Details

sample40.6s

Algorithm

intervals

Results

40.3s	3253×	body	10240	exit
78.0ms	3509×	pre	80	true
23.0ms	246×	body	80	valid
6.0ms	1×	body	2560	valid
5.0ms	3×	body	1280	valid
2.0ms	2×	body	640	valid
1.0ms	3×	body	320	valid
0.0ms	1×	body	160	valid

simplify24.0ms

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.2b	(/ (* (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)))

rewrite158.0ms

Algorithm

rewrite-expression-head

Rules

556×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
249×	`div-exp`
184×	`pow-to-exp`
97×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
62×	`times-frac`
54×	`prod-diff`
36×	`unpow-prod-down`
16×	`add-cbrt-cube`
15×	`distribute-lft-out`
10×	`associate-/r/`
6×	`pow1` `pow-unpow` `div-inv` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow-pow` `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 → 332

Calls

4 calls:

21.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
91.0ms	(/ (* (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)))

series745.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
65.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
565.0ms	(/ (* (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)))

simplify132.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (22.0ms)

Iter	Nodes	Cost
0	1281	8124
1	4389	7090
2	5001	7090

prune601.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.3b

localize27.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.0b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite130.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-exp-log`
99×	`*-un-lft-identity`
87×	`prod-exp`
70×	`add-sqr-sqrt`
66×	`div-exp`
65×	`add-cube-cbrt`
62×	`times-frac`
55×	`pow-exp`
54×	`prod-diff`
42×	`pow-to-exp`
18×	`unpow-prod-down` `add-cbrt-cube`
16×	`distribute-lft-out`
10×	`associate-/r/`
6×	`div-inv` `add-log-exp`
5×	`pow1` `cbrt-undiv` `flip3-+` `associate-/r*` `flip-+`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `associate-/l*`
3×	`pow-unpow` `fma-neg`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `pow-pow` `diff-log` `flip--` `distribute-lft-out--` `sqr-pow`

Counts

4 → 215

Calls

4 calls:

8.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
21.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
11.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
78.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series819.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
48.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
64.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
683.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify123.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1156	4971
1	4789	3939
2	5001	3939

prune690.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.3b

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
1.0b	(/ (* (fma (log 0.5) c_p (fma 0.5 (* s c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite133.0ms

Algorithm

rewrite-expression-head

Rules

147×	`*-un-lft-identity`
109×	`add-sqr-sqrt`
108×	`prod-diff`
99×	`add-cube-cbrt`
87×	`times-frac`
54×	`add-exp-log`
24×	`prod-exp`
22×	`distribute-lft-out`
18×	`add-cbrt-cube`
17×	`div-exp`
14×	`associate-/r/`
8×	`pow-to-exp` `pow-exp` `div-inv` `add-log-exp`
7×	`flip3-+` `flip-+`
6×	`fma-neg`
5×	`cbrt-undiv` `associate-/r*`
4×	`pow1` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `associate-/l*` `difference-of-squares`
2×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `flip--` `distribute-lft-out--`

Counts

4 → 218

Calls

4 calls:

23.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
8.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
21.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
69.0ms	(/ (* (fma (log 0.5) c_p (fma 0.5 (* s c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series745.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
49.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
621.0ms	(/ (* (fma (log 0.5) c_p (fma 0.5 (* s c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify61.0ms

Algorithm

egg-herbie

Counts

230 → 230

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1307	5968
1	5001	4137

prune811.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.3b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.2b	(/ (* (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 (fma (pow t 3) 0.020833333333333336 (- 0.5 (* 0.25 t))) c_n)))

rewrite109.0ms

Algorithm

rewrite-expression-head

Rules

558×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
250×	`div-exp`
184×	`pow-to-exp`
51×	`*-un-lft-identity`
37×	`times-frac`
36×	`unpow-prod-down`
31×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-cbrt-cube`
10×	`distribute-lft-out`
6×	`pow1` `pow-unpow` `associate-/r/`
5×	`cbrt-undiv` `associate-/r*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

4 → 293

Calls

4 calls:

10.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
60.0ms	(/ (* (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 (fma (pow t 3) 0.020833333333333336 (- 0.5 (* 0.25 t))) c_n)))

series776.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
612.0ms	(/ (* (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 (fma (pow t 3) 0.020833333333333336 (- 0.5 (* 0.25 t))) c_n)))

simplify112.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 1 (18.0ms)

Iter	Nodes	Cost
0	1003	5932
1	3398	5694
2	5001	5694

prune677.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.3b

regimes407.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	48
1	44	48

end0.0ms

sample6.4m

Algorithm

intervals

Results

6.4m	31523×	body	10240	exit
665.0ms	34021×	pre	80	true
208.0ms	2427×	body	80	valid
47.0ms	5×	body	5120	valid
21.0ms	7×	body	2560	valid
18.0ms	10×	body	1280	valid
10.0ms	16×	body	640	valid
5.0ms	22×	body	160	valid
4.0ms	11×	body	320	valid