Details

analyze4.4s

Algorithm

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	25%	75%	2
0%	25%	75%	3
0%	25%	75%	4
0%	25%	75%	5
0%	25%	75%	6
0%	25%	75%	7
0%	25%	75%	8
1.6%	23.4%	75%	9
1.6%	23.4%	75%	10
1.6%	23.4%	75%	11
1.6%	23.4%	75%	12
1.6%	23.4%	75%	13
1.6%	23.4%	75%	14

sample5.3s

Algorithm

intervals

Results

3.3s	474×	body	5120	exit
762.0ms	282×	body	1280	overflowed
446.0ms	2157×	body	80	overflowed
332.0ms	238×	body	640	overflowed
103.0ms	122×	body	320	overflowed
86.0ms	3593×	pre	80	true
34.0ms	241×	body	80	valid
28.0ms	63×	body	160	overflowed
7.0ms	1×	body	5120	valid
6.0ms	2×	body	1280	valid
3.0ms	1×	body	2560	valid
3.0ms	8×	body	160	valid
1.0ms	2×	body	320	valid
1.0ms	1×	body	640	valid
0.0ms	1×	body	80	invalid

simplify56.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	5035	43

prune5.0ms

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: 7.3b

Counts

2 → 1

localize24.0ms

Local error

Found 4 expressions with local error:

0.3b	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))
0.5b	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
1.5b	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p)
4.1b	(/.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n)) (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n)))

rewrite118.0ms

Algorithm

rewrite-expression-head

Rules

1192×	`add-exp-log_binary64`
692×	`pow-exp_binary64`
684×	`prod-exp_binary64`
593×	`div-exp_binary64`
344×	`pow-to-exp_binary64`
116×	`1-exp_binary64` `rec-exp_binary64`
42×	`*-un-lft-identity_binary64`
36×	`unpow-prod-down_binary64`
33×	`add-sqr-sqrt_binary64`
29×	`times-frac_binary64`
22×	`add-cube-cbrt_binary64`
16×	`add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`pow-unpow_binary64` `add-log-exp_binary64` `distribute-lft-out_binary64` `pow-pow_binary64` `difference-of-squares_binary64`
4×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-inv_binary64`
2×	`flip3-+_binary64` `sqr-pow_binary64` `inv-pow_binary64` `distribute-lft-out--_binary64` `pow-flip_binary64` `flip-+_binary64`
1×	`associate-/r_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `flip--_binary64`

Counts

4 → 471

Calls

4 calls:

11.0ms	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))
12.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
8.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p)
48.0ms	(/.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n)) (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n)))

series245.0ms

Counts

4 → 12

Calls

4 calls:

7.0ms	(-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))
16.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p)
16.0ms	(pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p)
205.0ms	(/.f64 (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s))))) c_n)) (.f64 (pow.f64 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))) c_p) (pow.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t))))) c_n)))

simplify112.0ms

Algorithm

egg-herbie

Counts

483 → 483

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5033	16646

prune165.0ms

Filtered

71 candidates to 483 candidates (-580.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	480	3	483
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	481	3	484

Merged error: 0.3b

Counts

484 → 3

localize7.0ms

Local error

Found 1 expressions with local error:

0.0b	(.f64 (.f64 s 1/2) (-.f64 c_p c_n))

rewrite10.0ms

Algorithm

rewrite-expression-head

Rules

6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-r_binary64`
4×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
3×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
2×	`sub-neg_binary64` `associate-*r/_binary64` `add-cube-cbrt_binary64`
1×	`add-log-exp_binary64` `flip3--_binary64` `distribute-lft-in_binary64` `associate-l_binary64` `distribute-rgt-in_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64` `*-commutative_binary64`

Counts

1 → 24

Calls

1 calls:

9.0ms

(*.f64 (*.f64 s 1/2) (-.f64 c_p c_n))

series11.0ms

Counts

1 → 3

Calls

1 calls:

11.0ms

(*.f64 (*.f64 s 1/2) (-.f64 c_p c_n))

simplify42.0ms

Algorithm

egg-herbie

Counts

27 → 27

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5006	217

prune26.0ms

Filtered

15 candidates to 27 candidates (-80.0%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	27	0	27
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	27	3	30

Merged error: 0.3b

Counts

30 → 3

localize29.0ms

Local error

Found 4 expressions with local error:

0.7b	(log.f64 (+.f64 1 (exp.f64 (neg.f64 s))))
1.7b	(log.f64 (+.f64 1 (exp.f64 (neg.f64 t))))
7.5b	(-.f64 (log.f64 (+.f64 1 (exp.f64 (neg.f64 s)))) (log.f64 (+.f64 1 (exp.f64 (neg.f64 t)))))
7.6b	(-.f64 (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))) (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

42×	`*-un-lft-identity_binary64`
38×	`log-prod_binary64`
36×	`add-sqr-sqrt_binary64`
15×	`associate--r+_binary64` `associate--l+_binary64`
14×	`pow1_binary64` `difference-of-squares_binary64`
12×	`distribute-lft-out--_binary64` `log-div_binary64`
10×	`add-cube-cbrt_binary64` `log-pow_binary64`
8×	`times-frac_binary64`
6×	`add-exp-log_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `flip3--_binary64` `associate--l-_binary64` `distribute-lft-out_binary64` `associate--r-_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `flip-+_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `rem-log-exp_binary64` `div-inv_binary64`

Counts

4 → 100

Calls

4 calls:

4.0ms	(log.f64 (+.f64 1 (exp.f64 (neg.f64 s))))
4.0ms	(log.f64 (+.f64 1 (exp.f64 (neg.f64 t))))
11.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 (neg.f64 s)))) (log.f64 (+.f64 1 (exp.f64 (neg.f64 t)))))
26.0ms	(-.f64 (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))) (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))))

series74.0ms

Counts

4 → 12

Calls

4 calls:

11.0ms	(log.f64 (+.f64 1 (exp.f64 (neg.f64 s))))
11.0ms	(log.f64 (+.f64 1 (exp.f64 (neg.f64 t))))
17.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 (neg.f64 s)))) (log.f64 (+.f64 1 (exp.f64 (neg.f64 t)))))
34.0ms	(-.f64 (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 s)))))) (log.f64 (-.f64 1 (/.f64 1 (+.f64 1 (exp.f64 (neg.f64 t)))))))

simplify53.0ms

Algorithm

egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (39.0ms)

Iter	Nodes	Cost
0	4910	1897
1	4910	1897

prune181.0ms

Filtered

79 candidates to 112 candidates (-41.8%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	1	1
Picked	1	0	1
Done	0	1	1
Total	112	3	115

Merged error: 0.2b

Counts

115 → 3

localize23.0ms

Local error

Found 4 expressions with local error:

0.0b	(.f64 c_n (-.f64 (.f64 t 1/2) (.f64 s (+.f64 1/2 (.f64 s 1/8)))))
0.7b	(log.f64 (+.f64 1 (exp.f64 (neg.f64 s))))
1.7b	(log.f64 (+.f64 1 (exp.f64 (neg.f64 t))))
7.5b	(-.f64 (log.f64 (+.f64 1 (exp.f64 (neg.f64 s)))) (log.f64 (+.f64 1 (exp.f64 (neg.f64 t)))))

rewrite28.0ms

Algorithm

rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
16×	`log-prod_binary64`
14×	`add-sqr-sqrt_binary64`
12×	`pow1_binary64`
10×	`add-cube-cbrt_binary64`
8×	`add-exp-log_binary64` `log-div_binary64`
6×	`log-pow_binary64` `add-cbrt-cube_binary64`
4×	`flip3-+_binary64` `add-log-exp_binary64` `associate--r+_binary64` `distribute-lft-out_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `associate--l+_binary64`
3×	`sub-neg_binary64` `associate-r_binary64` `associate-l_binary64`
2×	`flip3--_binary64` `associate--l-_binary64` `associate--r-_binary64` `rem-log-exp_binary64` `associate-*r/_binary64` `flip--_binary64`
1×	`pow-prod-down_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `*-commutative_binary64`

Counts

4 → 80

Calls

4 calls:

7.0ms	(.f64 c_n (-.f64 (.f64 t 1/2) (.f64 s (+.f64 1/2 (.f64 s 1/8)))))
4.0ms	(log.f64 (+.f64 1 (exp.f64 (neg.f64 s))))
4.0ms	(log.f64 (+.f64 1 (exp.f64 (neg.f64 t))))
11.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 (neg.f64 s)))) (log.f64 (+.f64 1 (exp.f64 (neg.f64 t)))))

series65.0ms

Counts

4 → 12

Calls

4 calls:

22.0ms	(.f64 c_n (-.f64 (.f64 t 1/2) (.f64 s (+.f64 1/2 (.f64 s 1/8)))))
11.0ms	(log.f64 (+.f64 1 (exp.f64 (neg.f64 s))))
12.0ms	(log.f64 (+.f64 1 (exp.f64 (neg.f64 t))))
20.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 (neg.f64 s)))) (log.f64 (+.f64 1 (exp.f64 (neg.f64 t)))))

simplify54.0ms

Algorithm

egg-herbie

Counts

92 → 92

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5039	1192

prune111.0ms

Filtered

63 candidates to 92 candidates (-46.0%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	92	0	92
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	92	3	95

Merged error: 0.2b

Counts

95 → 3

regimes394.0ms

bsearch2.4s

Steps

Iters	Range		Point
8	-489.62679574921134	-0.28629909339653153	-13.072407951153217

simplify3.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	109	57
1	109	57

end0.0ms

sample24.0s

Algorithm

intervals

Results

15.5s	2307×	body	5120	exit
3.4s	1313×	body	1280	overflowed
2.0s	10053×	body	80	overflowed
1.5s	1146×	body	640	overflowed
442.0ms	570×	body	320	overflowed
384.0ms	16865×	pre	80	true
143.0ms	1137×	body	80	valid
124.0ms	295×	body	160	overflowed
20.0ms	8×	body	1280	valid
14.0ms	2×	body	5120	valid
8.0ms	22×	body	160	valid
5.0ms	4×	body	640	valid
3.0ms	5×	body	320	valid
3.0ms	1×	body	2560	valid
0.0ms	2×	body	80	invalid

Details

analyze4.4s

sample5.3s

simplify56.0ms

prune5.0ms

localize24.0ms

rewrite118.0ms

series245.0ms

simplify112.0ms

prune165.0ms

localize7.0ms

rewrite10.0ms

series11.0ms

simplify42.0ms

prune26.0ms

localize29.0ms

rewrite49.0ms

series74.0ms

simplify53.0ms

prune181.0ms

localize23.0ms

rewrite28.0ms

series65.0ms

simplify54.0ms

prune111.0ms

regimes394.0ms

bsearch2.4s

simplify3.0ms

end0.0ms

sample24.0s

Profiling