Details

sample2.9s

Algorithm

intervals

Results

2.0s	271×	body	5120	exit
593.0ms	3394×	body	80	overflowed
96.0ms	3923×	pre	80	true
27.0ms	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

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

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

localize28.0ms

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)))

rewrite88.0ms

Algorithm

rewrite-expression-head

Rules

553×	`add-exp-log`
312×	`prod-exp`
262×	`pow-exp`
248×	`div-exp`
183×	`pow-to-exp`
23×	`add-sqr-sqrt` `*-un-lft-identity`
18×	`unpow-prod-down`
16×	`add-cbrt-cube`
15×	`times-frac`
13×	`add-cube-cbrt`
8×	`add-log-exp`
5×	`pow1`
4×	`cbrt-undiv` `cbrt-unprod` `difference-of-squares`
3×	`pow-unpow` `distribute-lft-out`
2×	`sub-neg` `flip3--` `diff-log` `associate-/r/` `flip--` `div-inv` `distribute-lft-out--`
1×	`pow-pow` `frac-2neg` `flip3-+` `clear-num` `associate-/r` `flip-+` `associate-/l` `sqr-pow`

Counts

4 → 249

Calls

4 calls:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
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)))

series793.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
51.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
620.0ms	(/ (* (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)))

simplify106.0ms

Algorithm

egg-herbie

Counts

261 → 261

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	903	5770
1	2946	5521
2	5002	5521

prune347.0ms

Filtered

261 candidates to 66 candidates (25.3%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	259	2	261
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	260	2	262

Merged error: 1.0b

Counts

262 → 2

localize21.0ms

Local error

Found 2 expressions with local error:

0.0b	(* 0.5 (* s c_n))
0.0b	(* 0.5 (* s c_p))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

12×	`pow1` `add-exp-log` `add-cbrt-cube`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
4×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2×	`associate-r` `*-commutative` `add-log-exp`

Counts

2 → 36

Calls

2 calls:

5.0ms	(* 0.5 (* s c_n))
5.0ms	(* 0.5 (* s c_p))

series40.0ms

Counts

2 → 6

Calls

2 calls:

19.0ms	(* 0.5 (* s c_n))
20.0ms	(* 0.5 (* s c_p))

simplify60.0ms

Algorithm

egg-herbie

Counts

42 → 42

Iterations

Useful iterations: 1 (5.0ms)

Iter	Nodes	Cost
0	153	142
1	595	112
2	2373	112
3	5002	112

prune58.0ms

Filtered

42 candidates to 22 candidates (52.4%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	41	1	42
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	41	3	44

Merged error: 1.0b

Counts

44 → 3

localize30.0ms

Local error

Found 4 expressions with local error:

0.2b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
2.4b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite71.0ms

Algorithm

rewrite-expression-head

Rules

168×	`add-exp-log`
88×	`prod-exp`
64×	`div-exp`
53×	`pow-exp`
41×	`pow-to-exp`
18×	`add-sqr-sqrt` `add-cbrt-cube`
10×	`*-un-lft-identity`
8×	`add-log-exp`
6×	`pow1` `add-cube-cbrt`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `difference-of-squares`
3×	`times-frac` `associate-r` `associate-l`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-r/` `associate-l/` `associate-/r/` `flip--` `flip-+` `distribute-lft-out--`
1×	`distribute-rgt-in` `frac-2neg` `distribute-lft-in` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `div-inv` `associate-/l*` `unswap-sqr`

Counts

4 → 123

Calls

4 calls:

5.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
10.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
41.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series984.0ms

Counts

4 → 12

Calls

4 calls:

103.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
53.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
48.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
780.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify100.0ms

Algorithm

egg-herbie

Counts

135 → 135

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	820	2647
1	3602	2390
2	5003	2390

prune351.0ms

Filtered

135 candidates to 59 candidates (43.7%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	134	1	135
Fresh	1	0	1
Picked	0	1	1
Done	0	1	1
Total	135	3	138

Merged error: 1.0b

Counts

138 → 3

localize13.0ms

Local error

Found 4 expressions with local error:

0.0b	(* 1/2 (* (pow (log 0.5) 2) (pow c_p 2)))
0.0b	(* 0.5 (* s c_p))
0.1b	(* (pow (log 0.5) 2) (pow c_p 2))
1.0b	(pow (log 0.5) 2)

rewrite26.0ms

Algorithm

rewrite-expression-head

Rules

45×	`add-exp-log`
31×	`prod-exp`
28×	`add-sqr-sqrt`
19×	`unpow-prod-down`
16×	`add-cbrt-cube` `unswap-sqr`
15×	`associate-l`
14×	`pow1`
13×	`pow-to-exp` `pow-exp`
12×	`add-cube-cbrt` `*-un-lft-identity`
11×	`unpow2` `sqr-pow`
10×	`associate-r`
7×	`cbrt-unprod`
5×	`pow-prod-down`
4×	`add-log-exp`
3×	`pow-unpow` `*-commutative`
2×	`log-pow`
1×	`pow-pow`

Counts

4 → 114

Calls

4 calls:

7.0ms	(* 1/2 (* (pow (log 0.5) 2) (pow c_p 2)))
5.0ms	(* 0.5 (* s c_p))
8.0ms	(* (pow (log 0.5) 2) (pow c_p 2))
2.0ms	(pow (log 0.5) 2)

series383.0ms

Counts

4 → 10

Calls

4 calls:

189.0ms	(* 1/2 (* (pow (log 0.5) 2) (pow c_p 2)))
26.0ms	(* 0.5 (* s c_p))
168.0ms	(* (pow (log 0.5) 2) (pow c_p 2))
0.0ms	(pow (log 0.5) 2)

simplify52.0ms

Algorithm

egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 2 (43.0ms)

Iter	Nodes	Cost
0	343	646
1	1473	541
2	5001	535

prune196.0ms

Filtered

124 candidates to 59 candidates (47.6%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	123	1	124
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	124	3	127

Merged error: 1.0b

Counts

127 → 3

regimes187.0ms

bsearch852.0ms

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	52	31
1	52	31

end0.0ms

sample10.8s

Algorithm

intervals

Results

7.4s	1114×	body	5120	exit
2.3s	13981×	body	80	overflowed
365.0ms	16221×	pre	80	true
119.0ms	1071×	body	80	valid
20.0ms	10×	body	1280	valid
20.0ms	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

simplify27.0ms

prune5.0ms

localize28.0ms

rewrite88.0ms

series793.0ms

simplify106.0ms

prune347.0ms

localize21.0ms

rewrite10.0ms

series40.0ms

simplify60.0ms

prune58.0ms

localize30.0ms

rewrite71.0ms

series984.0ms

simplify100.0ms

prune351.0ms

localize13.0ms

rewrite26.0ms

series383.0ms

simplify52.0ms

prune196.0ms

regimes187.0ms

bsearch852.0ms

simplify2.0ms

end0.0ms

sample10.8s

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