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

9.0ms

256×

body

valid

simplify4.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	57	14
1	57	14

prune7.0ms

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

localize15.0ms

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))))))
0.1b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

rewrite29.0ms

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:

4.0ms	(+ 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)))))

series20.0ms

Counts

3 → 9

Calls

3 calls:

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

simplify34.0ms

Algorithm

egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (22.0ms)

Iter	Nodes	Cost
0	5148	1959

prune169.0ms

Filtered

82 candidates to 114 candidates (-39.0%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	110	4	114
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	111	5	116

Merged error: 0b

Counts

116 → 5

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
0.0b	(* 6.0 (log (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))))
0.0b	(log (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
0.1b	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

rewrite54.0ms

Algorithm

rewrite-expression-head

Rules

126×	`*-un-lft-identity`
86×	`add-sqr-sqrt`
80×	`times-frac`
78×	`exp-prod`
54×	`log-pow`
50×	`add-cube-cbrt`
30×	`associate-r`
21×	`distribute-lft-out`
17×	`distribute-lft-out--` `difference-of-squares`
9×	`log-prod`
8×	`pow1` `add-exp-log` `associate-/r/` `add-cbrt-cube`
5×	`associate-/l*` `add-log-exp`
4×	`flip3-+` `associate-/r*` `flip-+` `div-inv`
3×	`distribute-rgt-in` `distribute-lft-in` `div-sub` `associate-l`
2×	`exp-diff` `associate-/l/`
1×	`cbrt-undiv` `log-div` `flip3--` `frac-2neg` `div-exp` `rem-log-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `rem-exp-log` `unswap-sqr`

Counts

4 → 171

Calls

4 calls:

8.0ms	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
16.0ms	(* 6.0 (log (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))))
10.0ms	(log (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
12.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

series35.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
8.0ms	(* 6.0 (log (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))))
7.0ms	(log (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
10.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

simplify42.0ms

Algorithm

egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5170	3208

prune297.0ms

Filtered

128 candidates to 183 candidates (-43.0%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	183	0	183
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	183	5	188

Merged error: 0b

Counts

188 → 5

localize14.0ms

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

rewrite67.0ms

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:

22.0ms	(* 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)))))
10.0ms	(pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)
11.0ms	(cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3))

series44.0ms

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	(pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3)
11.0ms	(cbrt (pow (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))) 3))

simplify83.0ms

Algorithm

egg-herbie

Counts

281 → 281

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5158	5747

prune299.0ms

Filtered

129 candidates to 281 candidates (-117.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	281	0	281
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	281	5	286

Merged error: 0b

Counts

286 → 5

localize13.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (* (/ (cbrt (- x 1.0)) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))) (cbrt (- x 1.0))) (/ (cbrt (- x 1.0)) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
0.2b	(cbrt (- x 1.0))
0.2b	(cbrt (- x 1.0))
0.2b	(cbrt (- x 1.0))

rewrite48.0ms

Algorithm

rewrite-expression-head

Rules

74×	`*-un-lft-identity`
62×	`associate-r`
58×	`add-sqr-sqrt`
56×	`times-frac`
50×	`cbrt-prod`
38×	`add-cube-cbrt`
32×	`sqrt-prod`
25×	`add-exp-log`
16×	`add-cbrt-cube`
14×	`cbrt-div`
10×	`prod-exp` `cbrt-unprod` `distribute-lft-out--` `difference-of-squares`
9×	`pow1` `frac-times`
8×	`distribute-lft-out`
7×	`flip3--` `associate-*l/` `flip--`
5×	`cbrt-undiv` `associate-*r/` `div-exp`
4×	`add-log-exp`
3×	`pow1/3` `pow-prod-down`
2×	`sqrt-div` `associate-/r/`
1×	`flip3-+` `associate-l` `*-commutative` `flip-+` `div-inv`

Counts

4 → 141

Calls

4 calls:

34.0ms	(* (* (/ (cbrt (- x 1.0)) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))) (cbrt (- x 1.0))) (/ (cbrt (- x 1.0)) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
3.0ms	(cbrt (- x 1.0))
3.0ms	(cbrt (- x 1.0))
3.0ms	(cbrt (- x 1.0))

series32.0ms

Counts

4 → 12

Calls

4 calls:

9.0ms	(* (* (/ (cbrt (- x 1.0)) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))) (cbrt (- x 1.0))) (/ (cbrt (- x 1.0)) (sqrt (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
7.0ms	(cbrt (- x 1.0))
7.0ms	(cbrt (- x 1.0))
8.0ms	(cbrt (- x 1.0))

simplify88.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4957	3354
1	4957	3354

prune364.0ms

Filtered

104 candidates to 153 candidates (-47.1%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	153	0	153
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	153	5	158

Merged error: 0b

Counts

158 → 5

regimes33.0ms

Accuracy

0% (0.0b remaining)

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

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	14
1	15	14

end0.0ms

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

sample392.0ms

Algorithm

intervals

Results

305.0ms	8000×	body	80	valid
0.0ms	2×	body	80	nan

Details

analyze3.0ms

sample15.0ms

simplify4.0ms

prune7.0ms

localize15.0ms

rewrite29.0ms

series20.0ms

simplify34.0ms

prune169.0ms

localize22.0ms

rewrite54.0ms

series35.0ms

simplify42.0ms

prune297.0ms

localize14.0ms

rewrite67.0ms

series44.0ms

simplify83.0ms

prune299.0ms

localize13.0ms

rewrite48.0ms

series32.0ms

simplify88.0ms

prune364.0ms

regimes33.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

analyze3.0ms

sample392.0ms

Profiling