Details

sample2.5s

Algorithm

intervals

Results

1.7s	239×	body	5120	exit
518.0ms	2859×	body	80	overflowed
73.0ms	3356×	pre	80	true
31.0ms	247×	body	80	valid
5.0ms	4×	body	640	valid
3.0ms	1×	body	1280	overflowed
1.0ms	1×	body	1280	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	320	valid
0.0ms	1×	body	160	overflowed

simplify26.0ms

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

prune7.0ms

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: 5.5b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
1.0b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
3.2b	(/ (* (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)))))
9.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
42.0ms	(/ (* (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)))

series226.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
189.0ms	(/ (* (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)))

simplify112.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (19.0ms)

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

prune321.0ms

Filtered

79 candidates to 279 candidates (-253.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	273	6	279
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	274	6	280

Merged error: 1.4b

Counts

280 → 6

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×	`associate-r` `*-commutative` `add-log-exp`

Counts

1 → 18

Calls

1 calls:

5.0ms

(* 0.5 (* s c_n))

series4.0ms

Counts

1 → 3

Calls

1 calls:

3.0ms

(* 0.5 (* s c_n))

simplify74.0ms

Algorithm

egg-herbie

Counts

21 → 21

Iterations

Useful iterations: 1 (3.0ms)

Iter	Nodes	Cost
0	86	71
1	318	56
2	1232	56
3	3436	56
4	5002	56

prune66.0ms

Filtered

11 candidates to 21 candidates (-90.9%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	21	0	21
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	21	6	27

Merged error: 1.4b

Counts

27 → 6

localize26.0ms

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 (neg s)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
1.5b	(/ (* (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)))

rewrite68.0ms

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:

6.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
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)))

series246.0ms

Counts

4 → 12

Calls

4 calls:

12.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
7.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (neg s)))))
16.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg s)))) c_p)
211.0ms	(/ (* (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)))

simplify106.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (20.0ms)

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

prune289.0ms

Filtered

72 candidates to 153 candidates (-112.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	152	1	153
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	152	7	159

Merged error: 1.4b

Counts

159 → 7

localize32.0ms

Local error

Found 4 expressions with local error:

1.0b	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
3.2b	(/ (* (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)))
3.2b	(/ (* (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)))
3.2b	(/ (* (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)))

rewrite192.0ms

Algorithm

rewrite-expression-head

Rules

1645×	`add-exp-log`
936×	`prod-exp`
782×	`pow-exp`
742×	`div-exp`
547×	`pow-to-exp`
40×	`add-cbrt-cube`
19×	`*-un-lft-identity`
18×	`unpow-prod-down`
15×	`times-frac`
13×	`add-sqr-sqrt` `add-cube-cbrt`
12×	`cbrt-undiv` `cbrt-unprod`
5×	`pow1`
4×	`div-inv` `add-log-exp`
3×	`pow-unpow` `frac-2neg` `clear-num` `associate-/r` `distribute-lft-out` `associate-/l`
2×	`associate-/r/`
1×	`pow-pow` `flip3-+` `flip-+` `sqr-pow`

Counts

4 → 591

Calls

4 calls:

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)))
46.0ms	(/ (* (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)))
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)))

series578.0ms

Counts

4 → 12

Calls

4 calls:

15.0ms	(pow (/ 1.0 (+ 1.0 (exp (neg t)))) c_p)
187.0ms	(/ (* (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)))
187.0ms	(/ (* (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)))
190.0ms	(/ (* (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)))

simplify178.0ms

Algorithm

egg-herbie

Counts

603 → 603

Iterations

Useful iterations: 1 (16.0ms)

Iter	Nodes	Cost
0	770	15650
1	2515	14997
2	5001	14997

prune691.0ms

Filtered

68 candidates to 603 candidates (-786.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	603	0	603
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	603	7	610

Merged error: 1.4b

Counts

610 → 7

regimes1.4s

bsearch659.0ms

Steps

Iters	Range		Point
9	-1.0243808655624229e-89	-6.284047631591266e-95	-5.436019021488309e-92

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	31
1	52	31

end0.0ms

sample7.8s

Algorithm

intervals

Results

5.2s	738×	body	5120	exit
1.7s	9574×	body	80	overflowed
232.0ms	11164×	pre	80	true
97.0ms	811×	body	80	valid
40.0ms	3×	body	5120	valid
15.0ms	4×	body	2560	valid
13.0ms	12×	body	640	valid
7.0ms	3×	body	1280	valid
4.0ms	11×	body	160	valid
3.0ms	1×	body	1280	overflowed
2.0ms	3×	body	320	valid
1.0ms	3×	body	160	overflowed
1.0ms	1×	body	640	overflowed

Details

sample2.5s

simplify26.0ms

prune7.0ms

localize22.0ms

rewrite86.0ms

series226.0ms

simplify112.0ms

prune321.0ms

localize8.0ms

rewrite5.0ms

series4.0ms

simplify74.0ms

prune66.0ms

localize26.0ms

rewrite68.0ms

series246.0ms

simplify106.0ms

prune289.0ms

localize32.0ms

rewrite192.0ms

series578.0ms

simplify178.0ms

prune691.0ms

regimes1.4s

bsearch659.0ms

simplify2.0ms

end0.0ms

sample7.8s

Profiling