Details

analyze67.0ms (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)

sample26.0ms (0.7%)

Algorithm

1×

intervals

Results

12.0ms	233×	body	128	valid
3.0ms	7×	body	1024	valid
2.0ms	10×	body	512	valid
1.0ms	6×	body	256	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 19 to 19 computations (0% saved)

simplify173.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (7.0ms)

Iter	Nodes	Cost
0	96	14
1	96	14

prune2.0ms (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: 0.9b

Counts

2 → 1

Compiler

Compiled 18 to 16 computations (11.1% saved)

localize8.0ms (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))
1.2b	(log.f64 (+.f64 1 (exp.f64 x)))

rewrite20.0ms (0.5%)

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:

7.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
5.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(+.f64 1 (exp.f64 x))

series163.0ms (4.2%)

Counts

3 → 9

Calls

3 calls:

77.0ms	(log.f64 (+.f64 1 (exp.f64 x)))
76.0ms	(-.f64 (log.f64 (+.f64 1 (exp.f64 x))) (*.f64 x y))
10.0ms	(+.f64 1 (exp.f64 x))

simplify64.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5066	767

prune53.0ms (1.4%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	49	5	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	50	5	55

Merged error: 0.7b

Counts

55 → 5

Compiler

Compiled 864 to 501 computations (42% saved)

localize16.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
1.2b	(log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)))
3.3b	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))
3.8b	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))

rewrite59.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`*-un-lft-identity_binary64_2124`
18×	`log-prod_binary64_2210` `add-sqr-sqrt_binary64_2146`
11×	`pow1_binary64_2185`
10×	`add-cube-cbrt_binary64_2159`
8×	`log-div_binary64_2211`
7×	`cancel-sign-sub-inv_binary64_2090` `distribute-lft-out--_binary64_2076` `log-pow_binary64_2213`
6×	`distribute-lft-out_binary64_2075` `add-log-exp_binary64_2163` `add-exp-log_binary64_2162`
5×	`difference-of-squares_binary64_2093` `associate--r+_binary64_2060`
4×	`associate--l+_binary64_2061` `flip3-+_binary64_2127` `flip-+_binary64_2098` `add-cbrt-cube_binary64_2160`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `rem-log-exp_binary64_2165` `associate--l-_binary64_2062` `diff-log_binary64_2216` `unpow2_binary64_2189` `associate--r-_binary64_2063` `sub-neg_binary64_2117`
1×	`unpow-prod-down_binary64_2203` `sqr-pow_binary64_2096` `distribute-rgt-out--_binary64_2078`

Counts

4 → 84

Calls

4 calls:

20.0ms	(-.f64 (log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
10.0ms	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))
10.0ms	(log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)))
8.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))

series938.0ms (24.3%)

Counts

4 → 12

Calls

4 calls:

543.0ms	(-.f64 (log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3))) (log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x)))))
213.0ms	(log.f64 (+.f64 1 (-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))))
141.0ms	(log.f64 (+.f64 1 (pow.f64 (exp.f64 x) 3)))
40.0ms	(-.f64 (pow.f64 (exp.f64 x) 2) (exp.f64 x))

simplify87.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

96 → 96

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4957	2219
1	4957	2219

prune137.0ms (3.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	96	0	96
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	96	5	101

Merged error: 0.7b

Counts

101 → 5

Compiler

Compiled 2824 to 1768 computations (37.4% saved)

localize10.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
0.0b	(sqrt.f64 (+.f64 1 (exp.f64 x)))
1.8b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
1.8b	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))

rewrite26.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64_2124`
16×	`sqrt-prod_binary64_2140`
14×	`log-prod_binary64_2210`
12×	`add-sqr-sqrt_binary64_2146`
10×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159`
8×	`sqrt-div_binary64_2141`
6×	`log-pow_binary64_2213` `add-exp-log_binary64_2162`
4×	`sqrt-pow1_binary64_2142` `distribute-lft-out_binary64_2075` `add-log-exp_binary64_2163` `pow1/2_binary64_2204` `flip3-+_binary64_2127` `log-div_binary64_2211` `flip-+_binary64_2098` `add-cbrt-cube_binary64_2160`
2×	`rem-log-exp_binary64_2165` `rem-sqrt-square_binary64_2137`

Counts

4 → 72

Calls

4 calls:

7.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
5.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
4.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
4.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

series287.0ms (7.4%)

Counts

4 → 12

Calls

4 calls:

112.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
106.0ms	(log.f64 (sqrt.f64 (+.f64 1 (exp.f64 x))))
35.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))
33.0ms	(sqrt.f64 (+.f64 1 (exp.f64 x)))

simplify75.0ms (2%)

Algorithm

1×	egg-herbie

Counts

84 → 84

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	5646	1170

prune99.0ms (2.6%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	84	0	84
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	84	5	89

Merged error: 0.7b

Counts

89 → 5

Compiler

Compiled 1891 to 1222 computations (35.4% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 2 (.f64 x (.f64 x 1/2)))
0.0b	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))) (*.f64 x y))
0.0b	(+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))
7.6b	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))

rewrite29.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-log-exp_binary64_2163` `*-un-lft-identity_binary64_2124`
8×	`log-prod_binary64_2210`
6×	`add-cube-cbrt_binary64_2159` `add-sqr-sqrt_binary64_2146`
5×	`pow1_binary64_2185` `add-exp-log_binary64_2162`
4×	`sum-log_binary64_2215` `associate--l+_binary64_2061` `flip3-+_binary64_2127` `log-div_binary64_2211` `flip-+_binary64_2098` `add-cbrt-cube_binary64_2160`
3×	`distribute-lft-out_binary64_2075`
2×	`associate--l-_binary64_2062` `+-commutative_binary64_2054`
1×	`flip--_binary64_2099` `flip3--_binary64_2128` `cancel-sign-sub-inv_binary64_2090` `rem-log-exp_binary64_2165` `log-pow_binary64_2213` `diff-log_binary64_2216` `associate-+r+_binary64_2056` `sub-neg_binary64_2117`

Counts

4 → 58

Calls

4 calls:

8.0ms	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))) (*.f64 x y))
6.0ms	(+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))
5.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
4.0ms	(+.f64 2 (.f64 x (.f64 x 1/2)))

series193.0ms (5%)

Counts

4 → 12

Calls

4 calls:

77.0ms	(-.f64 (log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))) (*.f64 x y))
64.0ms	(+.f64 2 (.f64 x (.f64 x 1/2)))
34.0ms	(log.f64 (+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2)))))
18.0ms	(+.f64 x (+.f64 2 (.f64 x (.f64 x 1/2))))

simplify69.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4886	1461
1	4886	1461

prune77.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	67	3	70
Fresh	1	1	2
Picked	1	0	1
Done	0	2	2
Total	69	6	75

Merged error: 0.7b

Counts

75 → 6

Compiler

Compiled 1493 to 950 computations (36.4% saved)

regimes92.0ms (2.4%)

Compiler: Compiled 850 to 687 computations (19.2% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	62	35
1	62	35

end0.0ms (0%)

sample1.1s (27.8%)

Algorithm

1×

intervals

Results

379.0ms	7366×	body	128	valid
89.0ms	206×	body	1024	valid
60.0ms	258×	body	512	valid
22.0ms	168×	body	256	valid
3.0ms	51×	body	128	invalid
3.0ms	2×	body	2048	valid
0.0ms	11×	body	128	overflowed

Compiler

Compiled 334 to 269 computations (19.5% saved)

Details

analyze67.0ms (1.7%)

sample26.0ms (0.7%)

simplify173.0ms (4.5%)

prune2.0ms (0.1%)

localize8.0ms (0.2%)

rewrite20.0ms (0.5%)

series163.0ms (4.2%)

simplify64.0ms (1.7%)

prune53.0ms (1.4%)

localize16.0ms (0.4%)

rewrite59.0ms (1.5%)

series938.0ms (24.3%)

simplify87.0ms (2.3%)

prune137.0ms (3.6%)

localize10.0ms (0.3%)

rewrite26.0ms (0.7%)

series287.0ms (7.4%)

simplify75.0ms (2%)

prune99.0ms (2.6%)

localize12.0ms (0.3%)

rewrite29.0ms (0.8%)

series193.0ms (5%)

simplify69.0ms (1.8%)

prune77.0ms (2%)

regimes92.0ms (2.4%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.1s (27.8%)

Profiling