Details

sample47.9s

Algorithm

intervals

Results

47.6s	3808×	body	10240	exit
84.0ms	4064×	pre	80	true
21.0ms	247×	body	80	valid
6.0ms	3×	body	1280	valid
1.0ms	2×	body	320	valid
1.0ms	1×	body	640	valid
1.0ms	3×	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: 7.0b

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.9b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.9b	(/ (* (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)))

rewrite157.0ms

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 (- s)))))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
12.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
92.0ms	(/ (* (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)))

series740.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
66.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
66.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
560.0ms	(/ (* (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 (21.0ms)

Iter	Nodes	Cost
0	1281	8124
1	4380	7090
2	5001	7090

prune591.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.6b

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))

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

prune50.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
24.8b	(cbrt (* 0.5 (* s c_n)))
24.8b	(cbrt (* 0.5 (* s c_n)))
24.8b	(cbrt (* 0.5 (* s c_n)))

rewrite22.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 66

Calls

4 calls:

7.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
6.0ms	(cbrt (* 0.5 (* s c_n)))
4.0ms	(cbrt (* 0.5 (* s c_n)))
4.0ms	(cbrt (* 0.5 (* s c_n)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
86.0ms	(cbrt (* 0.5 (* s c_n)))
87.0ms	(cbrt (* 0.5 (* s c_n)))
87.0ms	(cbrt (* 0.5 (* s c_n)))

simplify99.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (89.0ms)

Iter	Nodes	Cost
0	212	478
1	738	427
2	3536	370
3	5002	365

prune243.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 1.6b

localize9.0ms

Local error

Found 3 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.1b	(expm1 (log1p (* 0.5 (* s c_n))))
0.2b	(log1p (* 0.5 (* s c_n)))

rewrite7.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

3 → 42

Calls

3 calls:

6.0ms	(* 0.5 (* s c_n))
0.0ms	(expm1 (log1p (* 0.5 (* s c_n))))
0.0ms	(log1p (* 0.5 (* s c_n)))

series346.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(* 0.5 (* s c_n))
229.0ms	(expm1 (log1p (* 0.5 (* s c_n))))
100.0ms	(log1p (* 0.5 (* s c_n)))

simplify30.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (26.0ms)

Iter	Nodes	Cost
0	265	250
1	1006	219
2	5001	209

prune132.0ms

Pruning

7 alts after pruning (7 fresh and 0 done)

Merged error: 1.6b

regimes732.0ms

bsearch3.9s

Steps

Iters	Range		Point
6	-3.4158361945667567e-79	-5.1113148475473346e-80	-6.3436807628579684e-80

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	42
1	51	42

end0.0ms

sample6.4m

Algorithm

intervals

Results

6.3m	31417×	body	10240	exit
620.0ms	33809×	pre	80	true
193.0ms	2320×	body	80	valid
36.0ms	6×	body	5120	valid
33.0ms	20×	body	1280	valid
10.0ms	13×	body	640	valid
7.0ms	3×	body	2560	valid
6.0ms	26×	body	160	valid
2.0ms	4×	body	320	valid