Details

sample40.5s

Algorithm

intervals

Results

40.3s	3261×	body	10240	exit
82.0ms	3517×	pre	80	true
25.0ms	245×	body	80	valid
4.0ms	5×	body	640	valid
3.0ms	1×	body	1280	valid
2.0ms	1×	body	2560	valid
1.0ms	4×	body	160	valid

simplify25.0ms

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: 7.7b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
1.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.4b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.4b	(/ (* (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)))

rewrite163.0ms

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:

22.0ms	(- 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)
94.0ms	(/ (* (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)))

series751.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
63.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
571.0ms	(/ (* (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)))

simplify134.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (22.0ms)

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

prune610.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.5b

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 0.5 (* s c_n))

rewrite6.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1×	`expm1-log1p-u` `associate-r` `*-commutative` `log1p-expm1-u` `add-log-exp`

Counts

1 → 20

Calls

1 calls:

6.0ms

(* 0.5 (* s c_n))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(* 0.5 (* s c_n))

simplify73.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	88	77
1	320	62
2	1234	62
3	3438	62
4	5002	62

prune52.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
1.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.5b	(/ (* (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)))

rewrite135.0ms

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:

24.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
8.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
80.0ms	(/ (* (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)))

series834.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
691.0ms	(/ (* (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)))

simplify122.0ms

Algorithm

egg-herbie

Counts

227 → 227

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1156	4971
1	4787	3939
2	5001	3939

prune695.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

localize12.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma 1/2 (* (pow (log 0.5) 2) (pow c_p 2)) (fma 0.5 (* s c_p) 1))
0.2b	(* (pow (log 0.5) 2) (pow c_p 2))
1.0b	(pow (log 0.5) 2)

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

25×	`add-sqr-sqrt`
19×	`unpow-prod-down`
16×	`add-exp-log` `unswap-sqr`
11×	`unpow2` `sqr-pow`
9×	`add-cube-cbrt` `-un-lft-identity` `associate-l*` `prod-exp`
8×	`associate-r`
7×	`pow-to-exp` `pow-exp`
6×	`pow1`
5×	`add-cbrt-cube`
3×	`expm1-log1p-u` `pow-unpow` `log1p-expm1-u` `add-log-exp`
2×	`log-pow`
1×	`pow-pow` `pow-prod-down` `*-commutative` `cbrt-unprod` `fma-udef`

Counts

3 → 85

Calls

3 calls:

0.0ms	(fma 1/2 (* (pow (log 0.5) 2) (pow c_p 2)) (fma 0.5 (* s c_p) 1))
9.0ms	(* (pow (log 0.5) 2) (pow c_p 2))
2.0ms	(pow (log 0.5) 2)

series241.0ms

Counts

3 → 7

Calls

3 calls:

89.0ms	(fma 1/2 (* (pow (log 0.5) 2) (pow c_p 2)) (fma 0.5 (* s c_p) 1))
152.0ms	(* (pow (log 0.5) 2) (pow c_p 2))
0.0ms	(pow (log 0.5) 2)

simplify32.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	228	527
1	912	445
2	5002	440

prune193.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.5b

regimes315.0ms

bsearch1.7s

Steps

Iters	Range		Point
7	-1.414082875184719e-26	-7.437857922401063e-28	-7.639139057981639e-28

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	45	29
1	45	29

end0.0ms

sample5.3m

Algorithm

intervals

Results

5.3m	25949×	body	10240	exit
590.0ms	27992×	pre	80	true
186.0ms	1976×	body	80	valid
29.0ms	16×	body	1280	valid
10.0ms	12×	body	640	valid
8.0ms	29×	body	160	valid
7.0ms	3×	body	2560	valid
5.0ms	1×	body	5120	valid
2.0ms	6×	body	320	valid