Details

analyze3.0ms

Algorithm

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	25%	25%	3
50%	12.5%	37.5%	4
50%	6.2%	43.8%	5
50%	3.1%	46.9%	6
50%	1.6%	48.5%	7
50%	0.8%	49.2%	8
50%	0.4%	49.6%	9
50%	0.2%	49.8%	10
50%	0.1%	49.9%	11
50%	0%	50%	12
50%	0%	50%	13
50%	0%	50%	14

sample15.0ms

Algorithm

intervals

Results

10.0ms

256×

body

valid

simplify64.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4970	14
1	4970	14

prune8.0ms

Filtered

1 candidates to 1 candidates (0.0%)

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: 0.0b

Counts

2 → 2

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(+ x (+ 1.0 (* 4.0 (sqrt x))))
0.0b	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
0.0b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

rewrite33.0ms

Algorithm

rewrite-expression-head

Rules

67×	`*-un-lft-identity`
48×	`add-sqr-sqrt`
41×	`times-frac`
26×	`associate-r`
25×	`add-cube-cbrt`
12×	`distribute-lft-out`
10×	`add-exp-log` `add-cbrt-cube`
9×	`distribute-lft-out--` `difference-of-squares`
8×	`add-log-exp`
5×	`pow1` `associate-/l*`
4×	`associate-/r*` `associate-/r/`
3×	`flip3-+` `associate-l` `sum-log` `flip-+`
2×	`cbrt-undiv` `div-exp` `prod-exp` `cbrt-unprod` `div-inv` `associate-/l/` `unswap-sqr`
1×	`+-commutative` `associate-+r+` `flip3--` `frac-2neg` `div-sub` `associate-r/` `pow-prod-down` `clear-num` `-commutative` `flip--`

Counts

3 → 105

Calls

3 calls:

8.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
13.0ms	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

series21.0ms

Counts

3 → 9

Calls

3 calls:

4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
9.0ms	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

simplify33.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5591	1958

prune152.0ms

Filtered

82 candidates to 114 candidates (-39.0%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	111	3	114
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	112	4	116

Merged error: 0b

Counts

116 → 4

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ 1.0 (* 4.0 (sqrt x))))
0.0b	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
0.0b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
1.3b	(pow (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))) 6.0)

rewrite42.0ms

Algorithm

rewrite-expression-head

Rules

97×	`*-un-lft-identity`
63×	`add-sqr-sqrt`
60×	`times-frac`
52×	`exp-prod`
37×	`add-cube-cbrt`
27×	`pow-pow`
17×	`distribute-lft-out`
13×	`distribute-lft-out--` `difference-of-squares`
10×	`add-log-exp`
6×	`add-exp-log` `associate-/r/` `add-cbrt-cube`
5×	`pow1` `associate-/l*`
4×	`flip3-+` `associate-/r*` `flip-+`
3×	`unpow-prod-down` `pow-unpow` `sum-log` `div-inv`
2×	`div-sub` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `pow-to-exp` `associate-+r+` `flip3--` `frac-2neg` `exp-diff` `div-exp` `pow-exp` `clear-num` `flip--` `rem-exp-log` `sqr-pow`

Counts

4 → 138

Calls

4 calls:

5.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
9.0ms	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
10.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
12.0ms	(pow (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))) 6.0)

series37.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
9.0ms	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
15.0ms	(pow (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))) 6.0)

simplify50.0ms

Algorithm

egg-herbie

Counts

150 → 150

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	4982	2732
1	4982	2732

prune291.0ms

Filtered

108 candidates to 150 candidates (-38.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	150	0	150
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	150	4	154

Merged error: 0b

Counts

154 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 6.0 (cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)))
0.0b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
0.1b	(cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3))
0.1b	(pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)

rewrite70.0ms

Algorithm

rewrite-expression-head

Rules

210×	`*-un-lft-identity`
153×	`add-sqr-sqrt`
142×	`times-frac`
122×	`cbrt-prod`
80×	`add-cube-cbrt` `unpow-prod-down` `cube-prod`
61×	`associate-r`
36×	`distribute-lft-out`
29×	`distribute-lft-out--` `difference-of-squares`
14×	`associate-/r/`
11×	`add-exp-log`
10×	`add-cbrt-cube`
7×	`pow1` `flip3-+` `flip-+` `div-inv` `unswap-sqr`
5×	`associate-/l*`
4×	`associate-/r*` `add-log-exp` `sqr-pow`
3×	`cube-div` `cube-mult` `pow-unpow` `unpow3` `associate-l`
2×	`cbrt-undiv` `cbrt-div` `div-exp` `pow-exp` `associate-/l/` `rem-cube-cbrt`
1×	`pow-to-exp` `flip3--` `pow-pow` `frac-2neg` `pow1/3` `div-sub` `associate-r/` `pow-prod-down` `prod-exp` `clear-num` `-commutative` `flip--` `rem-cbrt-cube` `cbrt-unprod`

Counts

4 → 269

Calls

4 calls:

24.0ms	(* 6.0 (cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
12.0ms	(cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3))
11.0ms	(pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)

series45.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(* 6.0 (cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)))
8.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
11.0ms	(cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3))
12.0ms	(pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)

simplify72.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5308	5747

prune295.0ms

Filtered

130 candidates to 281 candidates (-116.2%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	281	4	285

Merged error: 0b

Counts

285 → 4

localize19.0ms

Local error

Found 4 expressions with local error:

0.3b	(* (+ 1.0 (* 4.0 (sqrt x))) (+ 1.0 (* 4.0 (sqrt x))))
4.3b	(/ (- x 1.0) (+ (pow x 3) (pow (+ 1.0 (* 4.0 (sqrt x))) 3)))
8.0b	(+ (* x x) (- (* (+ 1.0 (* 4.0 (sqrt x))) (+ 1.0 (* 4.0 (sqrt x)))) (* x (+ 1.0 (* 4.0 (sqrt x))))))
16.4b	(* (/ (- x 1.0) (+ (pow x 3) (pow (+ 1.0 (* 4.0 (sqrt x))) 3))) (+ (* x x) (- (* (+ 1.0 (* 4.0 (sqrt x))) (+ 1.0 (* 4.0 (sqrt x)))) (* x (+ 1.0 (* 4.0 (sqrt x)))))))

rewrite76.0ms

Algorithm

rewrite-expression-head

Rules

188×	`*-un-lft-identity`
91×	`times-frac`
85×	`add-sqr-sqrt`
55×	`distribute-lft-out`
54×	`associate-l`
44×	`unpow-prod-down` `cube-prod`
40×	`add-cube-cbrt`
19×	`distribute-lft-out--` `difference-of-squares`
13×	`pow1` `add-exp-log` `add-cbrt-cube`
11×	`flip3-+` `sum-cubes` `flip-+`
9×	`associate-/r*` `add-log-exp`
6×	`frac-times` `associate-r`
5×	`associate-/l*`
4×	`associate-*r/` `associate-/r/`
3×	`distribute-rgt-in` `associate-+r+` `distribute-lft-in` `swap-sqr` `associate-*l/` `prod-exp` `cbrt-unprod` `unswap-sqr`
2×	`cbrt-undiv` `div-exp` `pow-prod-down` `associate--l+` `sum-log` `*-commutative` `div-inv` `associate-/l/`
1×	`+-commutative` `pow2` `associate-+r-` `sub-neg` `flip3--` `frac-2neg` `pow-plus` `diff-log` `div-sub` `clear-num` `pow-sqr` `pow-prod-up` `flip--`

Counts

4 → 203

Calls

4 calls:

7.0ms	(* (+ 1.0 (* 4.0 (sqrt x))) (+ 1.0 (* 4.0 (sqrt x))))
17.0ms	(/ (- x 1.0) (+ (pow x 3) (pow (+ 1.0 (* 4.0 (sqrt x))) 3)))
9.0ms	(+ (* x x) (- (* (+ 1.0 (* 4.0 (sqrt x))) (+ 1.0 (* 4.0 (sqrt x)))) (* x (+ 1.0 (* 4.0 (sqrt x))))))
34.0ms	(* (/ (- x 1.0) (+ (pow x 3) (pow (+ 1.0 (* 4.0 (sqrt x))) 3))) (+ (* x x) (- (* (+ 1.0 (* 4.0 (sqrt x))) (+ 1.0 (* 4.0 (sqrt x)))) (* x (+ 1.0 (* 4.0 (sqrt x)))))))

series52.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(* (+ 1.0 (* 4.0 (sqrt x))) (+ 1.0 (* 4.0 (sqrt x))))
11.0ms	(/ (- x 1.0) (+ (pow x 3) (pow (+ 1.0 (* 4.0 (sqrt x))) 3)))
9.0ms	(+ (* x x) (- (* (+ 1.0 (* 4.0 (sqrt x))) (+ 1.0 (* 4.0 (sqrt x)))) (* x (+ 1.0 (* 4.0 (sqrt x))))))
24.0ms	(* (/ (- x 1.0) (+ (pow x 3) (pow (+ 1.0 (* 4.0 (sqrt x))) 3))) (+ (* x x) (- (* (+ 1.0 (* 4.0 (sqrt x))) (+ 1.0 (* 4.0 (sqrt x)))) (* x (+ 1.0 (* 4.0 (sqrt x)))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (38.0ms)

Iter	Nodes	Cost
0	5021	5996

prune491.0ms

Filtered

128 candidates to 215 candidates (-68.0%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	215	0	215
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	215	4	219

Merged error: 0b

Counts

219 → 4

regimes31.0ms

Accuracy

0% (0.0b remaining)

Error of 0.1b against oracle of 0.0b and baseline of 0.1b

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	26	16
1	26	16

end0.0ms

sample391.0ms

Algorithm

intervals

Results

303.0ms	8000×	body	80	valid
0.0ms	1×	body	80	nan

Details

analyze3.0ms

sample15.0ms

simplify64.0ms

prune8.0ms

localize9.0ms

rewrite33.0ms

series21.0ms

simplify33.0ms

prune152.0ms

localize13.0ms

rewrite42.0ms

series37.0ms

simplify50.0ms

prune291.0ms

localize11.0ms

rewrite70.0ms

series45.0ms

simplify72.0ms

prune295.0ms

localize19.0ms

rewrite76.0ms

series52.0ms

simplify68.0ms

prune491.0ms

regimes31.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample391.0ms

Profiling