Details

analyze444.0ms

Algorithm: search

sample41.0ms

Algorithm

intervals

Results

9.0ms	31×	body	2560	valid
9.0ms	172×	body	80	valid
5.0ms	22×	body	1280	valid
2.0ms	13×	body	640	valid
2.0ms	12×	body	320	valid
1.0ms	29×	body	80	nan
1.0ms	4×	body	5120	valid
1.0ms	21×	body	80	invalid
0.0ms	2×	body	160	valid

simplify9.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	21	9
1	42	9
2	76	9
3	94	9
4	102	9
5	102	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: 31.4b

Counts

2 → 1

localize10.0ms

Local error

Found 4 expressions with local error:

0.2b	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
0.7b	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
1.0b	(- (* b b) (* (* 3.0 a) c))
21.0b	(sqrt (- (* b b) (* (* 3.0 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) (* (* 3.0 a) c)))) (* 3.0 a))
7.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
3.0ms	(- (* b b) (* (* 3.0 a) c))
6.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series65.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ (+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* 3.0 a))
15.0ms	(+ (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))
9.0ms	(- (* b b) (* (* 3.0 a) c))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify47.0ms

Algorithm

egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 2 (38.0ms)

Iter	Nodes	Cost
0	391	774
1	1518	684
2	5001	674

prune160.0ms

Filtered

63 candidates to 82 candidates (-30.2%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	74	8	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	75	8	83

Merged error: 5.9b

Counts

83 → 8

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
2.9b	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
10.0b	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite40.0ms

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) (* (* 3.0 a) c))
16.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
12.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series125.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
45.0ms	(/ (/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (* 3.0 a))
55.0ms	(/ (+ 0 (* 3.0 (* a c))) (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))))
17.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify114.0ms

Algorithm

egg-herbie

Counts

160 → 160

Iterations

Useful iterations: 2 (91.0ms)

Iter	Nodes	Cost
0	634	2580
1	3161	2341
2	5001	2328

prune278.0ms

Filtered

106 candidates to 160 candidates (-50.9%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	158	2	160
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	158	10	168

Merged error: 5.9b

Counts

168 → 10

localize15.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
2.9b	(/ (* 1 (/ 3.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
10.2b	(/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite44.0ms

Algorithm

rewrite-expression-head

Rules

86×	`add-exp-log`
54×	`add-cbrt-cube`
40×	`div-exp`
30×	`prod-exp`
22×	`cbrt-undiv`
16×	`add-sqr-sqrt` `cbrt-unprod`
15×	`*-un-lft-identity`
8×	`times-frac` `1-exp` `associate-/l*`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `sqrt-prod`
4×	`distribute-lft-out--` `difference-of-squares`
3×	`flip3--` `flip--` `associate-/l/`
2×	`distribute-rgt-neg-in` `frac-2neg` `sqrt-div` `clear-num` `associate-/r*` `div-inv`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log` `div-sub` `associate-*r/`

Counts

4 → 101

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
18.0ms	(/ (* 1 (/ 3.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
14.0ms	(/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series79.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(- (* b b) (* (* 3.0 a) c))
35.0ms	(/ (* 1 (/ 3.0 (/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c)))) (* 3.0 a))
21.0ms	(/ (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c)))) (* a c))
14.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify87.0ms

Algorithm

egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	754	1551
1	4055	1213
2	5002	1201

prune143.0ms

Filtered

63 candidates to 113 candidates (-79.4%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	112	1	113
Fresh	1	7	8
Picked	0	1	1
Done	0	1	1
Total	113	10	123

Merged error: 5.9b

Counts

123 → 10

localize16.0ms

Local error

Found 4 expressions with local error:

1.0b	(- (* b b) (* (* 3.0 a) c))
2.9b	(/ (/ (/ 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 3.0 (* a c))) a)
9.8b	(/ (/ 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 3.0 (* a c)))
21.0b	(sqrt (- (* b b) (* (* 3.0 a) c)))

rewrite189.0ms

Algorithm

rewrite-expression-head

Rules

2691×	`times-frac`
1305×	`add-sqr-sqrt`
1304×	`*-un-lft-identity`
872×	`add-cube-cbrt`
221×	`associate-/l*`
216×	`distribute-lft-out--` `difference-of-squares`
178×	`div-inv`
111×	`sqrt-prod`
108×	`distribute-rgt-neg-in`
77×	`associate-/r/`
54×	`add-exp-log` `add-cbrt-cube`
38×	`flip3--` `flip--`
33×	`cbrt-undiv` `div-exp`
10×	`associate-/r*`
6×	`add-log-exp`
5×	`pow1`
4×	`prod-exp` `cbrt-unprod`
2×	`frac-2neg` `sqrt-div` `clear-num` `associate-/l/`
1×	`sub-neg` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `diff-log`

Counts

4 → 1078

Calls

4 calls:

4.0ms	(- (* b b) (* (* 3.0 a) c))
52.0ms	(/ (/ (/ 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 3.0 (* a c))) a)
19.0ms	(/ (/ 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 3.0 (* a c)))
4.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

series99.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- (* b b) (* (* 3.0 a) c))
36.0ms	(/ (/ (/ 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 3.0 (* a c))) a)
39.0ms	(/ (/ 3.0 (- (neg b) (sqrt (- (* b b) (* (* 3.0 a) c))))) (/ 3.0 (* a c)))
15.0ms	(sqrt (- (* b b) (* (* 3.0 a) c)))

simplify331.0ms

Algorithm

egg-herbie

Counts

1090 → 1090

Iterations

Useful iterations: 1 (103.0ms)

Iter	Nodes	Cost
0	3556	24944
1	5002	24439

prune4.3s

Filtered

693 candidates to 1090 candidates (-57.3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	1088	2	1090
Fresh	1	6	7
Picked	1	0	1
Done	1	1	2
Total	1091	9	1100

Merged error: 5.9b

Counts

1100 → 9

regimes430.0ms

Accuracy

95.5% (1.1b remaining)

Error of 6.8b against oracle of 5.7b and baseline of 30.2b

bsearch776.0ms

Steps

Iters	Range	Point
7	4.050479951513376e+135	4.880654514519628e+137	8.867700434171093e+136
11	-1.0290127703161618e-268	-3.772213730540425e-289	-1.997002166149416e-286
10	-9.207710188811221e+154	-1.1313532039137656e+145	-6.827152947135466e+146

Iters

Range

Point

4.050479951513376e+135

4.880654514519628e+137

8.867700434171093e+136

-1.0290127703161618e-268

-3.772213730540425e-289

-1.997002166149416e-286

-9.207710188811221e+154

-1.1313532039137656e+145

-6.827152947135466e+146

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	28
1	45	28

end0.0ms

analyze437.0ms

Algorithm: search

sample1.2s

Algorithm

intervals

Results

298.0ms	1036×	body	2560	valid
267.0ms	5229×	body	80	valid
205.0ms	867×	body	1280	valid
89.0ms	460×	body	640	valid
33.0ms	95×	body	5120	valid
31.0ms	666×	body	80	nan
31.0ms	223×	body	320	valid
18.0ms	368×	body	80	invalid
8.0ms	90×	body	160	valid

Details

analyze444.0ms

sample41.0ms

simplify9.0ms

prune4.0ms

localize10.0ms

rewrite30.0ms

series65.0ms

simplify47.0ms

prune160.0ms

localize15.0ms

rewrite40.0ms

series125.0ms

simplify114.0ms

prune278.0ms

localize15.0ms

rewrite44.0ms

series79.0ms

simplify87.0ms

prune143.0ms

localize16.0ms

rewrite189.0ms

series99.0ms

simplify331.0ms

prune4.3s

regimes430.0ms

bsearch776.0ms

simplify2.0ms

end0.0ms

analyze437.0ms

sample1.2s

Profiling