Details

analyze11.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
62.5%	25%	12.5%	4
68.7%	12.5%	18.8%	5
71.8%	6.2%	21.9%	6
73.4%	3.1%	23.5%	7
74.2%	1.6%	24.3%	8
74.6%	0.8%	24.6%	9
75%	0.4%	24.6%	10
75.1%	0.2%	24.7%	11
75.1%	0.1%	24.8%	12
75.1%	0%	24.8%	13
75.2%	0%	24.8%	14

Compiler

Compiled 7 to 6 computations (14.3% saved)

sample52.0ms (1.1%)

Algorithm

1×

intervals

Results

25.0ms	82×	body	1024	valid
5.0ms	33×	body	512	valid
5.0ms	108×	body	128	valid
4.0ms	11×	body	2048	valid
2.0ms	22×	body	256	valid

Compiler

Compiled 13 to 12 computations (7.7% saved)

simplify145.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	168	9
1	168	9

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

Error

38.3b

Counts

2 → 1

Compiler

Compiled 12 to 10 computations (16.7% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

4.7b	(-.f64 (exp.f64 x) 1)
0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
0.0b	(/.f64 (-.f64 (exp.f64 x) 1) x)
4.7b	(-.f64 (exp.f64 x) 1)

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_2146`
30×	`*-un-lft-identity_binary64_2124`
21×	`times-frac_binary64_2130`
15×	`add-cube-cbrt_binary64_2159`
10×	`difference-of-squares_binary64_2093`
7×	`associate-/l*_binary64_2069`
5×	`distribute-lft-out--_binary64_2076` `difference-of-sqr-1_binary64_2094`
4×	`add-log-exp_binary64_2163` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`cancel-sign-sub-inv_binary64_2090` `associate-/r*_binary64_2068`
2×	`flip--_binary64_2099` `flip3--_binary64_2128` `pow1_binary64_2185` `associate-/l/_binary64_2071`
1×	`clear-num_binary64_2123` `cbrt-undiv_binary64_2158` `diff-log_binary64_2216` `sub-neg_binary64_2117` `div-sub_binary64_2129` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

2 → 64

Calls

4 calls:

15.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
10.0ms	(-.f64 (exp.f64 x) 1)
0.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
0.0ms	(-.f64 (exp.f64 x) 1)

series65.0ms (1.4%)

Counts

2 → 12

Calls

2 calls:

36.0ms	(/.f64 (-.f64 (exp.f64 x) 1) x)
29.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 134 to 114 computations (14.9% saved)

simplify97.0ms (2%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (82.0ms)

Iter	Nodes	Cost
0	4961	1076
1	4961	1076

prune112.0ms (2.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	73	3	76
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	3	77

Error

0.0b

Counts

77 → 3

Compiler

Compiled 942 to 520 computations (44.8% saved)

localize10.0ms (0.2%)

Local error

Found 8 expressions with local error:

0.0b	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
0.0b	(+.f64 1/6 (*.f64 x 1/24))
0.0b	(+.f64 1 (.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24))))))
0.0b	(+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24))))
0.0b	(+.f64 1/6 (*.f64 x 1/24))
0.0b	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
0.3b	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
0.4b	(*.f64 x 1/24)

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64_2146`
10×	`pow1_binary64_2185` `add-cube-cbrt_binary64_2159` `add-exp-log_binary64_2162` `*-un-lft-identity_binary64_2124` `add-cbrt-cube_binary64_2160`
9×	`associate-l_binary64_2065` `associate-r_binary64_2064`
6×	`add-log-exp_binary64_2163`
4×	`associate-*r/_binary64_2066`
3×	`pow-prod-down_binary64_2195` `unswap-sqr_binary64_2092` `*-commutative_binary64_2055` `prod-exp_binary64_2173` `flip3-+_binary64_2127` `flip-+_binary64_2098` `cbrt-unprod_binary64_2157`
2×	`distribute-rgt-in_binary64_2074` `distribute-lft-in_binary64_2073`
1×	`sum-log_binary64_2215` `+-commutative_binary64_2054`

Counts

4 → 73

Calls

8 calls:

6.0ms	(*.f64 x 1/24)
6.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
5.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
3.0ms	(+.f64 1/6 (*.f64 x 1/24))
0.0ms	(+.f64 1/2 (.f64 x (+.f64 1/6 (.f64 x 1/24))))

series217.0ms (4.5%)

Counts

4 → 24

Calls

4 calls:

112.0ms	(.f64 x (+.f64 1/2 (.f64 x (+.f64 1/6 (*.f64 x 1/24)))))
55.0ms	(.f64 x (+.f64 1/6 (.f64 x 1/24)))
28.0ms	(+.f64 1/6 (*.f64 x 1/24))
21.0ms	(*.f64 x 1/24)

Compiler

Compiled 466 to 407 computations (12.7% saved)

simplify119.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	4884	1141
1	4884	1141

prune130.0ms (2.7%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	97	0	97
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	97	3	100

Error

0.0b

Counts

100 → 3

Compiler

Compiled 1678 to 1298 computations (22.6% saved)

localize8.0ms (0.2%)

Local error

Found 8 expressions with local error:

4.7b	(log.f64 (exp.f64 (-.f64 (exp.f64 x) 1)))
4.7b	(-.f64 (exp.f64 x) 1)
0.0b	(/.f64 (log.f64 (exp.f64 (-.f64 (exp.f64 x) 1))) x)
0.0b	(exp.f64 (-.f64 (exp.f64 x) 1))
0.0b	(/.f64 (log.f64 (exp.f64 (-.f64 (exp.f64 x) 1))) x)
0.0b	(exp.f64 (-.f64 (exp.f64 x) 1))
4.7b	(-.f64 (exp.f64 x) 1)
4.7b	(log.f64 (exp.f64 (-.f64 (exp.f64 x) 1)))

rewrite40.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

58×	`add-sqr-sqrt_binary64_2146`
51×	`*-un-lft-identity_binary64_2124`
42×	`exp-prod_binary64_2176`
40×	`log-pow_binary64_2213`
33×	`times-frac_binary64_2130`
30×	`add-cube-cbrt_binary64_2159`
14×	`difference-of-squares_binary64_2093`
11×	`associate-/l*_binary64_2069`
9×	`cancel-sign-sub-inv_binary64_2090` `pow1_binary64_2185` `add-log-exp_binary64_2163`
8×	`exp-sum_binary64_2170`
7×	`distribute-lft-out--_binary64_2076` `log-prod_binary64_2210` `difference-of-sqr-1_binary64_2094`
6×	`add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`exp-diff_binary64_2172` `associate-/r*_binary64_2068` `sub-neg_binary64_2117`
2×	`diff-log_binary64_2216` `rem-exp-log_binary64_2164` `log-div_binary64_2211`
1×	`flip--_binary64_2099` `clear-num_binary64_2123` `flip3--_binary64_2128` `cbrt-undiv_binary64_2158` `rem-log-exp_binary64_2165` `div-sub_binary64_2129` `div-inv_binary64_2121` `div-exp_binary64_2175` `frac-2neg_binary64_2135`

Counts

4 → 123

Calls

8 calls:

9.0ms	(/.f64 (log.f64 (exp.f64 (-.f64 (exp.f64 x) 1))) x)
8.0ms	(log.f64 (exp.f64 (-.f64 (exp.f64 x) 1)))
8.0ms	(exp.f64 (-.f64 (exp.f64 x) 1))
6.0ms	(-.f64 (exp.f64 x) 1)
0.0ms	(exp.f64 (-.f64 (exp.f64 x) 1))

series295.0ms (6.1%)

Counts

4 → 24

Calls

4 calls:

144.0ms	(/.f64 (log.f64 (exp.f64 (-.f64 (exp.f64 x) 1))) x)
95.0ms	(log.f64 (exp.f64 (-.f64 (exp.f64 x) 1)))
31.0ms	(exp.f64 (-.f64 (exp.f64 x) 1))
24.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 302 to 258 computations (14.6% saved)

simplify112.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

147 → 147

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	6074	1862

prune112.0ms (2.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	147	0	147
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	147	3	150

Error

0.0b

Counts

150 → 3

Compiler

Compiled 1786 to 1033 computations (42.2% saved)

localize25.0ms (0.5%)

Local error

Found 8 expressions with local error:

0.1b	(cbrt.f64 (-.f64 (exp.f64 x) 1))
0.1b	(cbrt.f64 (-.f64 (exp.f64 x) 1))
0.1b	(cbrt.f64 (-.f64 (exp.f64 x) 1))
0.0b	(*.f64 (cbrt.f64 (-.f64 (exp.f64 x) 1)) (cbrt.f64 (-.f64 (exp.f64 x) 1)))
0.6b	(cbrt.f64 x)
4.7b	(-.f64 (exp.f64 x) 1)
4.7b	(-.f64 (exp.f64 x) 1)
4.7b	(-.f64 (exp.f64 x) 1)

rewrite22.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64_2146`
17×	`*-un-lft-identity_binary64_2124`
10×	`add-log-exp_binary64_2163`
9×	`cancel-sign-sub-inv_binary64_2090`
8×	`add-cube-cbrt_binary64_2159`
6×	`difference-of-squares_binary64_2093`
4×	`pow1_binary64_2185` `add-exp-log_binary64_2162` `add-cbrt-cube_binary64_2160`
3×	`flip--_binary64_2099` `flip3--_binary64_2128` `distribute-lft-out--_binary64_2076` `diff-log_binary64_2216` `cbrt-prod_binary64_2155` `sub-neg_binary64_2117` `difference-of-sqr-1_binary64_2094`
1×	`pow1/3_binary64_2206`

Counts

4 → 65

Calls

8 calls:

6.0ms	(-.f64 (exp.f64 x) 1)
4.0ms	(-.f64 (exp.f64 x) 1)
4.0ms	(-.f64 (exp.f64 x) 1)
1.0ms	(cbrt.f64 x)
0.0ms	(*.f64 (cbrt.f64 (-.f64 (exp.f64 x) 1)) (cbrt.f64 (-.f64 (exp.f64 x) 1)))

series179.0ms (3.7%)

Counts

4 → 21

Calls

4 calls:

109.0ms	(cbrt.f64 x)
27.0ms	(-.f64 (exp.f64 x) 1)
22.0ms	(-.f64 (exp.f64 x) 1)
21.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 868 to 595 computations (31.5% saved)

simplify92.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	4883	777
1	4883	777

prune153.0ms (3.2%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	85	1	86
Fresh	0	0	0
Picked	1	0	1
Done	0	2	2
Total	86	3	89

Error

0.0b

Counts

89 → 3

Compiler

Compiled 2556 to 1337 computations (47.7% saved)

simplify9.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	128	445
1	128	445

regimes55.0ms (1.2%)

Accuracy

Total 0.2b remaining (90.1%)

Threshold costs 0.2b (90.1%)

Compiler

Compiled 287 to 215 computations (25.1% saved)

bsearch25.0ms (0.5%)

Steps

Iters	Range		Point
9	-2.392391663077377	-1.4530188996588901e-07	-0.0014603342715462273

Compiler

Compiled 1 to 1 computations (0% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	33	46
1	33	46

end0.0ms (0%)

sample2.6s (55.1%)

Algorithm

1×

intervals

Results

492.0ms	2665×	body	1024	valid
142.0ms	1301×	body	512	valid
92.0ms	3067×	body	128	valid
65.0ms	291×	body	2048	valid
46.0ms	676×	body	256	valid

Compiler

Compiled 944 to 705 computations (25.3% saved)

Pareto

-0.20611285286978465

Details

analyze11.0ms (0.2%)

sample52.0ms (1.1%)

simplify145.0ms (3%)

prune4.0ms (0.1%)

localize9.0ms (0.2%)

rewrite34.0ms (0.7%)

series65.0ms (1.4%)

simplify97.0ms (2%)

prune112.0ms (2.3%)

localize10.0ms (0.2%)

rewrite25.0ms (0.5%)

series217.0ms (4.5%)

simplify119.0ms (2.5%)

prune130.0ms (2.7%)

localize8.0ms (0.2%)

rewrite40.0ms (0.8%)

series295.0ms (6.1%)

simplify112.0ms (2.3%)

prune112.0ms (2.3%)

localize25.0ms (0.5%)

rewrite22.0ms (0.5%)

series179.0ms (3.7%)

simplify92.0ms (1.9%)

prune153.0ms (3.2%)

simplify9.0ms (0.2%)

regimes55.0ms (1.2%)

bsearch25.0ms (0.5%)

simplify2.0ms (0%)

end0.0ms (0%)

sample2.6s (55.1%)

Profiling