Details

sample2.3m

Algorithm

intervals

Results

2.3m	2933×	body	10240	exit
65.0ms	3189×	pre	80	true
41.0ms	248×	body	80	valid
29.0ms	4×	body	1280	valid
18.0ms	2×	body	2560	valid
1.0ms	1×	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: 5.6b

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.3b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.5b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.9b	(/ (* (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)))

rewrite148.0ms

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:

20.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
11.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
87.0ms	(/ (* (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)))

series749.0ms

Counts

4 → 12

Calls

4 calls:

49.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
564.0ms	(/ (* (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)))

simplify126.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (22.0ms)

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

prune628.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.1b

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:

5.0ms

(* 0.5 (* s c_n))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(* 0.5 (* s c_n))

simplify71.0ms

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

prune60.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.2b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.3b	(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)))

rewrite143.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 254

Calls

4 calls:

22.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
20.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
77.0ms	(/ (* (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)))

series848.0ms

Counts

4 → 12

Calls

4 calls:

44.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
49.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
686.0ms	(/ (* (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)))

simplify73.0ms

Algorithm

egg-herbie

Counts

266 → 266

Iterations

Useful iterations: 1 (27.0ms)

Iter	Nodes	Cost
0	1441	6977
1	5002	5446

prune780.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize43.0ms

Local error

Found 4 expressions with local error:

0.0b	(fma (log 0.5) c_p (fma 0.5 (* t c_p) 1))
0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.3b	(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 (fma (pow t 3) 0.020833333333333336 (- 0.5 (* 0.25 t))) c_n)))

rewrite134.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 190

Calls

4 calls:

0.0ms	(fma (log 0.5) c_p (fma 0.5 (* t c_p) 1))
33.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
72.0ms	(/ (* (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 (fma (pow t 3) 0.020833333333333336 (- 0.5 (* 0.25 t))) c_n)))

series917.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(fma (log 0.5) c_p (fma 0.5 (* t c_p) 1))
44.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
757.0ms	(/ (* (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 (fma (pow t 3) 0.020833333333333336 (- 0.5 (* 0.25 t))) c_n)))

simplify115.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (84.0ms)

Iter	Nodes	Cost
0	1065	4707
1	4498	3683
2	5001	3681

prune638.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 0.1b

regimes596.0ms

bsearch22.4s

Steps

Iters	Range		Point
7	-7.183956273494884e-71	-4.1021087505030886e-72	-7.1249341297495224e-71

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	28
1	47	28

end0.0ms

sample3.0m

Algorithm

intervals

Results

3.0m	3838×	body	10240	exit
81.0ms	4144×	pre	80	true
47.0ms	295×	body	80	valid
28.0ms	4×	body	1280	valid
17.0ms	2×	body	2560	valid
2.0ms	2×	body	320	valid
2.0ms	1×	body	640	valid
1.0ms	2×	body	160	valid