Details

analyze9.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	50%	50%	3
12.5%	25%	62.5%	4
18.7%	12.5%	68.8%	5
21.9%	6.2%	71.9%	6
23.4%	3.1%	73.5%	7
24.2%	1.6%	74.2%	8
24.6%	0.8%	74.6%	9
24.8%	0.4%	74.8%	10
24.9%	0.2%	74.9%	11
24.9%	0.1%	75%	12
25%	0%	75%	13
25%	0%	75%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample34.0ms (0.7%)

Algorithm

1×

intervals

Results

25.0ms	256×	body	128	valid
0.0ms	1×	body	128	nan

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify479.0ms (9.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (189.0ms)

Iter	Nodes	Cost
0	5574	20

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: 0.0b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize19.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
0.0b	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.0b	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))

rewrite150.0ms (2.9%)

Algorithm

1×	rewrite-expression-head

Rules

66×	`*-un-lft-identity_binary64_751`
50×	`times-frac_binary64_757`
43×	`add-sqr-sqrt_binary64_772`
31×	`add-cube-cbrt_binary64_783` `sqrt-prod_binary64_766`
16×	`distribute-lft-out_binary64_704`
15×	`log-prod_binary64_834`
13×	`div-inv_binary64_748`
10×	`difference-of-squares_binary64_720`
8×	`associate-/l*_binary64_698`
7×	`add-exp-log_binary64_786`
6×	`pow1_binary64_809` `add-log-exp_binary64_787` `add-cbrt-cube_binary64_784` `distribute-rgt-out_binary64_706`
4×	`sqrt-div_binary64_767`
3×	`log-div_binary64_835` `associate-/r*_binary64_697`
2×	`flip3-+_binary64_754` `associate-/l/_binary64_700` `distribute-rgt1-in_binary64_709` `flip--_binary64_726` `frac-add_binary64_759` `flip3--_binary64_755` `flip-+_binary64_725`
1×	`+-commutative_binary64_683` `rem-log-exp_binary64_789` `rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `log-pow_binary64_837` `cbrt-undiv_binary64_782` `sum-log_binary64_839` `frac-2neg_binary64_762` `clear-num_binary64_750` `sqrt-pow1_binary64_768` `div-exp_binary64_799`

Counts

4 → 117

Calls

4 calls:

50.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
49.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
14.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
7.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series573.0ms (11%)

Counts

4 → 12

Calls

4 calls:

198.0ms	(log.f64 (+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)))
177.0ms	(/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x)
112.0ms	(+.f64 (/.f64 1 x) (/.f64 (sqrt.f64 (-.f64 1 (*.f64 x x))) x))
86.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

simplify147.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

129 → 129

Iterations

Useful iterations: 0 (90.0ms)

Iter	Nodes	Cost
0	4851	2712
1	4851	2712

prune261.0ms (5%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	127	2	129
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	128	2	130

Merged error: 0b

Counts

130 → 2

Compiler

Compiled 2588 to 1669 computations (35.5% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)

rewrite34.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_779`
23×	`add-sqr-sqrt_binary64_772`
15×	`add-cube-cbrt_binary64_783` `*-un-lft-identity_binary64_751`
11×	`pow1_binary64_809`
9×	`pow1/3_binary64_830`
6×	`swap-sqr_binary64_718` `associate-l_binary64_694` `add-exp-log_binary64_786` `associate-r_binary64_693`
4×	`unswap-sqr_binary64_719` `add-log-exp_binary64_787` `add-cbrt-cube_binary64_784`
2×	`pow-sqr_binary64_724` `pow-prod-up_binary64_818` `pow-prod-down_binary64_819`
1×	`prod-exp_binary64_797` `pow-plus_binary64_811` `*-commutative_binary64_684` `cbrt-unprod_binary64_781` `pow2_binary64_829`

Counts

4 → 73

Calls

4 calls:

13.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
2.0ms	(cbrt.f64 x)
2.0ms	(cbrt.f64 x)
2.0ms	(cbrt.f64 x)

series1.3s (25.7%)

Counts

4 → 12

Calls

4 calls:

370.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
323.0ms	(cbrt.f64 x)
323.0ms	(cbrt.f64 x)
317.0ms	(cbrt.f64 x)

simplify130.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

85 → 85

Iterations

Useful iterations: 0 (104.0ms)

Iter	Nodes	Cost
0	4957	563
1	4957	563

prune179.0ms (3.4%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	85	0	85
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	85	2	87

Merged error: 0b

Counts

87 → 2

Compiler

Compiled 1937 to 1006 computations (48.1% saved)

localize23.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
0.0b	(sqrt.f64 (-.f64 1 (*.f64 x x)))
0.2b	(+.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (neg.f64 (log.f64 x)))

rewrite57.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_751`
10×	`distribute-lft-out_binary64_704` `add-sqr-sqrt_binary64_772`
9×	`pow1_binary64_809`
8×	`log-prod_binary64_834`
7×	`sqrt-prod_binary64_766`
6×	`add-cube-cbrt_binary64_783` `add-log-exp_binary64_787`
5×	`associate-+l+_binary64_686` `log-pow_binary64_837`
4×	`distribute-rgt-neg-in_binary64_711`
3×	`flip3-+_binary64_754` `add-cbrt-cube_binary64_784` `sum-log_binary64_839` `add-exp-log_binary64_786` `associate-+r+_binary64_685` `distribute-neg-in_binary64_714` `flip-+_binary64_725`
2×	`log-div_binary64_835` `+-commutative_binary64_683` `associate-+l-_binary64_688` `sqrt-div_binary64_767` `difference-of-squares_binary64_720`
1×	`rem-sqrt-square_binary64_764` `pow1/2_binary64_828` `unsub-neg_binary64_745` `flip--_binary64_726` `associate-+r-_binary64_687` `neg-log_binary64_841` `sqrt-pow1_binary64_768` `neg-sub0_binary64_746` `flip3--_binary64_755`

Counts

3 → 60

Calls

3 calls:

26.0ms	(+.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (neg.f64 (log.f64 x)))
13.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))
7.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))

series347.0ms (6.7%)

Counts

3 → 9

Calls

3 calls:

205.0ms	(+.f64 (log.f64 (+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))) (neg.f64 (log.f64 x)))
84.0ms	(sqrt.f64 (-.f64 1 (*.f64 x x)))
58.0ms	(+.f64 1 (sqrt.f64 (-.f64 1 (*.f64 x x))))

simplify126.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

69 → 69

Iterations

Useful iterations: 0 (96.0ms)

Iter	Nodes	Cost
0	4951	1291
1	4951	1291

prune130.0ms (2.5%)

Pruning

2 alts after pruning (0 fresh and 2 done)

	Pruned	Kept	Total
New	69	0	69
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	69	2	71

Merged error: 0b

Counts

71 → 2

Compiler

Compiled 1305 to 827 computations (36.6% saved)

regimes18.0ms (0.3%)

Compiler: Compiled 35 to 26 computations (25.7% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	32	32
1	32	32

end0.0ms (0%)

sample1.1s (21.3%)

Algorithm

1×

intervals

Results

769.0ms	8000×	body	128	valid
0.0ms	5×	body	128	nan

Compiler

Compiled 67 to 49 computations (26.9% saved)

Details

analyze9.0ms (0.2%)

sample34.0ms (0.7%)

simplify479.0ms (9.2%)

prune4.0ms (0.1%)

localize19.0ms (0.4%)

rewrite150.0ms (2.9%)

series573.0ms (11%)

simplify147.0ms (2.8%)

prune261.0ms (5%)

localize27.0ms (0.5%)

rewrite34.0ms (0.7%)

series1.3s (25.7%)

simplify130.0ms (2.5%)

prune179.0ms (3.4%)

localize23.0ms (0.4%)

rewrite57.0ms (1.1%)

series347.0ms (6.7%)

simplify126.0ms (2.4%)

prune130.0ms (2.5%)

regimes18.0ms (0.3%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.1s (21.3%)

Profiling