Details

sample38.5s

Algorithm

intervals

Results

38.2s	2836×	body	10240	exit
144.0ms	3092×	pre	80	true
38.0ms	253×	body	80	valid
2.0ms	1×	body	1280	valid
1.0ms	2×	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

prune13.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.5b

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.2b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.7b	(/ (* (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

557×	`add-exp-log`
312×	`prod-exp`
265×	`pow-exp`
249×	`div-exp`
185×	`pow-to-exp`
42×	`unpow-prod-down`
38×	`*-un-lft-identity`
29×	`add-sqr-sqrt`
26×	`times-frac`
24×	`add-cube-cbrt`
16×	`add-cbrt-cube`
9×	`pow-unpow`
7×	`pow1`
6×	`distribute-lft-out`
4×	`cbrt-undiv` `expm1-log1p-u` `associate-/r/` `cbrt-unprod` `log1p-expm1-u` `add-log-exp`
3×	`pow-pow` `div-inv` `sqr-pow`
2×	`flip3-+` `flip-+` `difference-of-squares`
1×	`frac-2neg` `clear-num` `associate-/r` `associate-/l` `distribute-lft-out--`

Counts

4 → 280

Calls

4 calls:

32.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
88.0ms	(/ (* (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)))

series255.0ms

Counts

4 → 12

Calls

4 calls:

19.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
16.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
204.0ms	(/ (* (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)))

simplify103.0ms

Algorithm

egg-herbie

Counts

292 → 292

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	1007	6085
1	3337	5843
2	5002	5843

prune1.6s

Pruning

3 alts after pruning (3 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))

series4.0ms

Counts

1 → 3

Calls

1 calls:

4.0ms

(* 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

prune124.0ms

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.1b	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
0.5b	(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)))

rewrite150.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 202

Calls

4 calls:

20.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
30.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
11.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
76.0ms	(/ (* (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)))

series277.0ms

Counts

4 → 12

Calls

4 calls:

8.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
21.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
233.0ms	(/ (* (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

214 → 214

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1173	4936
1	4812	3905
2	5001	3905

prune1.9s

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 0.1b

localize32.0ms

Local error

Found 4 expressions with local error:

0.5b	(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)))
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)))
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)))

rewrite253.0ms

Algorithm

rewrite-expression-head

Rules

493×	`add-exp-log`
261×	`prod-exp`
193×	`div-exp`
161×	`pow-exp`
124×	`pow-to-exp`
40×	`add-cbrt-cube`
19×	`*-un-lft-identity`
18×	`unpow-prod-down`
15×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-undiv` `cbrt-unprod`
5×	`pow1`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-unpow` `frac-2neg` `clear-num` `associate-/r` `distribute-lft-out` `associate-/l`
2×	`associate-/r/`
1×	`pow-pow` `flip3-+` `flip-+` `sqr-pow`

Counts

4 → 248

Calls

4 calls:

10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
76.0ms	(/ (* (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)))
76.0ms	(/ (* (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)))
76.0ms	(/ (* (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)))

series726.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
236.0ms	(/ (* (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)))
236.0ms	(/ (* (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)))
238.0ms	(/ (* (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)))

simplify106.0ms

Algorithm

egg-herbie

Counts

260 → 260

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	694	6627
1	2858	5986
2	5003	5974

prune2.0s

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 0.1b

regimes846.0ms

bsearch3.8s

Steps

Iters	Range		Point
6	-3.444845483985724e-119	-2.422812615369833e-120	-2.469112325337647e-120

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	82
1	49	82

end0.0ms

sample4.0m

Algorithm

intervals

Results

4.0m	18376×	body	10240	exit
831.0ms	19848×	pre	80	true
209.0ms	1429×	body	80	valid
19.0ms	10×	body	1280	valid
13.0ms	12×	body	640	valid
12.0ms	3×	body	2560	valid
5.0ms	13×	body	160	valid
3.0ms	5×	body	320	valid