Details

sample2.4s

Algorithm

intervals

Results

1.7s	248×	body	5120	exit
460.0ms	2673×	body	80	overflowed
72.0ms	3178×	pre	80	true
39.0ms	3×	body	5120	valid
26.0ms	242×	body	80	valid
8.0ms	2×	body	2560	valid
2.0ms	6×	body	160	valid
2.0ms	1×	body	1280	valid
2.0ms	2×	body	640	valid
1.0ms	1×	body	320	valid

simplify29.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	53	25
1	147	25
2	850	25
3	5001	25

prune5.0ms

Filtered

1 candidates to 0 candidates (0.0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Merged error: 6.5b

Counts

2 → 1

localize22.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.2b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
1.0b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
3.7b	(/ (* (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)))

rewrite93.0ms

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:

12.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
10.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
41.0ms	(/ (* (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)))

series804.0ms

Counts

4 → 12

Calls

4 calls:

47.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
72.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
70.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
616.0ms	(/ (* (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)))

simplify144.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (24.0ms)

Iter	Nodes	Cost
0	1281	8124
1	4389	7090
2	5001	7090

prune558.0ms

Filtered

344 candidates to 106 candidates (30.8%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	340	4	344
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	341	4	345

Merged error: 1.0b

Counts

345 → 4

localize11.0ms

Local error

Found 1 expressions with local error:

0.0b	(* 0.5 (* s c_n))

rewrite5.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1` `add-exp-log` `add-cbrt-cube`
3×	`associate-l` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
1×	`expm1-log1p-u` `associate-r` `*-commutative` `log1p-expm1-u` `add-log-exp`

Counts

1 → 20

Calls

1 calls:

5.0ms

(* 0.5 (* s c_n))

series20.0ms

Counts

1 → 3

Calls

1 calls:

20.0ms

(* 0.5 (* s c_n))

simplify76.0ms

Algorithm

egg-herbie

Counts

23 → 23

Iterations

Useful iterations: 1 (4.0ms)

Iter	Nodes	Cost
0	88	77
1	320	62
2	1234	62
3	3438	62
4	5002	62

prune52.0ms

Filtered

23 candidates to 13 candidates (56.5%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	21	2	23
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	21	6	27

Merged error: 1.0b

Counts

27 → 6

localize11.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
26.9b	(cbrt (* 0.5 (* s c_n)))
26.9b	(cbrt (* 0.5 (* s c_n)))
26.9b	(cbrt (* 0.5 (* s c_n)))

rewrite18.0ms

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×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `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 → 66

Calls

4 calls:

6.0ms	(* (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)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
92.0ms	(cbrt (* 0.5 (* s c_n)))
93.0ms	(cbrt (* 0.5 (* s c_n)))
92.0ms	(cbrt (* 0.5 (* s c_n)))

simplify108.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (101.0ms)

Iter	Nodes	Cost
0	212	478
1	738	427
2	3536	370
3	5002	365

prune247.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	4	4
Picked	1	0	1
Done	1	0	1
Total	78	6	84

Merged error: 1.0b

Counts

84 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
26.9b	(cbrt (* 0.5 (* s c_n)))
26.9b	(cbrt (* 0.5 (* s c_n)))
26.9b	(cbrt (* 0.5 (* s c_n)))

rewrite19.0ms

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×	`expm1-log1p-u` `swap-sqr` `associate-r` `associate-l` `add-cbrt-cube` `log1p-expm1-u` `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 → 66

Calls

4 calls:

6.0ms	(* (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)))

series416.0ms

Counts

4 → 12

Calls

4 calls:

137.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
92.0ms	(cbrt (* 0.5 (* s c_n)))
94.0ms	(cbrt (* 0.5 (* s c_n)))
93.0ms	(cbrt (* 0.5 (* s c_n)))

simplify99.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (93.0ms)

Iter	Nodes	Cost
0	212	478
1	738	427
2	3536	370
3	5002	365

prune241.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	78	6	84

Merged error: 1.0b

Counts

84 → 6

regimes711.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	47	32
1	47	32

end0.0ms

sample7.4s

Algorithm

intervals

Results

5.0s	733×	body	5120	exit
1.5s	8901×	body	80	overflowed
238.0ms	10418×	pre	80	true
82.0ms	748×	body	80	valid
79.0ms	5×	body	5120	valid
15.0ms	7×	body	1280	valid
8.0ms	2×	body	2560	valid
6.0ms	6×	body	640	valid
4.0ms	11×	body	160	valid
2.0ms	3×	body	320	valid
1.0ms	1×	body	320	overflowed
0.0ms	1×	body	160	overflowed