Details

sample40.6s

Algorithm

intervals

Results

40.4s	3135×	body	10240	exit
76.0ms	3391×	pre	80	true
23.0ms	251×	body	80	valid
1.0ms	1×	body	1280	valid
1.0ms	2×	body	640	valid
1.0ms	2×	body	160	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

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: 5.2b

Counts

2 → 1

localize21.0ms

Local error

Found 4 expressions with local error:

0.1b	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
0.7b	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
1.0b	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
3.4b	(/ (* (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)))

rewrite131.0ms

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:

11.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
7.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
40.0ms	(/ (* (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)))

series764.0ms

Counts

4 → 12

Calls

4 calls:

50.0ms	(- 1.0 (/ 1.0 (+ 1.0 (exp (- s)))))
69.0ms	(pow (/ 1.0 (+ 1.0 (exp (- t)))) c_p)
65.0ms	(pow (/ 1.0 (+ 1.0 (exp (- s)))) c_p)
581.0ms	(/ (* (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)))

simplify138.0ms

Algorithm

egg-herbie

Counts

344 → 344

Iterations

Useful iterations: 1 (23.0ms)

Iter	Nodes	Cost
0	1281	8124
1	4380	7090
2	5001	7090

prune555.0ms

Filtered

344 candidates to 106 candidates (30.8%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	339	5	344
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	340	5	345

Merged error: 1.3b

Counts

345 → 5

localize8.0ms

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))

series19.0ms

Counts

1 → 3

Calls

1 calls:

19.0ms

(* 0.5 (* s c_n))

simplify73.0ms

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

prune58.0ms

Filtered

23 candidates to 13 candidates (56.5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	20	3	23
Fresh	0	4	4
Picked	1	0	1
Done	0	0	0
Total	21	7	28

Merged error: 1.3b

Counts

28 → 7

localize15.0ms

Local error

Found 4 expressions with local error:

0.4b	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
26.8b	(cbrt (* 0.5 (* s c_n)))
26.8b	(cbrt (* 0.5 (* s c_n)))
26.8b	(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))))
4.0ms	(cbrt (* 0.5 (* s c_n)))
3.0ms	(cbrt (* 0.5 (* s c_n)))
4.0ms	(cbrt (* 0.5 (* s c_n)))

series399.0ms

Counts

4 → 12

Calls

4 calls:

131.0ms	(* (cbrt (* 0.5 (* s c_n))) (cbrt (* 0.5 (* s c_n))))
89.0ms	(cbrt (* 0.5 (* s c_n)))
89.0ms	(cbrt (* 0.5 (* s c_n)))
90.0ms	(cbrt (* 0.5 (* s c_n)))

simplify95.0ms

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

prune232.0ms

Filtered

78 candidates to 64 candidates (82.1%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	76	2	78
Fresh	1	5	6
Picked	1	0	1
Done	0	0	0
Total	78	7	85

Merged error: 1.3b

Counts

85 → 7

localize17.0ms

Local error

Found 4 expressions with local error:

0.2b	(* (pow (pow (cbrt (* 0.5 (* s c_n))) 6) 1/3) (cbrt (* 0.5 (* s c_n))))
26.8b	(cbrt (* 0.5 (* s c_n)))
26.8b	(cbrt (* 0.5 (* s c_n)))
43.0b	(pow (pow (cbrt (* 0.5 (* s c_n))) 6) 1/3)

rewrite23.0ms

Algorithm

rewrite-expression-head

Rules

28×	`unpow-prod-down`
19×	`add-sqr-sqrt`
14×	`add-exp-log`
12×	`associate-l`
11×	`add-cube-cbrt` `*-un-lft-identity`
8×	`pow-exp`
6×	`sqr-pow`
5×	`cbrt-prod` `prod-exp` `add-cbrt-cube` `unswap-sqr`
4×	`pow1` `expm1-log1p-u` `pow-to-exp` `associate-r` `log1p-expm1-u` `add-log-exp`
3×	`pow-unpow` `pow1/3`
2×	`unpow1/3` `cbrt-unprod`
1×	`pow-pow` `pow-prod-down` `*-commutative`

Counts

4 → 88

Calls

4 calls:

9.0ms	(* (pow (pow (cbrt (* 0.5 (* s c_n))) 6) 1/3) (cbrt (* 0.5 (* s c_n))))
4.0ms	(cbrt (* 0.5 (* s c_n)))
3.0ms	(cbrt (* 0.5 (* s c_n)))
4.0ms	(pow (pow (cbrt (* 0.5 (* s c_n))) 6) 1/3)

series612.0ms

Counts

4 → 12

Calls

4 calls:

57.0ms	(* (pow (pow (cbrt (* 0.5 (* s c_n))) 6) 1/3) (cbrt (* 0.5 (* s c_n))))
262.0ms	(cbrt (* 0.5 (* s c_n)))
89.0ms	(cbrt (* 0.5 (* s c_n)))
204.0ms	(pow (pow (cbrt (* 0.5 (* s c_n))) 6) 1/3)

simplify43.0ms

Algorithm

egg-herbie

Counts

100 → 100

Iterations

Useful iterations: 2 (34.0ms)

Iter	Nodes	Cost
0	312	815
1	1166	749
2	5001	619

prune278.0ms

Filtered

100 candidates to 77 candidates (77.0%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	98	2	100
Fresh	2	4	6
Picked	1	0	1
Done	0	0	0
Total	101	6	107

Merged error: 1.3b

Counts

107 → 6

regimes646.0ms

bsearch1.0ms

simplify2.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	55	42
1	55	42

end0.0ms

sample5.1m

Algorithm

intervals

Results

5.0m	24223×	body	10240	exit
541.0ms	26115×	pre	80	true
171.0ms	1836×	body	80	valid
19.0ms	11×	body	1280	valid
12.0ms	2×	body	5120	valid
11.0ms	13×	body	640	valid
10.0ms	5×	body	2560	valid
5.0ms	21×	body	160	valid
2.0ms	4×	body	320	valid