Details

sample42.3s

Algorithm

intervals

Results

41.9s	3399×	body	10240	exit
100.0ms	3656×	pre	80	true
22.0ms	242×	body	80	valid
6.0ms	1×	body	5120	valid
5.0ms	2×	body	1280	valid
3.0ms	4×	body	640	valid
2.0ms	1×	body	2560	valid
1.0ms	5×	body	160	valid
1.0ms	2×	body	320	valid

simplify25.0ms

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: 5.8b

localize21.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.2b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.9b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.7b	(/ (* (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)))

rewrite84.0ms

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 (- s)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
42.0ms	(/ (* (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)))

series945.0ms

Counts

4 → 12

Calls

4 calls:

46.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
762.0ms	(/ (* (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)))

simplify103.0ms

Algorithm

egg-herbie

Counts

279 → 279

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	976	5948
1	3142	5704
2	5001	5704

prune446.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.2b	(* c_p (+ (log 0.5) (* 0.5 t)))
0.2b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.2b	(/ (* (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)))

rewrite66.0ms

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:

9.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
5.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
38.0ms	(/ (* (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)))

series932.0ms

Counts

4 → 12

Calls

4 calls:

52.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
100.0ms	(* c_p (+ (log 0.5) (* 0.5 t)))
71.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
709.0ms	(/ (* (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)))

simplify104.0ms

Algorithm

egg-herbie

Counts

153 → 153

Iterations

Useful iterations: 1 (21.0ms)

Iter	Nodes	Cost
0	922	2823
1	4079	2572
2	5001	2572

prune460.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 1.0b

localize8.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))
0.0b	(* 0.5 (* s c_n))
0.0b	(* 0.5 (* s c_p))

rewrite17.0ms

Algorithm

rewrite-expression-head

Rules

13×	`pow1` `add-exp-log` `add-cbrt-cube`
8×	`add-log-exp`
6×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
2×	`diff-log` `associate-r` `*-commutative`
1×	`sub-neg` `flip3--` `associate--l+` `sum-log` `flip--`

Counts

3 → 50

Calls

3 calls:

7.0ms	(- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))
4.0ms	(* 0.5 (* s c_n))
5.0ms	(* 0.5 (* s c_p))

series94.0ms

Counts

3 → 9

Calls

3 calls:

53.0ms	(- (+ (* 0.5 (* s c_p)) 1) (* 0.5 (* s c_n)))
22.0ms	(* 0.5 (* s c_n))
19.0ms	(* 0.5 (* s c_p))

simplify142.0ms

Algorithm

egg-herbie

Counts

59 → 59

Iterations

Useful iterations: 2 (28.0ms)

Iter	Nodes	Cost
0	228	292
1	900	254
2	4892	245
3	5001	245

prune107.0ms

Pruning

4 alts after pruning (2 fresh and 2 done)

Merged error: 1.0b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
0.9b	(* (cbrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (cbrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))))
1.9b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.7b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (* (* (cbrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (cbrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (cbrt (- 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)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

1090×	`add-exp-log`
669×	`prod-exp`
500×	`pow-exp`
403×	`div-exp`
266×	`pow-to-exp`
58×	`add-sqr-sqrt`
56×	`*-un-lft-identity`
36×	`unpow-prod-down`
32×	`cbrt-prod`
30×	`add-cube-cbrt`
29×	`times-frac`
16×	`add-cbrt-cube`
13×	`pow1`
12×	`cbrt-div`
11×	`swap-sqr`
9×	`associate-r` `associate-l`
8×	`difference-of-squares`
6×	`pow-unpow` `flip3--` `pow1/3` `flip--` `distribute-lft-out` `distribute-lft-out--`
5×	`cbrt-unprod`
4×	`cbrt-undiv` `frac-times` `associate-/r/` `add-log-exp` `unswap-sqr`
3×	`div-inv`
2×	`pow-pow` `flip3-+` `associate-r/` `pow-prod-down` `associate-l/` `pow-sqr` `pow-prod-up` `flip-+` `sqr-pow`
1×	`pow2` `frac-2neg` `pow-plus` `clear-num` `associate-/r` `-commutative` `associate-/l*`

Counts

4 → 415

Calls

4 calls:

7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
24.0ms	(* (cbrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (cbrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
40.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (* (* (cbrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (cbrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (cbrt (- 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)))

series919.0ms

Counts

4 → 12

Calls

4 calls:

67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
184.0ms	(* (cbrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (cbrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))))
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
600.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (* (* (cbrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) (cbrt (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))))) (cbrt (- 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)))

simplify166.0ms

Algorithm

egg-herbie

Counts

427 → 427

Iterations

Useful iterations: 2 (73.0ms)

Iter	Nodes	Cost
0	1328	14040
1	3999	12775
2	5001	10667

prune695.0ms

Pruning

5 alts after pruning (2 fresh and 3 done)

Merged error: 0.3b

regimes526.0ms

bsearch4.3s

Steps

Iters	Range		Point
6	7.44355987242124e-38	4.027521570049322e-37	7.53494092164005e-38
0	1.52868909908113e-124	1.57491569023596e-124	1.551802394658545e-124

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	59	37
1	59	37

end0.0ms

sample1.8m

Algorithm

intervals

Results

1.8m	8918×	body	10240	exit
253.0ms	9580×	pre	80	true
59.0ms	634×	body	80	valid
25.0ms	3×	body	5120	valid
7.0ms	9×	body	640	valid
6.0ms	3×	body	1280	valid
5.0ms	2×	body	2560	valid
2.0ms	8×	body	160	valid
1.0ms	3×	body	320	valid