Details

sample2.4s

Algorithm

intervals

Results

1.6s	234×	body	5120	exit
496.0ms	2896×	body	80	overflowed
76.0ms	3388×	pre	80	true
43.0ms	1×	body	5120	valid
27.0ms	246×	body	80	valid
12.0ms	2×	body	2560	valid
4.0ms	2×	body	1280	valid
2.0ms	5×	body	160	valid
1.0ms	2×	body	320	overflowed

simplify27.0ms

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

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: 5.3b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.2b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) 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)))

rewrite95.0ms

Algorithm

rewrite-expression-head

Rules

555×	`add-exp-log`
312×	`prod-exp`
262×	`pow-exp`
249×	`div-exp`
183×	`pow-to-exp`
99×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
62×	`times-frac`
54×	`prod-diff`
18×	`unpow-prod-down` `add-cbrt-cube`
16×	`distribute-lft-out`
10×	`associate-/r/`
6×	`div-inv` `add-log-exp`
5×	`pow1` `cbrt-undiv` `flip3-+` `associate-/r*` `flip-+`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `associate-/l*`
3×	`pow-unpow` `fma-neg`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `pow-pow` `diff-log` `flip--` `distribute-lft-out--` `sqr-pow`

Counts

4 → 332

Calls

4 calls:

6.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
12.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
44.0ms	(/ (* (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)))

series755.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
52.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
611.0ms	(/ (* (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)))

simplify327.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (25.0ms)

Iter	Nodes	Cost
0	1256	8043
1	4486	6999
2	5001	6999

prune540.0ms

Filtered

344 candidates to 105 candidates (30.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	340	4	344
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	341	4	345

Merged error: 0.5b

Counts

345 → 4

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))

series22.0ms

Counts

1 → 3

Calls

1 calls:

22.0ms

(* 0.5 (* s c_n))

simplify82.0ms

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

prune45.0ms

Filtered

23 candidates to 13 candidates (56.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	23	0	23
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	23	4	27

Merged error: 0.5b

Counts

27 → 4

localize32.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.2b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.2b	(fma 0.5 (* t c_p) 1)
1.2b	(/ (* (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)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

168×	`add-exp-log`
87×	`prod-exp`
84×	`*-un-lft-identity`
65×	`div-exp`
61×	`add-sqr-sqrt`
56×	`add-cube-cbrt`
54×	`prod-diff`
53×	`pow-exp`
50×	`times-frac`
41×	`pow-to-exp`
18×	`add-cbrt-cube`
13×	`distribute-lft-out`
8×	`associate-/r/`
6×	`add-log-exp`
5×	`cbrt-undiv` `associate-/r*` `div-inv`
4×	`pow1` `expm1-log1p-u` `flip3-+` `cbrt-unprod` `flip-+` `log1p-expm1-u` `associate-/l*`
3×	`fma-neg`
2×	`frac-2neg` `clear-num` `difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `fma-udef` `distribute-lft-out--`

Counts

4 → 190

Calls

4 calls:

6.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
12.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
1.0ms	(fma 0.5 (* t c_p) 1)
34.0ms	(/ (* (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)))

series860.0ms

Counts

4 → 12

Calls

4 calls:

26.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
51.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
34.0ms	(fma 0.5 (* t c_p) 1)
748.0ms	(/ (* (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)))

simplify125.0ms

Algorithm

egg-herbie

Counts

202 → 202

Iterations

Useful iterations: 2 (86.0ms)

Iter	Nodes	Cost
0	1064	4673
1	4259	3635
2	5001	3631

prune558.0ms

Filtered

202 candidates to 90 candidates (44.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	201	5	206

Merged error: 0.5b

Counts

206 → 5

localize32.0ms

Local error

Found 4 expressions with local error:

0.1b	(* 0.020833333333333336 (pow t 3))
0.2b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) 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 (fma t 0.25 (- 0.5 (* 0.020833333333333336 (pow t 3))))) c_n)))

rewrite87.0ms

Algorithm

rewrite-expression-head

Rules

558×	`add-exp-log`
315×	`prod-exp`
263×	`pow-exp`
248×	`div-exp`
184×	`pow-to-exp`
86×	`*-un-lft-identity`
72×	`add-sqr-sqrt`
60×	`add-cube-cbrt`
54×	`prod-diff`
50×	`times-frac`
22×	`unpow-prod-down`
18×	`add-cbrt-cube`
12×	`associate-r` `distribute-lft-out`
8×	`associate-/r/`
6×	`add-log-exp`
5×	`pow1` `cbrt-unprod` `div-inv`
4×	`cbrt-undiv` `expm1-log1p-u` `flip3-+` `cube-prod` `flip-+` `log1p-expm1-u` `unswap-sqr`
3×	`pow-unpow` `fma-neg` `associate-l` `sqr-pow`
2×	`difference-of-squares`
1×	`cube-mult` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `diff-log` `unpow3` `clear-num` `associate-/r` `-commutative` `flip--` `associate-/l*` `distribute-lft-out--`

Counts

4 → 330

Calls

4 calls:

7.0ms	(* 0.020833333333333336 (pow t 3))
14.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
8.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
36.0ms	(/ (* (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 (fma t 0.25 (- 0.5 (* 0.020833333333333336 (pow t 3))))) c_n)))

series824.0ms

Counts

4 → 12

Calls

4 calls:

34.0ms	(* 0.020833333333333336 (pow t 3))
52.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
72.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
666.0ms	(/ (* (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 (fma t 0.25 (- 0.5 (* 0.020833333333333336 (pow t 3))))) c_n)))

simplify163.0ms

Algorithm

egg-herbie

Counts

342 → 342

Iterations

Useful iterations: 1 (28.0ms)

Iter	Nodes	Cost
0	1320	7898
1	4834	6860
2	5001	6860

prune679.0ms

Filtered

342 candidates to 101 candidates (29.5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	342	0	342
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	342	5	347

Merged error: 0.5b

Counts

347 → 5

regimes638.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	62	56
1	62	56

end0.0ms

sample21.7s

Algorithm

intervals

Results

14.8s	2226×	body	5120	exit
4.8s	29019×	body	80	overflowed
739.0ms	33672×	pre	80	true
254.0ms	2337×	body	80	valid
64.0ms	5×	body	5120	valid
30.0ms	14×	body	1280	valid
19.0ms	4×	body	2560	valid
13.0ms	12×	body	640	valid
10.0ms	30×	body	160	valid
7.0ms	14×	body	320	valid
4.0ms	5×	body	320	overflowed
2.0ms	2×	body	640	overflowed
2.0ms	4×	body	160	overflowed

Details

sample2.4s

simplify27.0ms

prune4.0ms

localize22.0ms

rewrite95.0ms

series755.0ms

simplify327.0ms

prune540.0ms

localize8.0ms

rewrite5.0ms

series22.0ms

simplify82.0ms

prune45.0ms

localize32.0ms

rewrite63.0ms

series860.0ms

simplify125.0ms

prune558.0ms

localize32.0ms

rewrite87.0ms

series824.0ms

simplify163.0ms

prune679.0ms

regimes638.0ms

bsearch1.0ms

simplify2.0ms

end0.0ms

sample21.7s

Profiling