Details

sample2.1s

Algorithm

intervals

Results

1.4s	203×	body	5120	exit
430.0ms	2552×	body	80	overflowed
71.0ms	3012×	pre	80	true
27.0ms	249×	body	80	valid
7.0ms	1×	body	5120	valid
3.0ms	1×	body	1280	valid
2.0ms	5×	body	160	valid
1.0ms	1×	body	640	overflowed

simplify28.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

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

prune4.0ms

Filtered

1 candidates to 0 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: 5.8b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.3b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.2b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.9b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- 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 → 267

Calls

4 calls:

10.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
8.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
8.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
45.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series846.0ms

Counts

4 → 12

Calls

4 calls:

53.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
75.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
75.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
642.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify106.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	976	5948
1	3142	5704
2	5001	5704

prune421.0ms

Filtered

279 candidates to 79 candidates (28.3%)

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: 0.5b

Counts

280 → 3

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite11.0ms

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:

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

series43.0ms

Counts

2 → 6

Calls

2 calls:

23.0ms	(* 0.5 (* s c_n))
19.0ms	(* 0.5 (* s c_p))

simplify59.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 1 (6.0ms)

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

prune65.0ms

Filtered

42 candidates to 22 candidates (52.4%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	40	2	42
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	40	5	45

Merged error: 0.5b

Counts

45 → 5

localize10.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.0b	(* 0.5 (* s c_p))
1.3b	(log (exp (* 0.5 (* s c_p))))

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

14×	`pow1`
13×	`add-exp-log` `add-cbrt-cube`
6×	`add-sqr-sqrt` `add-cube-cbrt` `-un-lft-identity` `associate-l*` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-log-exp`
3×	`log-prod` `log-pow`
2×	`associate-r` `*-commutative`
1×	`exp-prod` `exp-to-pow` `rem-log-exp`

Counts

3 → 50

Calls

3 calls:

5.0ms	(* 0.5 (* s c_n))
5.0ms	(* 0.5 (* s c_p))
2.0ms	(log (exp (* 0.5 (* s c_p))))

series62.0ms

Counts

3 → 9

Calls

3 calls:

23.0ms	(* 0.5 (* s c_n))
19.0ms	(* 0.5 (* s c_p))
20.0ms	(log (exp (* 0.5 (* s c_p))))

simplify61.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 1 (6.0ms)

Iter	Nodes	Cost
0	174	208
1	679	168
2	2509	168
3	5001	168

prune100.0ms

Filtered

59 candidates to 33 candidates (55.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	59	0	59
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	59	5	64

Merged error: 0.5b

Counts

64 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.3b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.2b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.9b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- (+ (* 0.020833333333333336 (pow t 3)) 0.5) (* 0.25 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 → 267

Calls

4 calls:

10.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
8.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
8.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
40.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- (+ (* 0.020833333333333336 (pow t 3)) 0.5) (* 0.25 t)) c_n)))

series872.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
76.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
78.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
669.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p) (pow (- (+ (* 0.020833333333333336 (pow t 3)) 0.5) (* 0.25 t)) c_n)))

simplify305.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	998	5949
1	3225	5709
2	5003	5709

prune502.0ms

Filtered

279 candidates to 80 candidates (28.7%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	279	0	279
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	279	5	284

Merged error: 0.5b

Counts

284 → 5

regimes318.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	18	6
1	18	6

end0.0ms

sample18.7s

Algorithm

intervals

Results

12.6s	1914×	body	5120	exit
4.1s	25548×	body	80	overflowed
654.0ms	29664×	pre	80	true
223.0ms	2135×	body	80	valid
32.0ms	15×	body	1280	valid
25.0ms	7×	body	2560	valid
25.0ms	2×	body	5120	valid
9.0ms	9×	body	640	valid
5.0ms	18×	body	160	valid
5.0ms	4×	body	640	overflowed
4.0ms	8×	body	320	valid
1.0ms	3×	body	160	overflowed
1.0ms	1×	body	320	overflowed