Details

analyze5.0ms

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

sample27.0ms

Algorithm

intervals

Results

17.0ms

256×

body

valid

simplify83.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (81.0ms)

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: 0.1b

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

rewrite35.0ms

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:

5.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
13.0ms	(* 6.0 (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
12.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))

series19.0ms

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))))))
7.0ms	(/ (- 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

prune205.0ms

Filtered

82 candidates to 114 candidates (-39.0%)

Pruning

5 alts after pruning (5 fresh and 0 done)

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

Merged error: 0b

Counts

116 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ x (+ 1.0 (* 4.0 (sqrt x))))
0.0b	(/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))
0.0b	(* 6.0 (/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))))
0.1b	(/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0)))

rewrite73.0ms

Algorithm

rewrite-expression-head

Rules

322×	`times-frac`
292×	`*-un-lft-identity`
220×	`add-sqr-sqrt`
140×	`add-cube-cbrt`
83×	`associate-r`
42×	`distribute-lft-out`
36×	`add-exp-log`
33×	`distribute-lft-out--` `difference-of-squares`
31×	`associate-/r*`
20×	`add-cbrt-cube`
18×	`associate-/r/`
15×	`div-exp`
10×	`div-inv`
9×	`add-log-exp`
8×	`flip3--` `flip--`
7×	`pow1` `cbrt-undiv` `prod-exp` `associate-/l*`
5×	`unswap-sqr`
4×	`rec-exp` `1-exp`
3×	`associate-l` `sum-log` `cbrt-unprod`
2×	`frac-2neg` `flip3-+` `clear-num` `flip-+` `associate-/l/`
1×	`+-commutative` `associate-+r+` `pow-flip` `associate-r/` `pow-prod-down` `un-div-inv` `-commutative` `inv-pow`

Counts

4 → 299

Calls

4 calls:

5.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
9.0ms	(/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))
28.0ms	(* 6.0 (/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))))
12.0ms	(/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0)))

series25.0ms

Counts

4 → 12

Calls

4 calls:

4.0ms	(+ x (+ 1.0 (* 4.0 (sqrt x))))
6.0ms	(/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))
8.0ms	(* 6.0 (/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0))))
7.0ms	(/ 1 (/ (+ x (+ 1.0 (* 4.0 (sqrt x)))) (- x 1.0)))

simplify98.0ms

Algorithm

egg-herbie

Counts

311 → 311

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4954	5899
1	4954	5899

prune439.0ms

Filtered

180 candidates to 311 candidates (-72.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	311	0	311
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	311	5	316

Merged error: 0b

Counts

316 → 5

localize10.0ms

Local error

Found 4 expressions with local error:

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

rewrite72.0ms

Algorithm

rewrite-expression-head

Rules

92×	`*-un-lft-identity`
56×	`times-frac`
54×	`add-sqr-sqrt`
28×	`add-cube-cbrt`
17×	`associate-r`
16×	`distribute-lft-out`
14×	`distribute-lft-out--`
12×	`associate-/r/`
10×	`add-exp-log` `add-cbrt-cube`
8×	`associate-/r*` `difference-of-squares`
6×	`pow1` `distribute-rgt-out--` `flip3-+` `flip-+` `div-inv` `associate-/l*` `add-log-exp`
4×	`associate-*r/`
3×	`sub-neg` `associate-l`
2×	`cbrt-undiv` `flip3--` `frac-2neg` `div-exp` `clear-num` `frac-sub` `flip--` `sub-div`
1×	`distribute-rgt-in` `distribute-lft-in` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 131

Calls

4 calls:

31.0ms	(* 6.0 (- (/ x (+ x (+ 1.0 (* 4.0 (sqrt x))))) (/ 1.0 (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
25.0ms	(- (/ x (+ x (+ 1.0 (* 4.0 (sqrt x))))) (/ 1.0 (+ x (+ 1.0 (* 4.0 (sqrt x))))))
6.0ms	(/ 1.0 (+ x (+ 1.0 (* 4.0 (sqrt x)))))
6.0ms	(/ x (+ x (+ 1.0 (* 4.0 (sqrt x)))))

series40.0ms

Counts

4 → 12

Calls

4 calls:

13.0ms	(* 6.0 (- (/ x (+ x (+ 1.0 (* 4.0 (sqrt x))))) (/ 1.0 (+ x (+ 1.0 (* 4.0 (sqrt x)))))))
12.0ms	(- (/ x (+ x (+ 1.0 (* 4.0 (sqrt x))))) (/ 1.0 (+ x (+ 1.0 (* 4.0 (sqrt x))))))
6.0ms	(/ 1.0 (+ x (+ 1.0 (* 4.0 (sqrt x)))))
8.0ms	(/ x (+ x (+ 1.0 (* 4.0 (sqrt x)))))

simplify43.0ms

Algorithm

egg-herbie

Counts

143 → 143

Iterations

Useful iterations: 0 (25.0ms)

Iter	Nodes	Cost
0	5383	3120

prune244.0ms

Filtered

111 candidates to 143 candidates (-28.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	143	0	143
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	143	5	148

Merged error: 0b

Counts

148 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

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

rewrite47.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 142

Calls

4 calls:

9.0ms	(log (pow (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))) 6.0))
9.0ms	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
11.0ms	(/ (- 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)

series47.0ms

Counts

4 → 12

Calls

4 calls:

17.0ms	(log (pow (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))) 6.0))
9.0ms	(exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x))))))
7.0ms	(/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))
14.0ms	(pow (exp (/ (- x 1.0) (+ x (+ 1.0 (* 4.0 (sqrt x)))))) 6.0)

simplify55.0ms

Algorithm

egg-herbie

Counts

154 → 154

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4992	3004
1	4992	3004

prune364.0ms

Filtered

110 candidates to 154 candidates (-40.0%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	154	0	154
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	154	5	159

Merged error: 0b

Counts

159 → 5

regimes68.0ms

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	27	16
1	27	16

end0.0ms

sample392.0ms

Algorithm

intervals

Results

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

Details

analyze5.0ms

sample27.0ms

simplify83.0ms

prune8.0ms

localize9.0ms

rewrite35.0ms

series19.0ms

simplify33.0ms

prune205.0ms

localize10.0ms

rewrite73.0ms

series25.0ms

simplify98.0ms

prune439.0ms

localize10.0ms

rewrite72.0ms

series40.0ms

simplify43.0ms

prune244.0ms

localize14.0ms

rewrite47.0ms

series47.0ms

simplify55.0ms

prune364.0ms

regimes68.0ms

bsearch0.0ms

simplify1.0ms

end0.0ms

sample392.0ms

Profiling