Details

sample38.8s

Algorithm

intervals

Results

38.5s	2986×	body	10240	exit
70.0ms	3242×	pre	80	true
23.0ms	251×	body	80	valid
2.0ms	1×	body	2560	valid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	160	valid
0.0ms	1×	body	320	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: 5.0b

localize25.0ms

Local error

Found 4 expressions with local error:

0.2b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) 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)))

rewrite85.0ms

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:

14.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
37.0ms	(/ (* (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)))

series931.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
234.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
585.0ms	(/ (* (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)))

simplify131.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (22.0ms)

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

prune579.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize8.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 0.5 (* s c_n))

rewrite5.0ms

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:

4.0ms

(* 0.5 (* s c_n))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(* 0.5 (* s c_n))

simplify74.0ms

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

prune44.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize10.0ms

Local error

Found 3 expressions with local error:

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

1.0ms	(log1p (* 0.5 (* s c_n)))
5.0ms	(* 0.5 (* s c_n))
1.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

series345.0ms

Counts

3 → 9

Calls

3 calls:

100.0ms	(log1p (* 0.5 (* s c_n)))
18.0ms	(* 0.5 (* s c_n))
227.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

simplify29.0ms

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

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (log1p (* 0.5 (* s c_n)))) (cbrt (log1p (* 0.5 (* s c_n)))))
27.7b	(cbrt (log1p (* 0.5 (* s c_n))))
27.7b	(cbrt (log1p (* 0.5 (* s c_n))))
27.7b	(cbrt (log1p (* 0.5 (* s c_n))))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 81

Calls

4 calls:

5.0ms	(* (cbrt (log1p (* 0.5 (* s c_n)))) (cbrt (log1p (* 0.5 (* s c_n)))))
1.0ms	(cbrt (log1p (* 0.5 (* s c_n))))
1.0ms	(cbrt (log1p (* 0.5 (* s c_n))))
1.0ms	(cbrt (log1p (* 0.5 (* s c_n))))

series2.4s

Counts

4 → 12

Calls

4 calls:

1.2s	(* (cbrt (log1p (* 0.5 (* s c_n)))) (cbrt (log1p (* 0.5 (* s c_n)))))
389.0ms	(cbrt (log1p (* 0.5 (* s c_n))))
384.0ms	(cbrt (log1p (* 0.5 (* s c_n))))
385.0ms	(cbrt (log1p (* 0.5 (* s c_n))))

simplify90.0ms

Algorithm

egg-herbie

Counts

93 → 93

Iterations

Useful iterations: 2 (76.0ms)

Iter	Nodes	Cost
0	828	1670
1	3976	1529
2	5001	1511

prune413.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.2b

regimes159.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	58
1	58	58

end0.0ms

sample9.3m

Algorithm

intervals

Results

9.2m	45266×	body	10240	exit
917.0ms	48821×	pre	80	true
306.0ms	3423×	body	80	valid
52.0ms	4×	body	5120	valid
52.0ms	31×	body	1280	valid
26.0ms	9×	body	2560	valid
16.0ms	20×	body	640	valid
14.0ms	54×	body	160	valid
5.0ms	13×	body	320	valid