Details

sample40.8s

Algorithm

intervals

Results

40.6s	3221×	body	10240	exit
80.0ms	3478×	pre	80	true
22.0ms	250×	body	80	valid
1.0ms	1×	body	1280	valid
1.0ms	4×	body	160	valid
1.0ms	1×	body	640	valid
0.0ms	1×	body	320	valid

simplify25.0ms

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

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: 5.5b

Counts

2 → 1

localize25.0ms

Local error

Found 4 expressions with local error:

0.4b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
0.5b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
2.2b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
2.4b	(/ (* (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)))

rewrite88.0ms

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:

14.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
38.0ms	(/ (* (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)))

series929.0ms

Counts

4 → 12

Calls

4 calls:

45.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- t)))))
67.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
68.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
749.0ms	(/ (* (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)))

simplify137.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (24.0ms)

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

prune540.0ms

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: 0.3b

Counts

345 → 4

localize8.0ms

Local error

Found 2 expressions with local error:

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

rewrite9.0ms

Algorithm

rewrite-expression-head

Rules

7×	`pow1` `add-exp-log` `add-cbrt-cube`
5×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
4×	`add-log-exp`
3×	`fma-neg` `associate-l` `prod-diff` `pow-prod-down` `prod-exp` `cbrt-unprod`
2×	`expm1-log1p-u` `log1p-expm1-u`
1×	`sub-neg` `flip3--` `diff-log` `associate-r` `*-commutative` `flip--`

Counts

2 → 40

Calls

2 calls:

4.0ms	(* 0.5 (* s c_n))
3.0ms	(- 1 (* 0.5 (* s c_n)))

series58.0ms

Counts

2 → 6

Calls

2 calls:

18.0ms	(* 0.5 (* s c_n))
40.0ms	(- 1 (* 0.5 (* s c_n)))

simplify101.0ms

Algorithm

egg-herbie

Counts

46 → 46

Iterations

Useful iterations: 2 (24.0ms)

Iter	Nodes	Cost
0	171	200
1	742	170
2	4071	169
3	5001	169

prune87.0ms

Filtered

46 candidates to 29 candidates (63.0%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	45	1	46
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	46	4	50

Merged error: 0.3b

Counts

50 → 4

localize11.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
28.4b	(cbrt (* 0.5 (* s c_n)))
28.4b	(cbrt (* 0.5 (* s c_n)))
28.4b	(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:

5.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
4.0ms	(cbrt (* 0.5 (* s c_n)))
3.0ms	(cbrt (* 0.5 (* s c_n)))
4.0ms	(cbrt (* 0.5 (* s c_n)))

series388.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
87.0ms	(cbrt (* 0.5 (* s c_n)))
87.0ms	(cbrt (* 0.5 (* s c_n)))
88.0ms	(cbrt (* 0.5 (* s c_n)))

simplify96.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (90.0ms)

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

prune220.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	77	5	82

Merged error: 0.3b

Counts

82 → 5

localize14.0ms

Local error

Found 4 expressions with local error:

0.5b	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
28.4b	(cbrt (* 0.5 (* s c_n)))
28.4b	(cbrt (* 0.5 (* s c_n)))
28.4b	(cbrt (* 0.5 (* s c_n)))

rewrite17.0ms

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:

5.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
3.0ms	(cbrt (* 0.5 (* s c_n)))
3.0ms	(cbrt (* 0.5 (* s c_n)))
4.0ms	(cbrt (* 0.5 (* s c_n)))

series385.0ms

Counts

4 → 12

Calls

4 calls:

126.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
86.0ms	(cbrt (* 0.5 (* s c_n)))
86.0ms	(cbrt (* 0.5 (* s c_n)))
87.0ms	(cbrt (* 0.5 (* s c_n)))

simplify96.0ms

Algorithm

egg-herbie

Counts

78 → 78

Iterations

Useful iterations: 3 (90.0ms)

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

prune233.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	77	1	78
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	78	5	83

Merged error: 0.3b

Counts

83 → 5

regimes476.0ms

bsearch0.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	16
1	21	16

end0.0ms

sample9.3m

Algorithm

intervals

Results

9.2m	45236×	body	10240	exit
979.0ms	48757×	pre	80	true
289.0ms	3408×	body	80	valid
49.0ms	7×	body	5120	valid
39.0ms	24×	body	1280	valid
20.0ms	7×	body	2560	valid
13.0ms	16×	body	640	valid
10.0ms	41×	body	160	valid
6.0ms	17×	body	320	valid