Details

analyze4.5s

Algorithm

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	25%	75%	2
0%	25%	75%	3
0%	25%	75%	4
0%	25%	75%	5
0%	25%	75%	6
0%	25%	75%	7
0%	25%	75%	8
1.6%	23.4%	75%	9
1.6%	23.4%	75%	10
1.6%	23.4%	75%	11
1.6%	23.4%	75%	12
1.6%	23.4%	75%	13
1.6%	23.4%	75%	14

sample1.3s

Algorithm

intervals

Results

832.0ms	123×	body	5120	exit
17.0ms	128×	body	80	valid
3.0ms	1×	body	1280	valid
3.0ms	1×	body	2560	valid
1.0ms	3×	body	160	valid

simplify48.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5092	43

prune12.0ms

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: 4.2b

Counts

2 → 1

localize31.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
0.2b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
0.2b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
3.7b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

rewrite89.0ms

Algorithm

rewrite-expression-head

Rules

556×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
249×	`div-exp`
184×	`pow-to-exp`
36×	`unpow-prod-down` `*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
16×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `distribute-lft-out` `add-log-exp`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod`
3×	`div-inv`
2×	`pow-pow` `flip3-+` `flip-+` `difference-of-squares` `sqr-pow`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `associate-/r` `flip--` `associate-/l` `distribute-lft-out--`

Counts

4 → 266

Calls

4 calls:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
42.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

series214.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
14.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
178.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

simplify109.0ms

Algorithm

egg-herbie

Counts

278 → 278

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	5002	9443

prune277.0ms

Filtered

75 candidates to 278 candidates (-270.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	275	3	278
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	276	3	279

Merged error: 0.1b

Counts

279 → 3

localize39.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (/ 1.0 (+ 1.0 (exp (neg s)))))
0.7b	(log (/ 1.0 (+ 1.0 (exp (neg t)))))
22.8b	(- (log (/ 1.0 (+ 1.0 (exp (neg s))))) (log (/ 1.0 (+ 1.0 (exp (neg t))))))
22.8b	(- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))))

rewrite53.0ms

Algorithm

rewrite-expression-head

Rules

84×	`log-prod`
74×	`*-un-lft-identity`
52×	`add-sqr-sqrt`
50×	`times-frac`
38×	`add-cube-cbrt`
24×	`associate--l+` `associate--r+`
14×	`pow1`
12×	`distribute-lft-out`
10×	`add-exp-log` `log-pow` `distribute-lft-out--`
8×	`log-div` `associate-/r/`
6×	`difference-of-squares`
4×	`flip3--` `flip3-+` `rem-log-exp` `add-cbrt-cube` `flip--` `flip-+` `div-inv` `add-log-exp`
3×	`associate--l-` `associate--r-`
2×	`sub-neg` `diff-log` `div-exp`

Counts

4 → 144

Calls

4 calls:

5.0ms	(log (/ 1.0 (+ 1.0 (exp (neg s)))))
5.0ms	(log (/ 1.0 (+ 1.0 (exp (neg t)))))
14.0ms	(- (log (/ 1.0 (+ 1.0 (exp (neg s))))) (log (/ 1.0 (+ 1.0 (exp (neg t))))))
22.0ms	(- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))))

series84.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(log (/ 1.0 (+ 1.0 (exp (neg s)))))
15.0ms	(log (/ 1.0 (+ 1.0 (exp (neg t)))))
22.0ms	(- (log (/ 1.0 (+ 1.0 (exp (neg s))))) (log (/ 1.0 (+ 1.0 (exp (neg t))))))
32.0ms	(- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))))

simplify70.0ms

Algorithm

egg-herbie

Counts

156 → 156

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4963	2785
1	4963	2785

prune486.0ms

Filtered

112 candidates to 156 candidates (-39.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	154	2	156
Fresh	2	0	2
Picked	1	0	1
Done	0	0	0
Total	157	2	159

Merged error: 0b

Counts

159 → 2

localize34.0ms

Local error

Found 4 expressions with local error:

0.1b	(* c_n (- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))))))
0.2b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
7.6b	(* c_p (- (* 0.5 (- s t)) (* s (* s 0.125))))
22.8b	(- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))))

rewrite65.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-sqr-sqrt`
30×	`*-un-lft-identity`
24×	`log-prod`
22×	`associate--l+`
16×	`pow1`
14×	`distribute-rgt-in` `distribute-lft-in`
13×	`distribute-lft-out--`
12×	`add-cube-cbrt` `difference-of-squares`
11×	`associate-r`
10×	`sub-neg`
8×	`add-exp-log` `log-div` `flip3--` `log-pow` `add-cbrt-cube` `flip--`
6×	`associate-l` `associate--r+` `associate--r-` `add-log-exp`
5×	`times-frac`
4×	`associate-*r/`
2×	`associate--l-` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 115

Calls

4 calls:

17.0ms	(* c_n (- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))))))
10.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
10.0ms	(* c_p (- (* 0.5 (- s t)) (* s (* s 0.125))))
25.0ms	(- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(* c_n (- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))))))
7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
19.0ms	(* c_p (- (* 0.5 (- s t)) (* s (* s 0.125))))
29.0ms	(- (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))) (log (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))))

simplify68.0ms

Algorithm

egg-herbie

Counts

127 → 127

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	4972	2861
1	4972	2861

prune272.0ms

Filtered

82 candidates to 127 candidates (-54.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	127	0	127
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	127	2	129

Merged error: 0b

Counts

129 → 2

localize34.0ms

Local error

Found 4 expressions with local error:

0.2b	(log (/ 1.0 (+ 1.0 (exp (neg s)))))
0.7b	(log (/ 1.0 (+ 1.0 (exp (neg t)))))
7.9b	(* c_n (- (* t 0.5) (* s (+ 0.5 (* s 0.125)))))
22.8b	(- (log (/ 1.0 (+ 1.0 (exp (neg s))))) (log (/ 1.0 (+ 1.0 (exp (neg t))))))

rewrite35.0ms

Algorithm

rewrite-expression-head

Rules

72×	`log-prod`
66×	`*-un-lft-identity`
48×	`times-frac`
42×	`add-sqr-sqrt`
38×	`add-cube-cbrt`
18×	`associate--l+` `associate--r+`
12×	`pow1` `add-exp-log` `distribute-lft-out`
8×	`associate-/r/`
6×	`log-pow` `add-cbrt-cube`
4×	`log-div` `flip3-+` `rem-log-exp` `flip-+` `div-inv` `distribute-lft-out--` `add-log-exp`
3×	`sub-neg` `associate-r` `associate-l`
2×	`flip3--` `associate-*r/` `div-exp` `flip--`
1×	`associate--l-` `distribute-rgt-in` `distribute-lft-in` `diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `associate--r-` `difference-of-squares` `unswap-sqr`

Counts

4 → 134

Calls

4 calls:

5.0ms	(log (/ 1.0 (+ 1.0 (exp (neg s)))))
5.0ms	(log (/ 1.0 (+ 1.0 (exp (neg t)))))
6.0ms	(* c_n (- (* t 0.5) (* s (+ 0.5 (* s 0.125)))))
14.0ms	(- (log (/ 1.0 (+ 1.0 (exp (neg s))))) (log (/ 1.0 (+ 1.0 (exp (neg t))))))

series70.0ms

Counts

4 → 12

Calls

4 calls:

14.0ms	(log (/ 1.0 (+ 1.0 (exp (neg s)))))
14.0ms	(log (/ 1.0 (+ 1.0 (exp (neg t)))))
21.0ms	(* c_n (- (* t 0.5) (* s (+ 0.5 (* s 0.125)))))
21.0ms	(- (log (/ 1.0 (+ 1.0 (exp (neg s))))) (log (/ 1.0 (+ 1.0 (exp (neg t))))))

simplify59.0ms

Algorithm

egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	5100	2270

prune318.0ms

Filtered

103 candidates to 146 candidates (-41.7%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	146	0	146
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	146	2	148

Merged error: 0b

Counts

148 → 2

regimes336.0ms

Accuracy

86.2% (0.5b remaining)

Error of 0.5b against oracle of 0.1b and baseline of 3.6b

bsearch903.0ms

Steps

Iters	Range		Point
9	-562522284131633.75	-51813932.088417776	-735106654.8181112

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	167	76
1	167	76

end0.0ms

sample48.2s

Algorithm

intervals

Results

24.2s	3799×	body	5120	exit
522.0ms	4068×	body	80	valid
61.0ms	27×	body	1280	valid
31.0ms	27×	body	640	valid
22.0ms	63×	body	160	valid
15.0ms	5×	body	2560	valid
7.0ms	11×	body	320	valid

Details

analyze4.5s

sample1.3s

simplify48.0ms

prune12.0ms

localize31.0ms

rewrite89.0ms

series214.0ms

simplify109.0ms

prune277.0ms

localize39.0ms

rewrite53.0ms

series84.0ms

simplify70.0ms

prune486.0ms

localize34.0ms

rewrite65.0ms

series101.0ms

simplify68.0ms

prune272.0ms

localize34.0ms

rewrite35.0ms

series70.0ms

simplify59.0ms

prune318.0ms

regimes336.0ms

bsearch903.0ms

simplify3.0ms

end0.0ms

sample48.2s

Profiling