Details

analyze958.0ms

Algorithm: search

sample30.0ms

Algorithm

intervals

Results

20.0ms

256×

body

valid

simplify41.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	55	18
1	138	18
2	450	18
3	1597	18
4	5001	18

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: 29.9b

Counts

2 → 1

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
0.1b	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
0.1b	(* (+ (* x 4.16438922228) 78.6994924154) x)
28.9b	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

rewrite57.0ms

Algorithm

rewrite-expression-head

Rules

18×	`add-sqr-sqrt`
15×	`add-exp-log` `add-cbrt-cube`
12×	`add-cube-cbrt` `*-un-lft-identity`
10×	`pow1`
9×	`associate-r` `associate-l`
8×	`associate-*l/` `associate-/l/`
7×	`flip3-+` `flip-+`
4×	`frac-times` `prod-exp` `cbrt-unprod` `add-log-exp`
3×	`flip3--` `times-frac` `pow-prod-down` `associate-/r` `-commutative` `flip--` `unswap-sqr`
2×	`cbrt-undiv` `associate-*r/` `div-exp` `associate-/r/`
1×	`frac-2neg` `clear-num` `div-inv` `associate-/l*`

Counts

4 → 91

Calls

4 calls:

12.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
9.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
7.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
27.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

series61.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x)
4.0ms	(* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x)
6.0ms	(* (+ (* x 4.16438922228) 78.6994924154) x)
43.0ms	(/ (* (- x 2.0) (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z)) (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))

simplify81.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	657	1279
1	3241	1119
2	5002	1119

prune228.0ms

Filtered

76 candidates to 103 candidates (-35.5%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	97	6	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	6	104

Merged error: 0.0b

Counts

104 → 6

localize27.0ms

Local error

Found 4 expressions with local error:

8.0b	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
18.1b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
18.2b	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
24.0b	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

rewrite119.0ms

Algorithm

rewrite-expression-head

Rules

126×	`add-sqr-sqrt`
108×	`times-frac`
95×	`*-un-lft-identity`
69×	`add-cube-cbrt`
63×	`sqrt-prod`
36×	`associate-l`
24×	`associate-r`
20×	`add-exp-log` `add-cbrt-cube`
13×	`distribute-lft-out--` `difference-of-squares`
12×	`associate-/r*`
10×	`sqrt-div`
9×	`unswap-sqr`
8×	`associate-/r/` `associate-/l*`
7×	`pow1`
6×	`cbrt-undiv` `flip3-+` `div-exp` `flip-+`
4×	`prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `add-log-exp`
2×	`frac-2neg` `clear-num`
1×	`frac-times` `rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `*-commutative` `flip--`

Counts

4 → 205

Calls

4 calls:

15.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
16.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
53.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
27.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

series106.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))
8.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
44.0ms	(* (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))))
48.0ms	(/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))

simplify124.0ms

Algorithm

egg-herbie

Counts

217 → 217

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	894	5675
1	3611	5204
2	5001	5070

prune836.0ms

Filtered

141 candidates to 217 candidates (-53.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	215	2	217
Fresh	2	3	5
Picked	0	1	1
Done	0	0	0
Total	217	6	223

Merged error: 0.0b

Counts

223 → 6

localize35.0ms

Local error

Found 4 expressions with local error:

18.0b	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
18.0b	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
18.1b	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
24.1b	(* (/ (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))

rewrite279.0ms

Algorithm

rewrite-expression-head

Rules

741×	`times-frac`
604×	`add-sqr-sqrt`
602×	`sqrt-prod`
430×	`*-un-lft-identity`
330×	`associate-l`
308×	`add-cube-cbrt`
61×	`distribute-lft-out--` `difference-of-squares`
40×	`unswap-sqr`
36×	`sqrt-div`
33×	`associate-r`
27×	`add-exp-log` `add-cbrt-cube`
24×	`associate-/r/`
14×	`flip3-+` `flip-+`
12×	`div-inv`
10×	`pow1` `cbrt-undiv` `div-exp`
8×	`sqrt-pow1`
6×	`prod-exp` `associate-/r*` `cbrt-unprod`
5×	`associate-/l*`
4×	`rem-sqrt-square` `pow1/2` `add-log-exp`
2×	`associate-/l/`
1×	`frac-times` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `associate-l/` `clear-num` `*-commutative` `flip--`

Counts

4 → 527

Calls

4 calls:

12.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
14.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
16.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
196.0ms	(* (/ (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))

series75.0ms

Counts

4 → 12

Calls

4 calls:

10.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
10.0ms	(sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
8.0ms	(/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))
47.0ms	(* (/ (/ (- x 2.0) (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606))) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))) (/ (+ (* (+ (* (+ (* (+ (* x 4.16438922228) 78.6994924154) x) 137.519416416) x) y) x) z) (sqrt (sqrt (+ (* (+ (* (+ (* (+ x 43.3400022514) x) 263.505074721) x) 313.399215894) x) 47.066876606)))))

simplify210.0ms

Algorithm

egg-herbie

Counts

539 → 539

Iterations

Useful iterations: 1 (33.0ms)

Iter	Nodes	Cost
0	1677	21205
1	5001	20043

prune4.9s

Filtered

313 candidates to 539 candidates (-72.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	539	0	539
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	539	6	545

Merged error: 0.0b

Counts

545 → 6

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (/ y (pow x 2)) (* 4.16438922228 x)) 110.1139242984811)
0.0b	(+ (/ y (pow x 2)) (* 4.16438922228 x))
7.3b	(/ y (pow x 2))

rewrite29.0ms

Algorithm

rewrite-expression-head

Rules

24×	`times-frac`
22×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
12×	`unpow-prod-down`
10×	`add-log-exp`
8×	`add-exp-log` `associate-/r*`
5×	`add-cbrt-cube`
4×	`unpow2` `sqr-pow`
3×	`pow1` `div-exp` `associate-/l*`
2×	`diff-log` `sum-log`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `pow-exp` `associate--l+` `clear-num` `flip--` `flip-+` `div-inv` `distribute-lft-out--` `difference-of-squares`

Counts

3 → 76

Calls

3 calls:

11.0ms	(- (+ (/ y (pow x 2)) (* 4.16438922228 x)) 110.1139242984811)
11.0ms	(+ (/ y (pow x 2)) (* 4.16438922228 x))
5.0ms	(/ y (pow x 2))

series21.0ms

Counts

3 → 9

Calls

3 calls:

7.0ms	(- (+ (/ y (pow x 2)) (* 4.16438922228 x)) 110.1139242984811)
9.0ms	(+ (/ y (pow x 2)) (* 4.16438922228 x))
5.0ms	(/ y (pow x 2))

simplify36.0ms

Algorithm

egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 2 (29.0ms)

Iter	Nodes	Cost
0	285	477
1	1055	444
2	5002	431

prune93.0ms

Filtered

54 candidates to 85 candidates (-57.4%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	83	2	85
Fresh	1	2	3
Picked	1	0	1
Done	0	2	2
Total	85	6	91

Merged error: 0b

Counts

91 → 6

regimes281.0ms

Accuracy

95.8% (1.1b remaining)

Error of 1.1b against oracle of 0.0b and baseline of 25.4b

bsearch95.0ms

Steps

Iters	Range		Point
10	14.72129995785005	5.423059072965189e+17	5.3455952747835283e+17
9	-2.276695170473967e+45	-4.477249197883295e+38	-1.4005530737927671e+44

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	40
1	74	40
2	74	40

end0.0ms

analyze953.0ms

Algorithm: search

sample817.0ms

Algorithm

intervals

Results

651.0ms	8000×	body	80	valid
0.0ms	5×	body	80	invalid

Details

analyze958.0ms

sample30.0ms

simplify41.0ms

prune4.0ms

localize27.0ms

rewrite57.0ms

series61.0ms

simplify81.0ms

prune228.0ms

localize27.0ms

rewrite119.0ms

series106.0ms

simplify124.0ms

prune836.0ms

localize35.0ms

rewrite279.0ms

series75.0ms

simplify210.0ms

prune4.9s

localize8.0ms

rewrite29.0ms

series21.0ms

simplify36.0ms

prune93.0ms

regimes281.0ms

bsearch95.0ms

simplify2.0ms

end0.0ms

analyze953.0ms

sample817.0ms

Profiling