Details

sample48.2s

Algorithm

intervals

Results

47.8s	3808×	body	10240	exit
91.0ms	4064×	pre	80	true
24.0ms	247×	body	80	valid
6.0ms	3×	body	1280	valid
1.0ms	2×	body	320	valid
1.0ms	1×	body	640	valid
1.0ms	3×	body	160	valid

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

prune4.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.0b

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.9b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.9b	(/ (* (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)))

rewrite151.0ms

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:

18.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
94.0ms	(/ (* (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)))

series912.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
66.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
734.0ms	(/ (* (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

279 → 279

Iterations

Useful iterations: 1 (17.0ms)

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

prune430.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.6b

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite12.0ms

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))
6.0ms	(* 0.5 (* s c_p))

series36.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(* 0.5 (* s c_n))
18.0ms	(* 0.5 (* s c_p))

simplify55.0ms

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

prune73.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.6b

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
24.8b	(cbrt (* 0.5 (* s c_n)))
24.8b	(cbrt (* 0.5 (* s c_n)))
24.8b	(cbrt (* 0.5 (* s c_n)))

rewrite20.0ms

Algorithm

rewrite-expression-head

Rules

11×	`pow1`
10×	`add-sqr-sqrt`
9×	`pow1/3`
8×	`add-cube-cbrt` `*-un-lft-identity`
7×	`cbrt-prod`
6×	`add-exp-log`
4×	`swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `add-log-exp`
2×	`pow-prod-down` `pow-sqr` `pow-prod-up`
1×	`pow2` `pow-plus` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

4 → 58

Calls

4 calls:

7.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
4.0ms	(cbrt (* 0.5 (* s c_n)))
4.0ms	(cbrt (* 0.5 (* s c_n)))
4.0ms	(cbrt (* 0.5 (* s c_n)))

series383.0ms

Counts

4 → 12

Calls

4 calls:

123.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
86.0ms	(cbrt (* 0.5 (* s c_n)))
85.0ms	(cbrt (* 0.5 (* s c_n)))
89.0ms	(cbrt (* 0.5 (* s c_n)))

simplify93.0ms

Algorithm

egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 3 (88.0ms)

Iter	Nodes	Cost
0	205	441
1	703	390
2	3412	330
3	5001	323

prune210.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.6b

localize26.0ms

Local error

Found 4 expressions with local error:

0.2b	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
0.3b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.5b	(/ (* (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)))

rewrite154.0ms

Algorithm

rewrite-expression-head

Rules

170×	`add-exp-log`
87×	`prod-exp`
65×	`div-exp`
56×	`pow-exp`
43×	`pow-to-exp`
25×	`add-sqr-sqrt` `*-un-lft-identity`
24×	`unpow-prod-down`
16×	`add-cbrt-cube`
15×	`add-cube-cbrt` `times-frac`
6×	`pow1` `pow-unpow` `add-log-exp`
4×	`cbrt-undiv` `associate-/r/` `cbrt-unprod` `difference-of-squares`
3×	`distribute-lft-out`
2×	`pow-pow` `flip3-+` `associate-*l/` `flip-+` `div-inv` `distribute-lft-out--` `sqr-pow`
1×	`sub-neg` `flip3--` `frac-2neg` `diff-log` `clear-num` `associate-/r` `flip--` `associate-/l`

Counts

4 → 139

Calls

4 calls:

33.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
18.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
86.0ms	(/ (* (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)))

series878.0ms

Counts

4 → 12

Calls

4 calls:

83.0ms	(pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)
46.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
682.0ms	(/ (* (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)))

simplify103.0ms

Algorithm

egg-herbie

Counts

151 → 151

Iterations

Useful iterations: 1 (19.0ms)

Iter	Nodes	Cost
0	878	2899
1	3999	2646
2	5002	2646

prune422.0ms

Pruning

5 alts after pruning (4 fresh and 1 done)

Merged error: 1.4b

regimes364.0ms

bsearch3.9s

Steps

Iters	Range		Point
6	-3.4158361945667567e-79	-5.1113148475473346e-80	-6.3436807628579684e-80

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	58	41
1	58	41

end0.0ms

sample6.4m

Algorithm

intervals

Results

6.3m	31417×	body	10240	exit
627.0ms	33809×	pre	80	true
196.0ms	2320×	body	80	valid
36.0ms	6×	body	5120	valid
34.0ms	20×	body	1280	valid
11.0ms	13×	body	640	valid
7.0ms	3×	body	2560	valid
6.0ms	26×	body	160	valid
2.0ms	4×	body	320	valid