Details

sample1.2m

Algorithm

intervals

Results

1.1m	3196×	body	10240	exit
760.0ms	3452×	pre	80	true
126.0ms	248×	body	80	valid
5.0ms	2×	body	1280	valid
4.0ms	2×	body	640	valid
1.0ms	2×	body	320	valid
1.0ms	2×	body	160	valid

simplify3.6s

Counts

1 → 1

Iterations

Iter	Nodes
done	5001
3	744
2	143
1	53
0	22

prune14.0ms

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 4.5b

localize124.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(/ (* (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)))
1.9b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

rewrite602.0ms

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×	`cbrt-undiv` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`fma-neg`
2×	`pow-pow` `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 → 332

Calls

4 calls:

89.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
39.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
373.0ms	(/ (* (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)))
50.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

series1.8s

Counts

4 → 12

Calls

4 calls:

111.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
167.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.4s	(/ (* (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)))
171.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)

simplify5.1s

Counts

344 → 344

Iterations

Iter	Nodes
done	5003
2	3989
1	1389
0	471

prune2.2s

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize25.0ms

Local error

Found 1 expressions with local error:

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

rewrite14.0ms

Algorithm

rewrite-expression-head

Rules

3×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity` `fma-neg` `prod-diff` `add-log-exp`
1×	`pow1` `add-exp-log` `expm1-log1p-u` `sub-neg` `flip3--` `diff-log` `associate--l+` `add-cbrt-cube` `flip--` `fma-udef` `log1p-expm1-u`

Counts

1 → 21

Calls

1 calls:

13.0ms

(- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))

series117.0ms

Counts

1 → 3

Calls

1 calls:

116.0ms

(- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))

simplify4.6s

Counts

24 → 24

Iterations

Iter	Nodes
done	5000
3	2586
2	465
1	131
0	51

prune229.0ms

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 0.1b

localize34.0ms

Local error

Found 3 expressions with local error:

0.0b	(- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))
0.0b	(- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))
0.0b	(* (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))) (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))))

rewrite104.0ms

Algorithm

rewrite-expression-head

Rules

27×	`add-sqr-sqrt`
18×	`pow1` `sqrt-prod`
15×	`add-cube-cbrt` `*-un-lft-identity`
12×	`sqrt-div`
8×	`flip3--` `sqrt-pow1` `pow1/2` `swap-sqr` `flip--`
7×	`add-log-exp`
6×	`fma-neg` `associate-r` `associate-l` `prod-diff`
5×	`add-exp-log` `pow-prod-up` `add-cbrt-cube`
4×	`frac-times` `unswap-sqr`
3×	`expm1-log1p-u` `pow-prod-down` `pow-sqr` `log1p-expm1-u`
2×	`sub-neg` `diff-log` `associate-r/` `associate-l/` `associate--l+` `fma-udef`
1×	`pow2` `pow-plus` `sqrt-unprod` `prod-exp` `rem-square-sqrt` `*-commutative` `cbrt-unprod`

Counts

3 → 101

Calls

3 calls:

11.0ms	(- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))
13.0ms	(- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))
73.0ms	(* (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))) (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))))

series403.0ms

Counts

3 → 9

Calls

3 calls:

147.0ms	(- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))
137.0ms	(- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))
118.0ms	(* (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))) (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))))

simplify4.0s

Counts

110 → 110

Iterations

Iter	Nodes
done	5001
3	2523
2	650
1	242
0	112

prune992.0ms

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

localize83.0ms

Local error

Found 4 expressions with local error:

0.0b	(* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))))
0.0b	(* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))))
0.0b	(* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))))
0.0b	(* (* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))))) (* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))))))

rewrite505.0ms

Algorithm

rewrite-expression-head

Rules

252×	`cbrt-div` `sqrt-div`
148×	`frac-times`
136×	`pow1`
126×	`flip3--` `flip--`
120×	`cbrt-prod`
106×	`add-sqr-sqrt`
62×	`pow1/3`
60×	`sqrt-prod`
55×	`pow-prod-up`
50×	`associate-r/` `associate-l/`
40×	`add-cube-cbrt` `*-un-lft-identity`
39×	`pow-sqr`
38×	`pow-prod-down`
34×	`swap-sqr`
28×	`associate-r` `associate-l` `unswap-sqr`
22×	`add-exp-log`
21×	`pow-plus`
16×	`pow2`
11×	`prod-exp` `cbrt-unprod`
8×	`add-cbrt-cube`
4×	`expm1-log1p-u` `*-commutative` `log1p-expm1-u` `add-log-exp`

Counts

4 → 354

Calls

4 calls:

77.0ms	(* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))))
71.0ms	(* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))))
66.0ms	(* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))))
235.0ms	(* (* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))))) (* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))))))

series3.9s

Counts

4 → 12

Calls

4 calls:

908.0ms	(* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))))
865.0ms	(* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))))
927.0ms	(* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))))
1.2s	(* (* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))))) (* (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5))))) (cbrt (sqrt (- (fma s (* c_p 0.5) 1) (* s (* c_n 0.5)))))))

simplify6.5s

Counts

366 → 366

Iterations

Iter	Nodes
done	5000
3	4921
2	1802
1	884
0	306

prune3.8s

Pruning

4 alts after pruning (3 fresh and 1 done)

Merged error: 0.1b

regimes2.0s

bsearch2.0ms

simplify20.0ms

Iterations

Iter	Nodes
done	51
1	51
0	43

end0.0ms

sample3.4m

Algorithm

intervals

Results

3.3m	9134×	body	10240	exit
751.0ms	9839×	pre	80	true
147.0ms	684×	body	80	valid
62.0ms	4×	body	320	valid
24.0ms	7×	body	1280	valid
19.0ms	2×	body	5120	valid
13.0ms	1×	body	2560	valid
5.0ms	2×	body	640	valid
3.0ms	5×	body	160	valid