Details

analyze100.0ms (1.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
25%	74.9%	0.1%	5
43.7%	43.7%	12.6%	6
53.1%	31.2%	15.7%	7
59.3%	18.7%	22%	8
62.4%	14%	23.5%	9
64.8%	8.6%	26.6%	10
66%	6.6%	27.4%	11
66.9%	4.1%	29%	12
67.4%	3.2%	29.4%	13
67.9%	2%	30.1%	14

Compiler

Compiled 10 to 9 computations (10% saved)

sample34.0ms (0.6%)

Algorithm

1×

intervals

Results

16.0ms	231×	body	128	valid
5.0ms	9×	body	1024	valid
3.0ms	8×	body	512	valid
1.0ms	8×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 19 to 19 computations (0% saved)

simplify255.0ms (4.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (12.0ms)

Iter	Nodes	Cost
0	96	14
1	96	14

prune4.0ms (0.1%)

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: 0.4b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize14.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
0.0b	(+.f64 1 (exp.f64 x))
0.4b	(log.f64 (+.f64 1 (exp.f64 x)))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`*-un-lft-identity_binary64_2124`
8×	`log-prod_binary64_2210`
6×	`add-log-exp_binary64_2163`
5×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
4×	`pow1_binary64_2185` `associate--l+_binary64_2061` `log-div_binary64_2211` `add-exp-log_binary64_2162`
3×	`distribute-lft-out_binary64_2075` `flip3-+_binary64_2127` `flip-+_binary64_2098` `add-cbrt-cube_binary64_2160`
2×	`associate--l-_binary64_2062`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `rem-log-exp_binary64_2165` `sum-log_binary64_2215` `log-pow_binary64_2213` `diff-log_binary64_2216` `+-commutative_binary64_2054` `sub-neg_binary64_2117`

Counts

3 → 45

Calls

3 calls:

9.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
7.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
6.0ms	(+.f64 1 (exp.f64 x))

series265.0ms (4.6%)

Counts

3 → 9

Calls

3 calls:

147.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
98.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
19.0ms	(+.f64 1 (exp.f64 x))

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (80.0ms)

Iter	Nodes	Cost
0	5066	767

prune89.0ms (1.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	4	55

Merged error: 0.3b

Counts

55 → 4

Compiler

Compiled 867 to 496 computations (42.8% saved)

localize29.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 3)
0.5b	(log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)))
4.0b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
4.2b	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))

rewrite54.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

21×	`*-un-lft-identity_binary64_2124`
17×	`add-sqr-sqrt_binary64_2146`
11×	`add-cube-cbrt_binary64_2159`
9×	`log-prod_binary64_2210`
7×	`pow1_binary64_2185`
6×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162`
5×	`add-cbrt-cube_binary64_2160`
4×	`difference-of-squares_binary64_2093` `unpow-prod-down_binary64_2203` `pow-pow_binary64_2196` `log-div_binary64_2211`
3×	`cancel-sign-sub-inv_binary64_2090` `pow-unpow_binary64_2201` `distribute-lft-out_binary64_2075` `cube-prod_binary64_2152` `exp-prod_binary64_2176`
2×	`rem-log-exp_binary64_2165` `distribute-lft-out--_binary64_2076` `log-pow_binary64_2213` `sqr-pow_binary64_2096` `unpow2_binary64_2189` `flip3-+_binary64_2127` `flip-+_binary64_2098`
1×	`flip--_binary64_2099` `unpow3_binary64_2190` `flip3--_binary64_2128` `cube-mult_binary64_2154` `pow-exp_binary64_2192` `diff-log_binary64_2216` `distribute-rgt-out--_binary64_2078` `sub-neg_binary64_2117` `pow-to-exp_binary64_2193` `rem-cube-cbrt_binary64_2147`

Counts

4 → 77

Calls

4 calls:

17.0ms	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))
14.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
12.0ms	(log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)))
4.0ms	(pow.f64 (exp.f64 x) 3)

series803.0ms (13.8%)

Counts

4 → 12

Calls

4 calls:

300.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
250.0ms	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))
195.0ms	(log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)))
57.0ms	(pow.f64 (exp.f64 x) 3)

simplify70.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

89 → 89

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	4992	1260
1	4992	1260

prune188.0ms (3.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	87	2	89
Fresh	0	3	3
Picked	1	0	1
Done	0	0	0
Total	88	5	93

Merged error: 0.3b

Counts

93 → 5

Compiler

Compiled 2512 to 1547 computations (38.4% saved)

localize45.0ms (0.8%)

Local error

Found 4 expressions with local error:

4.0b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
4.0b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
4.0b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
4.1b	(log.f64 (+.f64 1 (*.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)) (+.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)) -1))))

rewrite77.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_2146`
17×	`*-un-lft-identity_binary64_2124`
12×	`difference-of-squares_binary64_2093`
10×	`add-log-exp_binary64_2163`
9×	`cancel-sign-sub-inv_binary64_2090`
8×	`add-cube-cbrt_binary64_2159`
6×	`unpow2_binary64_2189`
5×	`pow1_binary64_2185` `add-exp-log_binary64_2162`
4×	`add-cbrt-cube_binary64_2160`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `unpow-prod-down_binary64_2203` `distribute-lft-out--_binary64_2076` `diff-log_binary64_2216` `log-prod_binary64_2210` `sqr-pow_binary64_2096` `distribute-rgt-out--_binary64_2078` `sub-neg_binary64_2117`
2×	`log-div_binary64_2211`
1×	`rem-log-exp_binary64_2165` `log-pow_binary64_2213` `flip3-+_binary64_2127` `flip-+_binary64_2098`

Counts

4 → 74

Calls

4 calls:

17.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
16.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
15.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
6.0ms	(log.f64 (+.f64 1 (*.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)) (+.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)) -1))))

series689.0ms (11.9%)

Counts

4 → 12

Calls

4 calls:

555.0ms	(log.f64 (+.f64 1 (*.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)) (+.f64 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)) -1))))
48.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
43.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
42.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))

simplify136.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (102.0ms)

Iter	Nodes	Cost
0	4962	1742
1	4962	1742

prune222.0ms (3.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	86	5	91

Merged error: 0.3b

Counts

91 → 5

Compiler

Compiled 4472 to 2741 computations (38.7% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

4.0b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
4.0b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
4.2b	(log.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
4.2b	(log.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))

rewrite50.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_2124`
22×	`add-sqr-sqrt_binary64_2146`
16×	`log-prod_binary64_2210`
10×	`sqrt-prod_binary64_2140` `add-cube-cbrt_binary64_2159`
8×	`difference-of-squares_binary64_2093` `pow1_binary64_2185` `add-log-exp_binary64_2163`
6×	`cancel-sign-sub-inv_binary64_2090` `log-pow_binary64_2213` `add-exp-log_binary64_2162`
4×	`distribute-lft-out--_binary64_2076` `distribute-lft-out_binary64_2075` `sqrt-div_binary64_2141` `unpow2_binary64_2189` `log-div_binary64_2211` `add-cbrt-cube_binary64_2160`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `rem-log-exp_binary64_2165` `unpow-prod-down_binary64_2203` `sqrt-pow1_binary64_2142` `diff-log_binary64_2216` `sqr-pow_binary64_2096` `pow1/2_binary64_2204` `distribute-rgt-out--_binary64_2078` `sub-neg_binary64_2117` `flip3-+_binary64_2127` `flip-+_binary64_2098`

Counts

4 → 82

Calls

4 calls:

11.0ms	(log.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
10.0ms	(log.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
8.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
8.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))

series638.0ms (11%)

Counts

4 → 12

Calls

4 calls:

297.0ms	(log.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
256.0ms	(log.f64 (sqrt.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
48.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
36.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))

simplify123.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	5109	1902

prune237.0ms (4.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	93	1	94
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	94	5	99

Merged error: 0.3b

Counts

99 → 5

Compiler

Compiled 3840 to 2423 computations (36.9% saved)

regimes123.0ms (2.1%)

Compiler: Compiled 982 to 747 computations (23.9% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	101	58
1	101	58

end0.0ms (0%)

sample1.4s (24.4%)

Algorithm

1×

intervals

Results

508.0ms	7361×	body	128	valid
131.0ms	230×	body	1024	valid
81.0ms	253×	body	512	valid
27.0ms	154×	body	256	valid
3.0ms	40×	body	128	invalid
2.0ms	2×	body	2048	valid
0.0ms	8×	body	128	overflowed

Compiler

Compiled 392 to 299 computations (23.7% saved)

Details

analyze100.0ms (1.7%)

sample34.0ms (0.6%)

simplify255.0ms (4.4%)

prune4.0ms (0.1%)

localize14.0ms (0.2%)

rewrite26.0ms (0.4%)

series265.0ms (4.6%)

simplify98.0ms (1.7%)

prune89.0ms (1.5%)

localize29.0ms (0.5%)

rewrite54.0ms (0.9%)

series803.0ms (13.8%)

simplify70.0ms (1.2%)

prune188.0ms (3.2%)

localize45.0ms (0.8%)

rewrite77.0ms (1.3%)

series689.0ms (11.9%)

simplify136.0ms (2.3%)

prune222.0ms (3.8%)

localize17.0ms (0.3%)

rewrite50.0ms (0.9%)

series638.0ms (11%)

simplify123.0ms (2.1%)

prune237.0ms (4.1%)

regimes123.0ms (2.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (24.4%)

Profiling