Details

analyze653.0ms (9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample62.0ms (0.9%)

Algorithm

1×

intervals

Results

33.0ms	89×	body	1024	valid
7.0ms	38×	body	512	valid
5.0ms	100×	body	128	valid
4.0ms	8×	body	2048	valid
2.0ms	21×	body	256	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify305.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

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: 40.8b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.3b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.5b	(-.f64 (exp.f64 x) 1)

rewrite37.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64_772`
29×	`*-un-lft-identity_binary64_751`
21×	`times-frac_binary64_757`
14×	`add-cube-cbrt_binary64_783`
10×	`difference-of-squares_binary64_720`
7×	`associate-/r*_binary64_697`
5×	`distribute-lft-out--_binary64_705` `difference-of-sqr-1_binary64_721`
4×	`add-log-exp_binary64_787` `add-cbrt-cube_binary64_784`
3×	`add-exp-log_binary64_786` `associate-/l*_binary64_698`
2×	`pow1_binary64_809` `flip--_binary64_726` `associate-/r/_binary64_699` `flip3--_binary64_755`
1×	`div-inv_binary64_748` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `sub-neg_binary64_744` `div-exp_binary64_799`

Counts

2 → 60

Calls

2 calls:

17.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
10.0ms	(-.f64 (exp.f64 x) 1)

series176.0ms (2.4%)

Counts

2 → 6

Calls

2 calls:

139.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
37.0ms	(-.f64 (exp.f64 x) 1)

simplify92.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (61.0ms)

Iter	Nodes	Cost
0	4932	1126
1	4932	1126

prune125.0ms (1.7%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	62	4	66
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	63	4	67

Merged error: 0b

Counts

67 → 4

Compiler

Compiled 967 to 484 computations (49.9% saved)

localize12.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
0.3b	(*.f64 x 1/12)

rewrite32.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-log-exp_binary64_787`
6×	`add-sqr-sqrt_binary64_772`
4×	`add-cube-cbrt_binary64_783` `pow1_binary64_809` `add-cbrt-cube_binary64_784` `*-un-lft-identity_binary64_751` `add-exp-log_binary64_786`
3×	`sum-log_binary64_839` `associate-l_binary64_694` `associate-r_binary64_693`
1×	`prod-exp_binary64_797` `+-commutative_binary64_683` `unswap-sqr_binary64_719` `flip3-+_binary64_754` `pow-prod-down_binary64_819` `*-commutative_binary64_684` `associate-+r+_binary64_685` `cbrt-unprod_binary64_781` `flip-+_binary64_725`

Counts

2 → 31

Calls

2 calls:

21.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))
7.0ms	(*.f64 x 1/12)

series85.0ms (1.2%)

Counts

2 → 6

Calls

2 calls:

45.0ms	(*.f64 x 1/12)
40.0ms	(+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))

simplify140.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

37 → 37

Iterations

Useful iterations: 0 (121.0ms)

Iter	Nodes	Cost
0	4895	417
1	4895	417

prune62.0ms (0.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	37	0	37
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	37	4	41

Merged error: 0b

Counts

41 → 4

Compiler

Compiled 546 to 430 computations (21.2% saved)

localize10.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
3.8b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite33.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`*-un-lft-identity_binary64_751` `add-sqr-sqrt_binary64_772`
18×	`times-frac_binary64_757`
13×	`add-cube-cbrt_binary64_783`
10×	`difference-of-squares_binary64_720`
6×	`associate-/r*_binary64_697` `add-exp-log_binary64_786`
5×	`distribute-lft-out--_binary64_705`
4×	`add-log-exp_binary64_787` `add-cbrt-cube_binary64_784`
3×	`pow1_binary64_809` `associate-/l*_binary64_698`
2×	`flip--_binary64_726` `associate-/r/_binary64_699` `flip3--_binary64_755` `div-exp_binary64_799`
1×	`1-exp_binary64_792` `rec-exp_binary64_798` `inv-pow_binary64_833` `div-inv_binary64_748` `diff-log_binary64_840` `cbrt-undiv_binary64_782` `frac-2neg_binary64_762` `clear-num_binary64_750` `sub-neg_binary64_744` `pow-flip_binary64_822`

Counts

2 → 59

Calls

2 calls:

14.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
10.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

series174.0ms (2.4%)

Counts

2 → 6

Calls

2 calls:

130.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
44.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

simplify133.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	5267	1034

prune98.0ms (1.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	65	0	65
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	65	4	69

Merged error: 0b

Counts

69 → 4

Compiler

Compiled 886 to 562 computations (36.6% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(pow.f64 (exp.f64 x) 3)
0.2b	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
0.3b	(/.f64 (exp.f64 x) (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1)))))
3.5b	(-.f64 (pow.f64 (exp.f64 x) 3) 1)

rewrite220.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

402×	`times-frac_binary64_757`
385×	`add-sqr-sqrt_binary64_772`
266×	`*-un-lft-identity_binary64_751`
164×	`add-cube-cbrt_binary64_783`
136×	`difference-of-squares_binary64_720`
68×	`difference-of-sqr-1_binary64_721`
57×	`associate-/r*_binary64_697`
54×	`unpow-prod-down_binary64_827` `cube-prod_binary64_776`
52×	`sqr-pow_binary64_723`
19×	`associate-/l*_binary64_698`
17×	`distribute-lft-out--_binary64_705`
12×	`add-cbrt-cube_binary64_784`
11×	`associate-/r/_binary64_699`
9×	`add-exp-log_binary64_786`
6×	`add-log-exp_binary64_787` `div-inv_binary64_748`
5×	`flip3-+_binary64_754` `pow1_binary64_809` `flip-+_binary64_725`
4×	`pow-pow_binary64_820` `cbrt-undiv_binary64_782` `div-exp_binary64_799`
3×	`exp-prod_binary64_800` `pow-unpow_binary64_825`
2×	`associate-/l/_binary64_700` `flip--_binary64_726` `frac-2neg_binary64_762` `clear-num_binary64_750` `flip3--_binary64_755`
1×	`cube-mult_binary64_778` `pow-to-exp_binary64_817` `div-sub_binary64_756` `pow-exp_binary64_816` `rem-cube-cbrt_binary64_773` `diff-log_binary64_840` `unpow3_binary64_814` `sub-neg_binary64_744`

Counts

4 → 368

Calls

4 calls:

43.0ms	(/.f64 (exp.f64 x) (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1)))))
28.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
16.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) 1)
7.0ms	(pow.f64 (exp.f64 x) 3)

series942.0ms (13%)

Counts

4 → 12

Calls

4 calls:

418.0ms	(/.f64 (exp.f64 x) (/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1)))))
360.0ms	(/.f64 (-.f64 (pow.f64 (exp.f64 x) 3) 1) (+.f64 1 (*.f64 (exp.f64 x) (+.f64 (exp.f64 x) 1))))
95.0ms	(-.f64 (pow.f64 (exp.f64 x) 3) 1)
69.0ms	(pow.f64 (exp.f64 x) 3)

simplify393.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

380 → 380

Iterations

Useful iterations: 0 (131.0ms)

Iter	Nodes	Cost
0	4953	17546
1	4953	17546

prune1.5s (20.5%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	380	0	380
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	380	4	384

Merged error: 0b

Counts

384 → 4

Compiler

Compiled 13679 to 8252 computations (39.7% saved)

regimes97.0ms (1.3%)

Compiler: Compiled 252 to 181 computations (28.2% saved)

bsearch1.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	38	51
1	38	51

end0.0ms (0%)

sample1.9s (25.5%)

Algorithm

1×

intervals

Results

820.0ms	2702×	body	1024	valid
232.0ms	1302×	body	512	valid
155.0ms	3098×	body	128	valid
85.0ms	260×	body	2048	valid
73.0ms	638×	body	256	valid
1.0ms	2×	body	2048	invalid
0.0ms	2×	body	128	overflowed

Compiler

Compiled 109 to 81 computations (25.7% saved)

Details

analyze653.0ms (9%)

sample62.0ms (0.9%)

simplify305.0ms (4.2%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

rewrite37.0ms (0.5%)

series176.0ms (2.4%)

simplify92.0ms (1.3%)

prune125.0ms (1.7%)

localize12.0ms (0.2%)

rewrite32.0ms (0.4%)

series85.0ms (1.2%)

simplify140.0ms (1.9%)

prune62.0ms (0.9%)

localize10.0ms (0.1%)

rewrite33.0ms (0.5%)

series174.0ms (2.4%)

simplify133.0ms (1.8%)

prune98.0ms (1.4%)

localize20.0ms (0.3%)

rewrite220.0ms (3%)

series942.0ms (13%)

simplify393.0ms (5.4%)

prune1.5s (20.5%)

regimes97.0ms (1.3%)

bsearch1.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.9s (25.5%)

Profiling