Details

sample40.6s

Algorithm

intervals

Results

40.3s	3287×	body	10240	exit
87.0ms	3543×	pre	80	true
23.0ms	242×	body	80	valid
15.0ms	1×	body	5120	valid
8.0ms	2×	body	2560	valid
2.0ms	1×	body	1280	valid
2.0ms	7×	body	160	valid
1.0ms	2×	body	640	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: 7.3b

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.0b	(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)))

rewrite86.0ms

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:

11.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
41.0ms	(/ (* (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)))

series778.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
72.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
586.0ms	(/ (* (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	4389	7090
2	5001	7090

prune742.0ms

Pruning

4 alts after pruning (4 fresh and 0 done)

Merged error: 0.7b

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:

5.0ms

(* 0.5 (* s c_n))

series18.0ms

Counts

1 → 3

Calls

1 calls:

18.0ms

(* 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

prune55.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

localize10.0ms

Local error

Found 3 expressions with local error:

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

rewrite9.0ms

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:

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

series346.0ms

Counts

3 → 9

Calls

3 calls:

18.0ms	(* 0.5 (* s c_n))
228.0ms	(expm1 (log1p (* 0.5 (* s c_n))))
100.0ms	(log1p (* 0.5 (* s c_n)))

simplify31.0ms

Algorithm

egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 2 (26.0ms)

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

prune146.0ms

Pruning

5 alts after pruning (5 fresh and 0 done)

Merged error: 0.7b

localize12.0ms

Local error

Found 4 expressions with local error:

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))))))
0.5b	(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:

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

series1.1s

Counts

4 → 12

Calls

4 calls:

18.0ms	(* 0.5 (* s c_n))
320.0ms	(expm1 (log1p (log1p (* 0.5 (* s c_n)))))
626.0ms	(expm1 (expm1 (log1p (log1p (* 0.5 (* s c_n))))))
100.0ms	(log1p (* 0.5 (* s c_n)))

simplify33.0ms

Algorithm

egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	289	343
1	1079	304
2	5001	296

prune190.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 0.7b

regimes587.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	49	34
1	49	34

end0.0ms

sample8.3m

Algorithm

intervals

Results

8.3m	40445×	body	10240	exit
938.0ms	43583×	pre	80	true
284.0ms	3033×	body	80	valid
63.0ms	8×	body	5120	valid
37.0ms	19×	body	1280	valid
22.0ms	7×	body	2560	valid
13.0ms	48×	body	160	valid
10.0ms	13×	body	640	valid
4.0ms	10×	body	320	valid