Details

analyze585.0ms

Algorithm

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
6.2%	93.7%	0.1%	5
6.2%	90.5%	3.2%	6
21.9%	67.1%	11%	7
23.4%	64.8%	11.8%	8
32%	52.7%	15.3%	9
33.2%	51.3%	15.5%	10
37.7%	45.2%	17.2%	11
38.3%	44.4%	17.2%	12
40.6%	41.3%	18%	13
41%	41%	18%	14

sample87.0ms

Algorithm

intervals

Results

9.0ms	182×	body	80	valid
7.0ms	22×	body	640	valid
6.0ms	22×	body	1280	valid
2.0ms	17×	body	320	valid
1.0ms	13×	body	160	valid

simplify113.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	5039	12

prune7.0ms

Filtered

1 candidates to 1 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 18.2b

Counts

2 → 1

localize18.0ms

Local error

Found 3 expressions with local error:

0.0b	(/ (- x y) (- 1.0 y))
17.4b	(- 1.0 (/ (- x y) (- 1.0 y)))
25.2b	(log (- 1.0 (/ (- x y) (- 1.0 y))))

rewrite36.0ms

Algorithm

rewrite-expression-head

Rules

50×	`add-sqr-sqrt`
44×	`*-un-lft-identity`
27×	`times-frac`
16×	`add-cube-cbrt` `difference-of-squares`
14×	`distribute-lft-out--`
6×	`add-exp-log` `log-prod`
5×	`associate-/r` `add-cbrt-cube` `associate-/l` `add-log-exp`
4×	`pow1` `flip3--` `flip--`
2×	`log-div` `div-sub` `associate-/r/` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `frac-2neg` `diff-log` `div-exp` `rem-log-exp` `clear-num` `log-pow` `div-inv` `associate--r-`

Counts

3 → 84

Calls

3 calls:

7.0ms	(/ (- x y) (- 1.0 y))
13.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
13.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

series28.0ms

Counts

3 → 9

Calls

3 calls:

6.0ms	(/ (- x y) (- 1.0 y))
11.0ms	(- 1.0 (/ (- x y) (- 1.0 y)))
12.0ms	(log (- 1.0 (/ (- x y) (- 1.0 y))))

simplify52.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5817	1253

prune187.0ms

Filtered

71 candidates to 93 candidates (-31.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	89	4	93
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	90	4	94

Merged error: 0.1b

Counts

94 → 4

localize23.0ms

Local error

Found 4 expressions with local error:

0.2b	(cbrt (- 1.0 y))
0.2b	(cbrt (- 1.0 y))
17.4b	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))
25.2b	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

39×	`add-sqr-sqrt`
15×	`*-un-lft-identity`
14×	`cbrt-prod`
12×	`times-frac` `difference-of-squares`
9×	`log-prod`
7×	`add-cube-cbrt`
6×	`add-log-exp`
5×	`pow1` `add-exp-log`
4×	`cbrt-div` `flip3--` `add-cbrt-cube` `flip--` `distribute-lft-out--`
2×	`log-div` `pow1/3` `div-sub`
1×	`sub-neg` `diff-log` `rem-log-exp` `log-pow` `associate--r-`

Counts

4 → 68

Calls

4 calls:

3.0ms	(cbrt (- 1.0 y))
3.0ms	(cbrt (- 1.0 y))
44.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))
43.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))

series33.0ms

Counts

4 → 12

Calls

4 calls:

6.0ms	(cbrt (- 1.0 y))
6.0ms	(cbrt (- 1.0 y))
9.0ms	(- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y))))
12.0ms	(log (- 1.0 (/ (/ (- x y) (* (cbrt (- 1.0 y)) (cbrt (- 1.0 y)))) (cbrt (- 1.0 y)))))

simplify52.0ms

Algorithm

egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	6060	1211

prune186.0ms

Filtered

67 candidates to 80 candidates (-19.4%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	80	4	84

Merged error: 0.1b

Counts

84 → 4

localize43.0ms

Local error

Found 4 expressions with local error:

0.3b	(- (log (+ (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3))) (log (+ (* 1.0 1.0) (* (- x y) (/ (+ 1.0 (/ (- x y) (- 1.0 y))) (- 1.0 y))))))
17.4b	(+ (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3))
24.5b	(log (+ (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3)))
31.5b	(log (+ (* 1.0 1.0) (* (- x y) (/ (+ 1.0 (/ (- x y) (- 1.0 y))) (- 1.0 y)))))

rewrite142.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity`
24×	`log-prod`
15×	`distribute-lft-out`
12×	`unpow-prod-down` `cube-prod`
10×	`pow1` `add-sqr-sqrt`
9×	`associate--l+`
8×	`add-cube-cbrt` `log-div`
6×	`add-exp-log` `log-pow` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`add-cbrt-cube` `distribute-lft-out--`
3×	`sum-cubes` `associate--r+`
2×	`associate--l-` `rem-log-exp` `associate--r-`
1×	`+-commutative` `sub-neg` `flip3--` `diff-log` `sum-log` `flip--` `difference-of-squares`

Counts

4 → 83

Calls

4 calls:

50.0ms	(- (log (+ (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3))) (log (+ (* 1.0 1.0) (* (- x y) (/ (+ 1.0 (/ (- x y) (- 1.0 y))) (- 1.0 y))))))
42.0ms	(+ (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3))
43.0ms	(log (+ (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3)))
4.0ms	(log (+ (* 1.0 1.0) (* (- x y) (/ (+ 1.0 (/ (- x y) (- 1.0 y))) (- 1.0 y)))))

series192.0ms

Counts

4 → 12

Calls

4 calls:

72.0ms	(- (log (+ (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3))) (log (+ (* 1.0 1.0) (* (- x y) (/ (+ 1.0 (/ (- x y) (- 1.0 y))) (- 1.0 y))))))
39.0ms	(+ (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3))
45.0ms	(log (+ (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3)))
36.0ms	(log (+ (* 1.0 1.0) (* (- x y) (/ (+ 1.0 (/ (- x y) (- 1.0 y))) (- 1.0 y)))))

simplify53.0ms

Algorithm

egg-herbie

Counts

95 → 95

Iterations

Useful iterations: 0 (36.0ms)

Iter	Nodes	Cost
0	4983	2789
1	4983	2789

prune263.0ms

Filtered

69 candidates to 95 candidates (-37.7%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	95	4	99

Merged error: 0.0b

Counts

99 → 4

localize59.0ms

Local error

Found 4 expressions with local error:

12.6b	(/ (+ (pow (pow 1.0 3) 3) (pow (pow (/ (- y x) (- 1.0 y)) 3) 3)) (+ (pow 1.0 6) (- (pow (/ (- y x) (- 1.0 y)) 6) (* (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3)))))
17.3b	(+ (pow (pow 1.0 3) 3) (pow (pow (/ (- y x) (- 1.0 y)) 3) 3))
24.5b	(log (/ (+ (pow (pow 1.0 3) 3) (pow (pow (/ (- y x) (- 1.0 y)) 3) 3)) (+ (pow 1.0 6) (- (pow (/ (- y x) (- 1.0 y)) 6) (* (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3))))))
31.5b	(log (+ (* 1.0 1.0) (* (- x y) (/ (+ 1.0 (/ (- x y) (- 1.0 y))) (- 1.0 y)))))

rewrite779.0ms

Algorithm

rewrite-expression-head

Rules

588×	`*-un-lft-identity`
360×	`unpow-prod-down` `cube-prod`
261×	`distribute-lft-out`
200×	`times-frac`
109×	`log-prod`
66×	`add-sqr-sqrt` `add-cube-cbrt`
25×	`associate-/l*`
10×	`add-exp-log` `sum-cubes`
6×	`pow1` `add-cbrt-cube` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`associate-/r*` `associate-/r/`
3×	`log-div` `rem-log-exp`
2×	`div-exp` `log-pow` `div-inv` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `clear-num` `sum-log`

Counts

4 → 309

Calls

4 calls:

214.0ms	(/ (+ (pow (pow 1.0 3) 3) (pow (pow (/ (- y x) (- 1.0 y)) 3) 3)) (+ (pow 1.0 6) (- (pow (/ (- y x) (- 1.0 y)) 6) (* (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3)))))
160.0ms	(+ (pow (pow 1.0 3) 3) (pow (pow (/ (- y x) (- 1.0 y)) 3) 3))
377.0ms	(log (/ (+ (pow (pow 1.0 3) 3) (pow (pow (/ (- y x) (- 1.0 y)) 3) 3)) (+ (pow 1.0 6) (- (pow (/ (- y x) (- 1.0 y)) 6) (* (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3))))))
4.0ms	(log (+ (* 1.0 1.0) (* (- x y) (/ (+ 1.0 (/ (- x y) (- 1.0 y))) (- 1.0 y)))))

series3.1s

Counts

4 → 12

Calls

4 calls:

333.0ms	(/ (+ (pow (pow 1.0 3) 3) (pow (pow (/ (- y x) (- 1.0 y)) 3) 3)) (+ (pow 1.0 6) (- (pow (/ (- y x) (- 1.0 y)) 6) (* (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3)))))
315.0ms	(+ (pow (pow 1.0 3) 3) (pow (pow (/ (- y x) (- 1.0 y)) 3) 3))
2.4s	(log (/ (+ (pow (pow 1.0 3) 3) (pow (pow (/ (- y x) (- 1.0 y)) 3) 3)) (+ (pow 1.0 6) (- (pow (/ (- y x) (- 1.0 y)) 6) (* (pow 1.0 3) (pow (/ (- y x) (- 1.0 y)) 3))))))
34.0ms	(log (+ (* 1.0 1.0) (* (- x y) (/ (+ 1.0 (/ (- x y) (- 1.0 y))) (- 1.0 y)))))

simplify143.0ms

Algorithm

egg-herbie

Counts

321 → 321

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5375	18767

prune820.0ms

Filtered

95 candidates to 321 candidates (-237.9%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	319	2	321
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	320	5	325

Merged error: 0.0b

Counts

325 → 5

regimes162.0ms

Accuracy

99.7% (0.0b remaining)

Error of 0.1b against oracle of 0.1b and baseline of 16.9b

bsearch147.0ms

Steps

Iters	Range		Point
9	48930.695132614965	233578622587.4121	108586372.29727396
7	-6578151851438.381	-92967594979.03426	-94616551573.23618

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	140	48
1	140	48

end0.0ms

sample2.3s

Algorithm

intervals

Results

270.0ms	5674×	body	80	valid
211.0ms	836×	body	1280	valid
145.0ms	773×	body	640	valid
62.0ms	468×	body	320	valid
22.0ms	249×	body	160	valid

Details

analyze585.0ms

sample87.0ms

simplify113.0ms

prune7.0ms

localize18.0ms

rewrite36.0ms

series28.0ms

simplify52.0ms

prune187.0ms

localize23.0ms

rewrite96.0ms

series33.0ms

simplify52.0ms

prune186.0ms

localize43.0ms

rewrite142.0ms

series192.0ms

simplify53.0ms

prune263.0ms

localize59.0ms

rewrite779.0ms

series3.1s

simplify143.0ms

prune820.0ms

regimes162.0ms

bsearch147.0ms

simplify3.0ms

end0.0ms

sample2.3s

Profiling