Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample25.0ms (0.7%)

Algorithm

1×

intervals

Results

8.0ms	56×	body	1280	valid
5.0ms	140×	body	80	valid
4.0ms	33×	body	640	valid
2.0ms	17×	body	320	valid
1.0ms	10×	body	160	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify117.0ms (3.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (98.0ms)

Iter	Nodes	Cost
0	682	19
1	682	19

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: 27.2b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize6.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.1b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite67.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
20×	`distribute-lft-out_binary64`
18×	`distribute-lft-out--_binary64`
14×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64` `difference-of-sqr-1_binary64`
4×	`associate-/r/_binary64`
3×	`pow1_binary64` `insert-posit16`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `frac-sub_binary64`

Counts

3 → 116

Calls

3 calls:

44.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
10.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))

series137.0ms (4.1%)

Counts

3 → 9

Calls

3 calls:

82.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
28.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
27.0ms	(/.f64 x (+.f64 x 1))

simplify130.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (94.0ms)

Iter	Nodes	Cost
0	4944	2341
1	4944	2341

prune177.0ms (5.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	122	3	125
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	123	3	126

Merged error: 0.0b

Counts

126 → 3

Compiler

Compiled 2561 to 1829 computations (28.6% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
0.0b	(pow.f64 (/.f64 x (+.f64 x 1)) 3)
3.1b	(-.f64 (cbrt.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
22.1b	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3))

rewrite130.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

108×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
87×	`times-frac_binary64`
54×	`cbrt-prod_binary64`
51×	`add-cube-cbrt_binary64`
40×	`unpow-prod-down_binary64` `cube-prod_binary64`
24×	`difference-of-squares_binary64`
20×	`distribute-lft-out_binary64`
10×	`associate-/r/_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`associate-/r*_binary64`
6×	`add-log-exp_binary64` `distribute-lft-out--_binary64`
5×	`flip3-+_binary64` `pow1_binary64` `difference-of-sqr-1_binary64` `div-inv_binary64` `flip-+_binary64`
4×	`sqr-pow_binary64` `associate-/l*_binary64` `insert-posit16`
3×	`pow-unpow_binary64` `cube-div_binary64`
2×	`cbrt-div_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `rem-cube-cbrt_binary64` `div-exp_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `cube-mult_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `rem-cbrt-cube_binary64` `diff-log_binary64` `pow1/3_binary64` `pow-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-sub_binary64`

Counts

4 → 194

Calls

4 calls:

87.0ms	(-.f64 (cbrt.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
10.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
10.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3))
9.0ms	(pow.f64 (/.f64 x (+.f64 x 1)) 3)

series167.0ms (5%)

Counts

4 → 12

Calls

4 calls:

80.0ms	(-.f64 (cbrt.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
34.0ms	(cbrt.f64 (pow.f64 (/.f64 x (+.f64 x 1)) 3))
32.0ms	(pow.f64 (/.f64 x (+.f64 x 1)) 3)
22.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

simplify139.0ms (4.2%)

Algorithm

1×	egg-herbie

Counts

206 → 206

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5039	4042

prune271.0ms (8.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	206	3	209

Merged error: 0.0b

Counts

209 → 3

Compiler

Compiled 4661 to 3411 computations (26.8% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 1 (*.f64 x (+.f64 x 3)))
0.0b	(*.f64 x (+.f64 x 3))

rewrite13.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
4×	`add-log-exp_binary64` `pow1_binary64` `associate-r_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`associate-l_binary64`
2×	`flip3-+_binary64` `associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `insert-posit16` `flip-+_binary64` `associate-+r+_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `+-commutative_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 38

Calls

2 calls:

8.0ms	(*.f64 x (+.f64 x 3))
4.0ms	(+.f64 1 (*.f64 x (+.f64 x 3)))

series83.0ms (2.5%)

Counts

2 → 6

Calls

2 calls:

63.0ms	(*.f64 x (+.f64 x 3))
19.0ms	(+.f64 1 (*.f64 x (+.f64 x 3)))

simplify90.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

44 → 44

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	5056	473

prune30.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	44	0	44
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	44	3	47

Merged error: 0.0b

Counts

47 → 3

Compiler

Compiled 510 to 373 computations (26.9% saved)

localize11.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
0.1b	(/.f64 -1 (*.f64 x x))
0.2b	(/.f64 3 (pow.f64 x 3))
7.8b	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

rewrite98.0ms (3%)

Algorithm

1×	rewrite-expression-head

Rules

54×	`*-un-lft-identity_binary64` `times-frac_binary64`
39×	`add-sqr-sqrt_binary64`
35×	`add-cube-cbrt_binary64`
14×	`add-exp-log_binary64`
13×	`associate-/r*_binary64`
12×	`unpow-prod-down_binary64` `cube-prod_binary64`
11×	`add-log-exp_binary64` `add-cbrt-cube_binary64`
9×	`unpow3_binary64`
6×	`distribute-lft-out_binary64` `associate-/l*_binary64`
5×	`div-exp_binary64`
4×	`pow1_binary64` `distribute-rgt-out_binary64` `sqr-pow_binary64` `div-inv_binary64` `insert-posit16` `cube-mult_binary64`
3×	`cbrt-undiv_binary64` `frac-sub_binary64`
2×	`flip3-+_binary64` `diff-log_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip-+_binary64` `sum-log_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `associate--r+_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `distribute-rgt1-in_binary64` `prod-exp_binary64` `+-commutative_binary64` `flip--_binary64` `pow-exp_binary64`

Counts

4 → 132

Calls

4 calls:

43.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))
36.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
7.0ms	(/.f64 3 (pow.f64 x 3))
6.0ms	(/.f64 -1 (*.f64 x x))

series220.0ms (6.6%)

Counts

4 → 12

Calls

4 calls:

104.0ms	(+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3)))
54.0ms	(/.f64 3 (pow.f64 x 3))
34.0ms	(/.f64 -1 (*.f64 x x))
27.0ms	(-.f64 (/.f64 -1 (*.f64 x x)) (+.f64 (/.f64 3 x) (/.f64 3 (pow.f64 x 3))))

simplify76.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

144 → 144

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5321	2304

prune165.0ms (5%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	142	2	144
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	142	5	147

Merged error: 0.0b

Counts

147 → 5

Compiler

Compiled 2970 to 2058 computations (30.7% saved)

regimes24.0ms (0.7%)

Compiler: Compiled 90 to 72 computations (20% saved)

bsearch216.0ms (6.5%)

Steps

Iters	Range		Point
8	35.58495201638691	1254642.8873960227	11876.322726290642
9	-44588592.991518244	-0.8112377315077776	-8626.574718385837

Compiler

Compiled 1 to 1 computations (0% saved)

simplify7.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	91	60
1	91	60

end0.0ms (0%)

sample895.0ms (27%)

Algorithm

1×

intervals

Results

255.0ms	1692×	body	1280	valid
161.0ms	1300×	body	640	valid
141.0ms	4109×	body	80	valid
55.0ms	617×	body	320	valid
18.0ms	282×	body	160	valid

Compiler

Compiled 142 to 113 computations (20.4% saved)

Details

analyze4.0ms (0.1%)

sample25.0ms (0.7%)

simplify117.0ms (3.5%)

prune2.0ms (0.1%)

localize6.0ms (0.2%)

rewrite67.0ms (2%)

series137.0ms (4.1%)

simplify130.0ms (3.9%)

prune177.0ms (5.3%)

localize9.0ms (0.3%)

rewrite130.0ms (3.9%)

series167.0ms (5%)

simplify139.0ms (4.2%)

prune271.0ms (8.2%)

localize4.0ms (0.1%)

rewrite13.0ms (0.4%)

series83.0ms (2.5%)

simplify90.0ms (2.7%)

prune30.0ms (0.9%)

localize11.0ms (0.3%)

rewrite98.0ms (3%)

series220.0ms (6.6%)

simplify76.0ms (2.3%)

prune165.0ms (5%)

regimes24.0ms (0.7%)

bsearch216.0ms (6.5%)

simplify7.0ms (0.2%)

end0.0ms (0%)

sample895.0ms (27%)

Profiling