783

prune117.0ms

Filtered

61 candidates to 94 candidates (-54.1%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	91	3	94
Fresh	3	4	7
Picked	1	0	1
Done	0	1	1
Total	95	8	103

Merged error: 6.5b

Counts

103 → 8

regimes336.0ms

Accuracy

92.7% (1.8b remaining)

Error of 7.4b against oracle of 5.7b and baseline of 30.0b

bsearch651.0ms

Steps

Iters	Range	Point
10	7.5269478862554305e+118	3.4285257224842633e+129	1.5359794844464924e+125
7	-1.409110570450201e-229	-1.945100572356394e-231	-3.372635669507716e-231
4	-2.6486253350114714e-06	-1.665290143965488e-06	-2.6103317825148153e-06

Iters

Range

Point

7.5269478862554305e+118

3.4285257224842633e+129

1.5359794844464924e+125

-1.409110570450201e-229

-1.945100572356394e-231

-3.372635669507716e-231

-2.6486253350114714e-06

-1.665290143965488e-06

-2.6103317825148153e-06

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	24
1	40	24

end0.0ms

analyze463.0ms

Algorithm: search

sample1.3s

Algorithm

intervals

Results

327.0ms	1041×	body	2560	valid
286.0ms	5202×	body	80	valid
217.0ms	856×	body	1280	valid
96.0ms	474×	body	640	valid
37.0ms	95×	body	5120	valid
34.0ms	666×	body	80	nan
33.0ms	221×	body	320	valid
20.0ms	371×	body	80	invalid
11.0ms	111×	body	160	valid

Details

analyze464.0ms

sample47.0ms

simplify10.0ms

prune4.0ms

localize12.0ms

rewrite27.0ms

series67.0ms

simplify44.0ms

prune158.0ms

localize16.0ms

rewrite43.0ms

series130.0ms

simplify112.0ms

prune290.0ms

localize16.0ms

rewrite23.0ms

series45.0ms

simplify63.0ms

prune129.0ms

localize13.0ms

rewrite32.0ms

series91.0ms

simplify50.0ms

prune117.0ms

regimes336.0ms

bsearch651.0ms

simplify1.0ms

end0.0ms

analyze463.0ms

sample1.3s

Profiling