Details

sample20.9s

Algorithm

intervals

sampling

Space saved by range analysis: 75%

Space saved by search: 75%

Guaranteed chance to sample good point: 6.25%

Results

3.6s	522×	body	5120	exit
748.0ms	297×	body	1280	overflowed
437.0ms	2284×	body	80	overflowed
310.0ms	235×	body	640	overflowed
89.0ms	118×	body	320	overflowed
86.0ms	3777×	pre	80	true
28.0ms	241×	body	80	valid
26.0ms	64×	body	160	overflowed
13.0ms	1×	body	5120	valid
5.0ms	5×	body	640	valid
3.0ms	1×	body	2560	valid
2.0ms	6×	body	160	valid
1.0ms	2×	body	320	valid
0.0ms	1×	body	80	invalid

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

prune5.0ms

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: 6.7b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
2.4b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
2.9b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg 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`
36×	`unpow-prod-down` `*-un-lft-identity`
27×	`add-sqr-sqrt`
26×	`times-frac`
22×	`add-cube-cbrt`
16×	`add-cbrt-cube`
6×	`pow1` `pow-unpow` `distribute-lft-out` `add-log-exp`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod`
3×	`div-inv`
2×	`pow-pow` `flip3-+` `flip-+` `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 → 267

Calls

4 calls:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
41.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

series202.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
13.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
14.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
168.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

simplify104.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	982	5948
1	3157	5704
2	5003	5704

prune264.0ms

Filtered

79 candidates to 279 candidates (-253.2%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	277	2	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	278	2	280

Merged error: 0.4b

Counts

280 → 2

localize7.0ms

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:

4.0ms	(* 0.5 (* s c_n))
5.0ms	(* 0.5 (* s c_p))

series6.0ms

Counts

2 → 6

Calls

2 calls:

3.0ms	(* 0.5 (* s c_n))
3.0ms	(* 0.5 (* s c_p))

simplify56.0ms

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

prune36.0ms

Filtered

22 candidates to 42 candidates (-90.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	42	0	42
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	42	2	44

Merged error: 0.4b

Counts

44 → 2

localize25.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
0.2b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
1.2b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

rewrite63.0ms

Algorithm

rewrite-expression-head

Rules

171×	`add-exp-log`
88×	`prod-exp`
65×	`div-exp`
55×	`pow-exp`
42×	`pow-to-exp`
23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
18×	`unpow-prod-down` `add-cbrt-cube`
15×	`add-cube-cbrt`
14×	`times-frac`
7×	`pow1`
6×	`add-log-exp`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `associate-/r/`
3×	`pow-unpow` `flip3-+` `associate-r` `associate-l` `flip-+` `distribute-lft-out`
2×	`associate-r/` `associate-l/` `div-inv` `difference-of-squares`
1×	`distribute-rgt-in` `sub-neg` `flip3--` `pow-pow` `frac-2neg` `distribute-lft-in` `diff-log` `pow-prod-down` `clear-num` `associate-/r` `-commutative` `flip--` `associate-/l*` `distribute-lft-out--` `unswap-sqr` `sqr-pow`

Counts

4 → 141

Calls

4 calls:

11.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
5.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
35.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

series224.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
11.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
13.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
193.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))

simplify105.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (20.0ms)

Iter	Nodes	Cost
0	920	2823
1	4062	2572
2	5002	2572

prune244.0ms

Filtered

72 candidates to 153 candidates (-112.5%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	153	2	155

Merged error: 0.4b

Counts

155 → 2

localize31.0ms

Local error

Found 4 expressions with local error:

1.2b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))
1.2b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))
1.7b	(sqrt (/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n))))
1.7b	(sqrt (/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n))))

rewrite151.0ms

Algorithm

rewrite-expression-head

Rules

328×	`add-exp-log`
174×	`prod-exp`
128×	`div-exp`
106×	`pow-exp`
82×	`pow-to-exp`
28×	`add-cbrt-cube`
14×	`sqrt-prod`
8×	`cbrt-undiv` `add-sqr-sqrt` `associate-*l/` `associate-/r/` `cbrt-unprod`
6×	`pow1` `add-cube-cbrt` `*-un-lft-identity`
4×	`flip3-+` `times-frac` `flip-+` `div-inv` `add-log-exp`
2×	`rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `sqrt-div` `clear-num` `associate-/r` `associate-/l`

Counts

4 → 178

Calls

4 calls:

39.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))
35.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))
35.0ms	(sqrt (/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n))))
32.0ms	(sqrt (/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n))))

series772.0ms

Counts

4 → 12

Calls

4 calls:

193.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))
195.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n)))
191.0ms	(sqrt (/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n))))
193.0ms	(sqrt (/ (* (pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg s))))) c_n)) (* (+ (* c_p (+ (log 0.5) (* 0.5 t))) 1) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (neg t))))) c_n))))

simplify99.0ms

Algorithm

egg-herbie

Counts

190 → 190

Iterations

Useful iterations: 1 (14.0ms)

Iter	Nodes	Cost
0	617	5452
1	2898	4958
2	5003	4958

prune449.0ms

Filtered

68 candidates to 190 candidates (-179.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	189	1	190
Fresh	0	0	0
Picked	1	0	1
Done	0	1	1
Total	190	2	192

Merged error: 0.4b

Counts

192 → 2

regimes411.0ms

bsearch3.3s

Steps

Iters	Range		Point
10	-12873.275831682608	-5.107967110095968e-08	-7.293725585434315e-05

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	116
1	59	116

end0.0ms

sample1.5min

Algorithm

intervals

sampling

Space saved by range analysis: 75%

Space saved by search: 75%

Guaranteed chance to sample good point: 6.25%

Results

48.3s	7164×	body	5120	exit
10.1s	4040×	body	1280	overflowed
6.0s	31216×	body	80	overflowed
4.7s	3538×	body	640	overflowed
1.4s	1807×	body	320	overflowed
1.2s	52212×	pre	80	true
409.0ms	3446×	body	80	valid
375.0ms	895×	body	160	overflowed
73.0ms	5×	body	5120	valid
30.0ms	13×	body	1280	valid
28.0ms	7×	body	2560	valid
26.0ms	23×	body	640	valid
11.0ms	34×	body	160	valid
11.0ms	17×	body	320	valid
10.0ms	1×	body	5120	overflowed
1.0ms	6×	body	80	invalid

Details

sample20.9s

simplify24.0ms

prune5.0ms

localize21.0ms

rewrite86.0ms

series202.0ms

simplify104.0ms

prune264.0ms

localize7.0ms

rewrite10.0ms

series6.0ms

simplify56.0ms

prune36.0ms

localize25.0ms

rewrite63.0ms

series224.0ms

simplify105.0ms

prune244.0ms

localize31.0ms

rewrite151.0ms

series772.0ms

simplify99.0ms

prune449.0ms

regimes411.0ms

bsearch3.3s

simplify2.0ms

end0.0ms

sample1.5min

Profiling