Details

sample2.9s

Algorithm

intervals

Results

2.0s	271×	body	5120	exit
585.0ms	3394×	body	80	overflowed
92.0ms	3923×	pre	80	true
26.0ms	239×	body	80	valid
8.0ms	4×	body	1280	valid
3.0ms	8×	body	160	valid
2.0ms	1×	body	2560	valid
2.0ms	2×	body	640	valid
2.0ms	3×	body	320	valid
0.0ms	1×	body	160	overflowed

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	53	25
1	147	25
2	850	25
3	5001	25

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 7.9b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
1.5b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
4.4b	(/ (* (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)))

rewrite96.0ms

Algorithm

rewrite-expression-head

Rules

553×	`add-exp-log`
312×	`prod-exp`
262×	`pow-exp`
248×	`div-exp`
183×	`pow-to-exp`
145×	`*-un-lft-identity`
109×	`add-sqr-sqrt`
108×	`prod-diff`
99×	`add-cube-cbrt`
87×	`times-frac`
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 → 371

Calls

4 calls:

15.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
11.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
39.0ms	(/ (* (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)))

series780.0ms

Counts

4 → 12

Calls

4 calls:

51.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
49.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
72.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
607.0ms	(/ (* (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)))

simplify109.0ms

Algorithm

egg-herbie

Counts

383 → 383

Iterations

Useful iterations: 1 (37.0ms)

Iter	Nodes	Cost
0	1530	10036
1	5001	8504

prune621.0ms

Filtered

383 candidates to 112 candidates (29.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	381	2	383
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	382	2	384

Merged error: 1.0b

Counts

384 → 2

localize8.0ms

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))

series21.0ms

Counts

1 → 3

Calls

1 calls:

21.0ms

(* 0.5 (* s c_n))

simplify85.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	88	77
1	320	62
2	1234	62
3	3438	62
4	5002	62

prune44.0ms

Filtered

23 candidates to 13 candidates (56.5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	22	1	23
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	23	2	25

Merged error: 1.0b

Counts

25 → 2

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))))

series379.0ms

Counts

3 → 9

Calls

3 calls:

109.0ms	(log1p (* 0.5 (* s c_n)))
19.0ms	(* 0.5 (* s c_n))
250.0ms	(expm1 (log1p (* 0.5 (* s c_n))))

simplify32.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (28.0ms)

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

prune130.0ms

Filtered

51 candidates to 37 candidates (72.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	49	2	51
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	50	3	53

Merged error: 1.0b

Counts

53 → 3

localize17.0ms

Local error

Found 4 expressions with local error:

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

rewrite8.0ms

Algorithm

rewrite-expression-head

Rules

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

Counts

4 → 53

Calls

4 calls:

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

series1.2s

Counts

4 → 12

Calls

4 calls:

109.0ms	(log1p (* 0.5 (* s c_n)))
19.0ms	(* 0.5 (* s c_n))
342.0ms	(expm1 (log1p (log1p (* 0.5 (* s c_n)))))
693.0ms	(expm1 (expm1 (log1p (log1p (* 0.5 (* s c_n))))))

simplify36.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (30.0ms)

Iter	Nodes	Cost
0	289	343
1	1079	304
2	5002	296

prune173.0ms

Filtered

65 candidates to 49 candidates (75.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	65	3	68

Merged error: 1.0b

Counts

68 → 3

regimes208.0ms

bsearch862.0ms

Steps

Iters	Range		Point
9	-691.3040501824005	-0.0037296439327094135	-0.0037629092859684343

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	33
1	49	33

end0.0ms

sample10.7s

Algorithm

intervals

Results

7.4s	1114×	body	5120	exit
2.3s	13981×	body	80	overflowed
354.0ms	16221×	pre	80	true
113.0ms	1071×	body	80	valid
20.0ms	10×	body	1280	valid
19.0ms	3×	body	5120	valid
12.0ms	12×	body	640	valid
7.0ms	2×	body	2560	valid
6.0ms	18×	body	160	valid
4.0ms	7×	body	320	valid
1.0ms	1×	body	640	overflowed
1.0ms	1×	body	320	overflowed
0.0ms	1×	body	160	overflowed

Details

sample2.9s

simplify29.0ms

prune5.0ms

localize25.0ms

rewrite96.0ms

series780.0ms

simplify109.0ms

prune621.0ms

localize8.0ms

rewrite6.0ms

series21.0ms

simplify85.0ms

prune44.0ms

localize10.0ms

rewrite7.0ms

series379.0ms

simplify32.0ms

prune130.0ms

localize17.0ms

rewrite8.0ms

series1.2s

simplify36.0ms

prune173.0ms

regimes208.0ms

bsearch862.0ms

simplify2.0ms

end0.0ms

sample10.7s

Profiling