Details

sample39.5s

Algorithm

intervals

Results

39.2s	3199×	body	10240	exit
84.0ms	3455×	pre	80	true
22.0ms	246×	body	80	valid
4.0ms	2×	body	1280	valid
3.0ms	3×	body	640	valid
2.0ms	1×	body	2560	valid
1.0ms	3×	body	160	valid
1.0ms	1×	body	320	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

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

Merged error: 6.8b

localize22.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
4.2b	(/ (* (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)))

rewrite138.0ms

Algorithm

rewrite-expression-head

Rules

558×	`add-exp-log`
312×	`prod-exp`
264×	`pow-exp`
250×	`div-exp`
184×	`pow-to-exp`
51×	`*-un-lft-identity`
37×	`times-frac`
36×	`unpow-prod-down`
31×	`add-sqr-sqrt` `add-cube-cbrt`
18×	`add-cbrt-cube`
10×	`distribute-lft-out`
6×	`pow1` `pow-unpow` `associate-/r/`
5×	`cbrt-undiv` `associate-/r*`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `associate-/l*` `add-log-exp`
3×	`flip3-+` `flip-+`
2×	`pow-pow` `frac-2neg` `clear-num` `sqr-pow`

Counts

4 → 293

Calls

4 calls:

8.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
12.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
90.0ms	(/ (* (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)))

series742.0ms

Counts

4 → 12

Calls

4 calls:

25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
579.0ms	(/ (* (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)))

simplify107.0ms

Algorithm

egg-herbie

Counts

305 → 305

Iterations

Useful iterations: 1 (17.0ms)

Iter	Nodes	Cost
0	993	6127
1	3350	5877
2	5002	5877

prune549.0ms

Filtered

305 candidates to 99 candidates (32.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

Merged error: 1.5b

localize26.0ms

Local error

Found 4 expressions with local error:

0.0b	(/ 1.0 (+ 1.0 (exp (- s))))
0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.7b	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

173×	`add-exp-log`
87×	`prod-exp`
67×	`div-exp`
55×	`pow-exp`
53×	`*-un-lft-identity`
42×	`pow-to-exp`
37×	`times-frac`
31×	`add-sqr-sqrt` `add-cube-cbrt`
20×	`add-cbrt-cube`
18×	`unpow-prod-down`
11×	`distribute-lft-out`
9×	`associate-/r*`
7×	`associate-/l*`
6×	`cbrt-undiv` `associate-/r/`
5×	`pow1`
4×	`expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`pow-unpow` `frac-2neg` `flip3-+` `clear-num` `flip-+`
1×	`pow-pow` `sqr-pow`

Counts

4 → 176

Calls

4 calls:

8.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
9.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
80.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series826.0ms

Counts

4 → 12

Calls

4 calls:

30.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
701.0ms	(/ (* (pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify92.0ms

Algorithm

egg-herbie

Counts

188 → 188

Iterations

Useful iterations: 2 (69.0ms)

Iter	Nodes	Cost
0	871	2983
1	3666	2728
2	5002	2724

prune646.0ms

Filtered

188 candidates to 101 candidates (53.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

Merged error: 1.5b

localize29.0ms

Local error

Found 4 expressions with local error:

0.0b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.0b	(/ 1.0 (+ 1.0 (exp (- s))))
0.0b	(/ 1.0 (+ 1.0 (exp (- t))))
2.7b	(/ (* (fma (log 0.5) c_p (fma 0.5 (* s c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

rewrite115.0ms

Algorithm

rewrite-expression-head

Rules

101×	`*-un-lft-identity`
70×	`add-sqr-sqrt`
65×	`add-cube-cbrt`
62×	`times-frac`
56×	`add-exp-log`
54×	`prod-diff`
24×	`prod-exp`
20×	`add-cbrt-cube`
18×	`div-exp`
17×	`distribute-lft-out`
10×	`associate-/r/`
9×	`associate-/r*`
8×	`pow-to-exp` `pow-exp`
7×	`associate-/l*`
6×	`cbrt-undiv` `div-inv` `add-log-exp`
5×	`flip3-+` `flip-+`
4×	`pow1` `expm1-log1p-u` `cbrt-unprod` `log1p-expm1-u`
3×	`frac-2neg` `fma-neg` `clear-num`
2×	`difference-of-squares`
1×	`sub-neg` `flip3--` `diff-log` `flip--` `distribute-lft-out--`

Counts

4 → 179

Calls

4 calls:

23.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
8.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
8.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
69.0ms	(/ (* (fma (log 0.5) c_p (fma 0.5 (* s c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

series738.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
30.0ms	(/ 1.0 (+ 1.0 (exp (- s))))
25.0ms	(/ 1.0 (+ 1.0 (exp (- t))))
638.0ms	(/ (* (fma (log 0.5) c_p (fma 0.5 (* s c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- s))))) c_n)) (* (fma (log 0.5) c_p (fma 0.5 (* t c_p) 1)) (pow (- 1.0 (/ 1.0 (+ 1.0 (exp (- t))))) c_n)))

simplify105.0ms

Algorithm

egg-herbie

Counts

191 → 191

Iterations

Useful iterations: 2 (74.0ms)

Iter	Nodes	Cost
0	1025	3971
1	4157	2922
2	5001	2918

prune743.0ms

Filtered

191 candidates to 107 candidates (56.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

Merged error: 1.5b

localize12.0ms

Local error

Found 2 expressions with local error:

0.2b	(* (pow (log 0.5) 2) (pow c_p 2))
1.0b	(pow (log 0.5) 2)

rewrite13.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt`
19×	`unpow-prod-down`
16×	`unswap-sqr`
15×	`add-exp-log`
11×	`unpow2` `sqr-pow`
9×	`associate-l` `prod-exp`
8×	`add-cube-cbrt` `-un-lft-identity` `associate-r*`
7×	`pow-to-exp` `pow-exp`
5×	`pow1`
4×	`add-cbrt-cube`
3×	`pow-unpow`
2×	`expm1-log1p-u` `log-pow` `log1p-expm1-u` `add-log-exp`
1×	`pow-pow` `pow-prod-down` `*-commutative` `cbrt-unprod`

Counts

2 → 75

Calls

2 calls:

9.0ms	(* (pow (log 0.5) 2) (pow c_p 2))
1.0ms	(pow (log 0.5) 2)

series157.0ms

Counts

2 → 4

Calls

2 calls:

157.0ms	(* (pow (log 0.5) 2) (pow c_p 2))
0.0ms	(pow (log 0.5) 2)

simplify180.0ms

Algorithm

egg-herbie

Counts

79 → 79

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	206	405
1	818	338
2	4725	332
3	5001	332

prune274.0ms

Filtered

79 candidates to 41 candidates (51.9%)

Pruning

3 alts after pruning (0 fresh and 3 done)

Merged error: 1.5b

regimes215.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	44	48
1	44	48

end0.0ms

sample2.0m

Algorithm

intervals

Results

1.9m	9589×	body	10240	exit
211.0ms	10328×	pre	80	true
64.0ms	712×	body	80	valid
23.0ms	3×	body	5120	valid
8.0ms	2×	body	2560	valid
7.0ms	8×	body	640	valid
7.0ms	4×	body	1280	valid
2.0ms	8×	body	160	valid
1.0ms	2×	body	320	valid