Details

sample2.7s

Algorithm

intervals

Results

1.8s	252×	body	5120	exit
580.0ms	3213×	body	80	overflowed
83.0ms	3722×	pre	80	true
26.0ms	251×	body	80	valid
7.0ms	1×	body	2560	valid
3.0ms	3×	body	640	valid
1.0ms	1×	body	160	overflowed
0.0ms	1×	body	160	valid

simplify26.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	53	25
1	147	25
2	850	25
3	5001	25

prune7.0ms

Filtered

1 candidates to 0 candidates (100.0%)

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: 5.0b

Counts

2 → 1

localize26.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
1.0b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
2.7b	(/ (* (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)))

rewrite88.0ms

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 → 267

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)
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
43.0ms	(/ (* (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)))

series239.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
20.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
197.0ms	(/ (* (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)))

simplify118.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	982	5948
1	3157	5704
2	5002	5704

prune835.0ms

Filtered

279 candidates to 79 candidates (71.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	276	3	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	277	3	280

Merged error: 0.9b

Counts

280 → 3

localize27.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
0.2b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
1.5b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

rewrite69.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-exp-log`
88×	`prod-exp`
65×	`div-exp`
55×	`pow-exp`
42×	`pow-to-exp`
23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
18×	`unpow-prod-down` `add-cbrt-cube`
15×	`add-cube-cbrt`
14×	`times-frac`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/`
3×	`pow-unpow` `flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
2×	`associate-r/` `associate-l/` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `flip--` `associate-/l*` `distribute-lft-out--` `unswap-sqr` `sqr-pow`

Counts

4 → 141

Calls

4 calls:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
7.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
39.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

series264.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg t)))))
17.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
14.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
225.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

simplify112.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	921	2823
1	4030	2572
2	5003	2572

prune801.0ms

Filtered

153 candidates to 72 candidates (52.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	152	4	156

Merged error: 0.9b

Counts

156 → 4

localize16.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 0.5 (* s c_p))
0.0b	(* 0.5 (* s c_n))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2×	`associate-r` `*-commutative` `add-log-exp`

Counts

2 → 36

Calls

2 calls:

4.0ms	(* 0.5 (* s c_p))
5.0ms	(* 0.5 (* s c_n))

series7.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(* 0.5 (* s c_p))
4.0ms	(* 0.5 (* s c_n))

simplify64.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	153	142
1	595	112
2	2373	112
3	5002	112

prune75.0ms

Filtered

42 candidates to 22 candidates (47.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	42	4	46

Merged error: 0.9b

Counts

46 → 4

localize28.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
1.0b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
2.7b	(/ (* (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 (- (+ (* 0.020833333333333336 (pow t 3)) 0.5) (* 0.25 t)) c_n)))

rewrite90.0ms

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 → 267

Calls

4 calls:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
44.0ms	(/ (* (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 (- (+ (* 0.020833333333333336 (pow t 3)) 0.5) (* 0.25 t)) c_n)))

series260.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
18.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
220.0ms	(/ (* (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 (- (+ (* 0.020833333333333336 (pow t 3)) 0.5) (* 0.25 t)) c_n)))

simplify129.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1011	5949
1	3279	5709
2	5001	5709

prune927.0ms

Filtered

279 candidates to 80 candidates (71.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	279	0	279
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	279	4	283

Merged error: 0.9b

Counts

283 → 4

regimes868.0ms

bsearch2.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	33
1	58	33

end0.0ms

sample3.9s

Algorithm

intervals

Results

2.5s	367×	body	5120	exit
892.0ms	5012×	body	80	overflowed
132.0ms	5773×	pre	80	true
40.0ms	384×	body	80	valid
10.0ms	2×	body	2560	valid
5.0ms	5×	body	640	valid
2.0ms	1×	body	1280	valid
0.0ms	1×	body	160	overflowed
0.0ms	1×	body	160	valid

Details

sample2.7s

simplify26.0ms

prune7.0ms

localize26.0ms

rewrite88.0ms

series239.0ms

simplify118.0ms

prune835.0ms

localize27.0ms

rewrite69.0ms

series264.0ms

simplify112.0ms

prune801.0ms

localize16.0ms

rewrite10.0ms

series7.0ms

simplify64.0ms

prune75.0ms

localize28.0ms

rewrite90.0ms

series260.0ms

simplify129.0ms

prune927.0ms

regimes868.0ms

bsearch2.0ms

simplify2.0ms

end0.0ms

sample3.9s

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