Details

analyze478.0ms

Algorithm: search

sample45.0ms

Algorithm

intervals

Results

10.0ms	32×	body	2560	valid
9.0ms	165×	body	80	valid
7.0ms	27×	body	1280	valid
4.0ms	21×	body	640	valid
1.0ms	4×	body	5120	valid
1.0ms	24×	body	80	nan
1.0ms	14×	body	80	invalid
1.0ms	5×	body	320	valid
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: 34.3b

Counts

2 → 1

localize215.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))) (* 2.0 a))
0.3b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite29.0ms

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))
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)))

series68.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ (+ (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))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (37.0ms)

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

prune150.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	75	7	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	76	7	83

Merged error: 6.4b

Counts

83 → 7

localize13.0ms

Local error

Found 4 expressions with local error:

0.1b	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite31.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 114

Calls

4 calls:

13.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
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)))

series73.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(/ 1 (/ (* 2.0 a) (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
16.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

126 → 126

Iterations

Useful iterations: 2 (52.0ms)

Iter	Nodes	Cost
0	528	1585
1	2596	1372
2	5001	1305

prune150.0ms

Filtered

72 candidates to 126 candidates (-75.0%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	123	3	126
Fresh	2	4	6
Picked	0	1	1
Done	0	0	0
Total	125	8	133

Merged error: 6.3b

Counts

133 → 8

localize14.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
0.3b	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
1.2b	(- (* b b) (* (* 4.0 a) c))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

333×	`times-frac`
221×	`*-un-lft-identity`
122×	`add-sqr-sqrt`
121×	`add-cube-cbrt`
87×	`add-exp-log`
58×	`div-exp`
50×	`distribute-lft-out`
31×	`div-inv`
25×	`distribute-rgt-neg-in` `add-cbrt-cube`
21×	`associate-/r*`
17×	`associate-/r/`
15×	`rec-exp` `1-exp`
13×	`cbrt-undiv`
12×	`prod-exp`
10×	`add-log-exp`
9×	`flip3-+` `flip-+`
7×	`associate-/l*`
5×	`pow1`
3×	`sqrt-prod`
2×	`flip3--` `sqrt-div` `sum-log` `flip--` `cbrt-unprod`
1×	`+-commutative` `neg-sub0` `associate-+l-` `sub-neg` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `diff-log` `neg-log` `clear-num` `associate-/l/`

Counts

4 → 263

Calls

4 calls:

20.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
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)))

series74.0ms

Counts

4 → 12

Calls

4 calls:

37.0ms	(/ (/ 1 (* 2.0 a)) (/ 1 (+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))))
14.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
8.0ms	(- (* b b) (* (* 4.0 a) c))
14.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

simplify67.0ms

Algorithm

egg-herbie

Counts

275 → 275

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1114	4690
1	5001	4131

prune317.0ms

Filtered

116 candidates to 275 candidates (-137.1%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	275	0	275
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	275	8	283

Merged error: 6.3b

Counts

283 → 8

localize16.0ms

Local error

Found 4 expressions with local error:

1.3b	(- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))
3.0b	(/ (/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c))))) (* 2.0 a))
10.7b	(/ (+ 0 (* 4.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 4.0 a) c)))))
23.9b	(sqrt (- (* b b) (* (* 4.0 a) c)))

rewrite48.0ms

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:

10.0ms	(- (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)))))
3.0ms	(sqrt (- (* b b) (* (* 4.0 a) c)))

series130.0ms

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

simplify116.0ms

Algorithm

egg-herbie

Counts

166 → 166

Iterations

Useful iterations: 2 (89.0ms)

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

prune257.0ms

Filtered

110 candidates to 166 candidates (-50.9%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	165	1	166
Fresh	0	5	5
Picked	1	0	1
Done	0	2	2
Total	166	8	174

Merged error: 6.3b

Counts

174 → 8

regimes275.0ms

Accuracy

88.5% (3.3b remaining)

Error of 8.8b against oracle of 5.5b and baseline of 34.1b

bsearch844.0ms

Steps

Iters	Range	Point
9	5.009638685812967e+118	3.204623881760618e+124	5.740317269058856e+120
8	-6.601867524827876e-296	-1.3317919070310298e-298	-3.900224684404305e-298
10	-1.6015727729009017e+119	-1.463789235069504e+107	-1.2735944960369567e+116

Iters

Range

Point

5.009638685812967e+118

3.204623881760618e+124

5.740317269058856e+120

-6.601867524827876e-296

-1.3317919070310298e-298

-3.900224684404305e-298

-1.6015727729009017e+119

-1.463789235069504e+107

-1.2735944960369567e+116

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	32
1	52	32

end0.0ms

analyze472.0ms

Algorithm: search

sample1.3s

Algorithm

intervals

Results

336.0ms	1066×	body	2560	valid
285.0ms	5146×	body	80	valid
241.0ms	911×	body	1280	valid
93.0ms	453×	body	640	valid
36.0ms	689×	body	80	nan
33.0ms	88×	body	5120	valid
33.0ms	214×	body	320	valid
23.0ms	419×	body	80	invalid
13.0ms	122×	body	160	valid

Details

analyze478.0ms

sample45.0ms

simplify10.0ms

prune4.0ms

localize215.0ms

rewrite29.0ms

series68.0ms

simplify47.0ms

prune150.0ms

localize13.0ms

rewrite31.0ms

series73.0ms

simplify67.0ms

prune150.0ms

localize14.0ms

rewrite49.0ms

series74.0ms

simplify67.0ms

prune317.0ms

localize16.0ms

rewrite48.0ms

series130.0ms

simplify116.0ms

prune257.0ms

regimes275.0ms

bsearch844.0ms

simplify2.0ms

end0.0ms

analyze472.0ms

sample1.3s

Profiling