Details

sample36.8s

Algorithm

intervals

Results

36.5s	2875×	body	10240	exit
64.0ms	3131×	pre	80	true
39.0ms	2×	body	5120	valid
23.0ms	249×	body	80	valid
4.0ms	2×	body	1280	valid
2.0ms	1×	body	2560	valid
1.0ms	2×	body	160	valid

simplify23.0ms

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: 6.5b

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.2b	(/ (* (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)))

rewrite243.0ms

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:

29.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
18.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
18.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
160.0ms	(/ (* (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)))

series718.0ms

Counts

4 → 12

Calls

4 calls:

41.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
65.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
64.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
548.0ms	(/ (* (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)))

simplify100.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (16.0ms)

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

prune445.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

localize9.0ms

Local error

Found 2 expressions with local error:

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

rewrite30.0ms

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:

15.0ms	(* 0.5 (* s c_n))
15.0ms	(* 0.5 (* s c_p))

series37.0ms

Counts

2 → 6

Calls

2 calls:

17.0ms	(* 0.5 (* s c_n))
19.0ms	(* 0.5 (* s c_p))

simplify54.0ms

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

prune79.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize11.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.0b	(* 0.5 (* s c_p))
0.4b	(- (+ (log (exp (* 0.5 (* s c_p)))) 1) (* 0.5 (* s c_n)))
0.4b	(log (exp (* 0.5 (* s c_p))))

rewrite99.0ms

Algorithm

rewrite-expression-head

Rules

15×	`pow1`
14×	`add-exp-log` `add-cbrt-cube`
9×	`add-log-exp`
7×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
3×	`log-prod` `log-pow`
2×	`diff-log` `associate-r` `*-commutative`
1×	`sub-neg` `exp-prod` `flip3--` `exp-to-pow` `rem-log-exp` `associate--l+` `sum-log` `flip--`

Counts

4 → 64

Calls

4 calls:

15.0ms	(* 0.5 (* s c_n))
14.0ms	(* 0.5 (* s c_p))
63.0ms	(- (+ (log (exp (* 0.5 (* s c_p)))) 1) (* 0.5 (* s c_n)))
4.0ms	(log (exp (* 0.5 (* s c_p))))

series101.0ms

Counts

4 → 12

Calls

4 calls:

16.0ms	(* 0.5 (* s c_n))
20.0ms	(* 0.5 (* s c_p))
47.0ms	(- (+ (log (exp (* 0.5 (* s c_p)))) 1) (* 0.5 (* s c_n)))
17.0ms	(log (exp (* 0.5 (* s c_p))))

simplify32.0ms

Algorithm

egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 2 (27.0ms)

Iter	Nodes	Cost
0	253	389
1	1024	326
2	5001	317

prune161.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize32.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.7b	(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)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite223.0ms

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:

18.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
28.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
19.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
152.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series864.0ms

Counts

4 → 12

Calls

4 calls:

91.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
46.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
66.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
661.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify101.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	923	2823
1	4047	2572
2	5002	2572

prune439.0ms

Pruning

5 alts after pruning (3 fresh and 2 done)

Merged error: 0.7b

regimes666.0ms

bsearch19.6s

Steps

Iters	Range		Point
4	1.6398577187421343e-15	2.534599250284959e-15	1.6881971243140533e-15
10	-5.919811206286693e+19	-5753004.918784462	-752262852.4271613

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	72	58
1	72	58

end0.0ms

sample4.0m

Algorithm

intervals

Results

3.9m	19239×	body	10240	exit
375.0ms	20746×	pre	80	true
132.0ms	1459×	body	80	valid
84.0ms	8×	body	5120	valid
23.0ms	12×	body	1280	valid
8.0ms	3×	body	2560	valid
6.0ms	8×	body	640	valid
3.0ms	12×	body	160	valid
2.0ms	5×	body	320	valid