Details

sample39.7s

Algorithm

intervals

Results

39.4s	2924×	body	10240	exit
99.0ms	3180×	pre	80	true
27.0ms	247×	body	80	valid
3.0ms	3×	body	640	valid
1.0ms	3×	body	320	valid
1.0ms	3×	body	160	valid

simplify595.0ms

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	847
2	147
1	53
0	22

prune12.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 7.5b

localize38.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.2b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.5b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
5.4b	(/ (* (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)))

rewrite210.0ms

Algorithm

rewrite-expression-head

Rules

556×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
249×	`div-exp`
184×	`pow-to-exp`
97×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
62×	`times-frac`
54×	`prod-diff`
36×	`unpow-prod-down`
16×	`add-cbrt-cube`
15×	`distribute-lft-out`
10×	`associate-/r/`
6×	`pow1` `pow-unpow` `div-inv` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`expm1-log1p-u` `cbrt-undiv` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow-pow` `difference-of-squares` `sqr-pow`
1×	`clear-num` `associate-/r` `sub-neg` `frac-2neg` `flip3--` `diff-log` `flip--` `associate-/l` `distribute-lft-out--`

Counts

4 → 332

Calls

4 calls:

32.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
15.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
131.0ms	(/ (* (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)))

series790.0ms

Counts

4 → 12

Calls

4 calls:

48.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
71.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
71.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
599.0ms	(/ (* (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)))

simplify460.0ms

Counts

344 → 344

Iterations

Iter	Nodes
done	5000
1	1517
0	477

prune853.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize49.0ms

Local error

Found 4 expressions with local error:

0.3b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
1.5b	(log (/ 1.0 (+ (exp (- t)) 1.0)))
9.0b	(- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma c_p (log (/ 1.0 (+ (exp (- t)) 1.0))) (* (log (- 1.0 (/ 1.0 (+ (exp (- t)) 1.0)))) c_n)))
28.5b	(fma (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p (- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma c_p (log (/ 1.0 (+ (exp (- t)) 1.0))) (* (log (- 1.0 (/ 1.0 (+ (exp (- t)) 1.0)))) c_n))))

rewrite27.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
33×	`*-un-lft-identity`
24×	`times-frac`
21×	`add-sqr-sqrt` `add-cube-cbrt`
10×	`add-exp-log`
6×	`pow1` `distribute-lft-out` `add-log-exp`
4×	`expm1-log1p-u` `add-cbrt-cube` `rem-log-exp` `associate-/r/` `log1p-expm1-u`
3×	`prod-diff`
2×	`log-div` `flip3-+` `div-exp` `log-pow` `flip-+` `fma-udef` `div-inv`
1×	`sub-neg` `flip3--` `fma-neg` `diff-log` `flip--` `associate--r+`

Counts

4 → 91

Calls

4 calls:

7.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
11.0ms	(log (/ 1.0 (+ (exp (- t)) 1.0)))
7.0ms	(- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma c_p (log (/ 1.0 (+ (exp (- t)) 1.0))) (* (log (- 1.0 (/ 1.0 (+ (exp (- t)) 1.0)))) c_n)))
0.0ms	(fma (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p (- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma c_p (log (/ 1.0 (+ (exp (- t)) 1.0))) (* (log (- 1.0 (/ 1.0 (+ (exp (- t)) 1.0)))) c_n))))

series855.0ms

Counts

4 → 12

Calls

4 calls:

70.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
71.0ms	(log (/ 1.0 (+ (exp (- t)) 1.0)))
331.0ms	(- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma c_p (log (/ 1.0 (+ (exp (- t)) 1.0))) (* (log (- 1.0 (/ 1.0 (+ (exp (- t)) 1.0)))) c_n)))
382.0ms	(fma (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p (- (* (log (- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))) c_n) (fma c_p (log (/ 1.0 (+ (exp (- t)) 1.0))) (* (log (- 1.0 (/ 1.0 (+ (exp (- t)) 1.0)))) c_n))))

simplify707.0ms

Counts

103 → 103

Iterations

Iter	Nodes
done	5000
2	1982
1	614
0	285

prune684.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- s))))
0.2b	(* (log 0.5) c_p)
0.3b	(log (/ 1.0 (+ 1.0 (exp (- s)))))
37.7b	(fma (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p (- (* t (* 0.5 c_n)) (fma (* 0.5 s) c_n (* (log 0.5) c_p))))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

37×	`*-un-lft-identity`
25×	`add-sqr-sqrt`
24×	`times-frac`
23×	`add-cube-cbrt`
18×	`log-prod`
11×	`add-exp-log`
8×	`pow1` `add-cbrt-cube`
7×	`distribute-lft-out`
4×	`expm1-log1p-u` `associate-/r` `associate-l*` `associate-/r/` `log1p-expm1-u` `add-log-exp`
3×	`associate-r` `associate-/l*`
2×	`flip3-+` `div-exp` `rem-log-exp` `log-pow` `flip-+` `div-inv`
1×	`cbrt-undiv` `log-div` `clear-num` `frac-2neg` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `fma-udef` `unswap-sqr`

Counts

4 → 97

Calls

4 calls:

13.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
6.0ms	(* (log 0.5) c_p)
12.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
0.0ms	(fma (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p (- (* t (* 0.5 c_n)) (fma (* 0.5 s) c_n (* (log 0.5) c_p))))

series423.0ms

Counts

4 → 12

Calls

4 calls:

27.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
161.0ms	(* (log 0.5) c_p)
71.0ms	(log (/ 1.0 (+ 1.0 (exp (- s)))))
164.0ms	(fma (log (/ 1.0 (+ 1.0 (exp (- s))))) c_p (- (* t (* 0.5 c_n)) (fma (* 0.5 s) c_n (* (log 0.5) c_p))))

simplify538.0ms

Counts

109 → 109

Iterations

Iter	Nodes
done	5000
2	1575
1	433
0	191

prune515.0ms

Pruning

2 alts after pruning (2 fresh and 0 done)

Merged error: 0.0b

localize14.0ms

Local error

Found 3 expressions with local error:

0.0b	(fma c_p s (* t c_n))
0.0b	(* 0.5 (- (fma c_p s (* t c_n)) (* c_n s)))
0.0b	(- (fma c_p s (* t c_n)) (* c_n s))

rewrite24.0ms

Algorithm

rewrite-expression-head

Rules

11×	`add-sqr-sqrt`
9×	`*-un-lft-identity` `prod-diff` `add-cube-cbrt`
6×	`distribute-rgt-in` `distribute-lft-in`
5×	`pow1` `add-cbrt-cube` `add-exp-log` `add-log-exp`
4×	`fma-udef`
3×	`expm1-log1p-u` `sub-neg` `fma-neg` `associate-r` `associate-l` `associate--l+` `log1p-expm1-u`
2×	`flip3--` `associate-*r/` `flip--`
1×	`diff-log` `pow-prod-down` `prod-exp` `*-commutative` `cbrt-unprod` `unswap-sqr`

Counts

3 → 65

Calls

3 calls:

0.0ms	(fma c_p s (* t c_n))
13.0ms	(* 0.5 (- (fma c_p s (* t c_n)) (* c_n s)))
8.0ms	(- (fma c_p s (* t c_n)) (* c_n s))

series119.0ms

Counts

3 → 9

Calls

3 calls:

40.0ms	(fma c_p s (* t c_n))
44.0ms	(* 0.5 (- (fma c_p s (* t c_n)) (* c_n s)))
35.0ms	(- (fma c_p s (* t c_n)) (* c_n s))

simplify373.0ms

Counts

74 → 74

Iterations

Iter	Nodes
done	5001
2	1051
1	234
0	98

prune262.0ms

Pruning

2 alts after pruning (1 fresh and 1 done)

Merged error: 0.0b

regimes362.0ms

bsearch0.0ms

simplify1.0ms

Iterations

Iter	Nodes
done	14
1	14
0	11

end0.0ms

sample9.2m

Algorithm

intervals

Results

9.1m	42921×	body	10240	exit
2.5s	46358×	pre	80	true
465.0ms	3320×	body	80	valid
160.0ms	9×	body	5120	valid
62.0ms	19×	body	1280	valid
24.0ms	8×	body	2560	valid
22.0ms	25×	body	640	valid
12.0ms	41×	body	160	valid
6.0ms	14×	body	320	valid