Details

analyze484.0ms

Algorithm: search

sample49.0ms

Algorithm

intervals

Results

13.0ms	36×	body	2560	valid
9.0ms	165×	body	80	valid
7.0ms	27×	body	1280	valid
3.0ms	14×	body	640	valid
2.0ms	29×	body	80	nan
1.0ms	4×	body	5120	valid
1.0ms	22×	body	80	invalid
1.0ms	8×	body	320	valid
0.0ms	2×	body	160	valid

simplify11.0ms

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

localize13.0ms

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)))

rewrite30.0ms

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:

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

series73.0ms

Counts

4 → 12

Calls

4 calls:

28.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
17.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
12.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify49.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (40.0ms)

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

prune167.0ms

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

localize18.0ms

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)))

rewrite47.0ms

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:

4.0ms	(- (* b b) (* (* 4.0 a) c))
17.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
16.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series142.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 4.0 a) c))
49.0ms	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
68.0ms	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify124.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (98.0ms)

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

prune309.0ms

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

localize19.0ms

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)))

rewrite26.0ms

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:

9.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
7.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series47.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
9.0ms	(- (* b b) (* (* 4.0 a) c))
2.0ms	(/ (* 2.0 a) (* 4.0 (* a c)))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (59.0ms)

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

prune134.0ms

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

localize14.0ms

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)))

rewrite35.0ms

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:

16.0ms	(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
8.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
4.0ms	(- (* b b) (* (* 4.0 a) c))
4.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series100.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(/ 1 (* (/ 0.5 c) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
17.0ms	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
10.0ms	(- (* b b) (* (* 4.0 a) c))
16.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify55.0ms

Algorithm

egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 2 (44.0ms)

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

prune118.0ms

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

regimes351.0ms

Accuracy

92.7% (1.8b remaining)

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

bsearch685.0ms

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

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	24
1	40	24

end0.0ms

analyze482.0ms

Algorithm: search

sample1.3s

Algorithm

intervals

Results

332.0ms	1041×	body	2560	valid
283.0ms	5202×	body	80	valid
223.0ms	856×	body	1280	valid
95.0ms	474×	body	640	valid
36.0ms	221×	body	320	valid
36.0ms	95×	body	5120	valid
34.0ms	666×	body	80	nan
20.0ms	371×	body	80	invalid
13.0ms	111×	body	160	valid

Details

analyze484.0ms

sample49.0ms

simplify11.0ms

prune4.0ms

localize13.0ms

rewrite30.0ms

series73.0ms

simplify49.0ms

prune167.0ms

localize18.0ms

rewrite47.0ms

series142.0ms

simplify124.0ms

prune309.0ms

localize19.0ms

rewrite26.0ms

series47.0ms

simplify67.0ms

prune134.0ms

localize14.0ms

rewrite35.0ms

series100.0ms

simplify55.0ms

prune118.0ms

regimes351.0ms

bsearch685.0ms

simplify2.0ms

end0.0ms

analyze482.0ms

sample1.3s

Profiling