Details

analyze9.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	25%	75%	0
0%	25%	75%	1
0%	12.5%	87.5%	2
0%	6.3%	93.7%	3
0%	3.1%	96.9%	4
0%	1.6%	98.4%	5
0%	0.8%	99.2%	6
0%	0.4%	99.6%	7
0%	0.2%	99.8%	8
0.1%	0.1%	99.8%	9
0.1%	0%	99.9%	10
0.1%	0%	99.9%	11
0.1%	0%	99.9%	12
0.1%	0%	99.9%	13
0.1%	0%	99.9%	14

Compiler

Compiled 106 to 71 computations (33% saved)

sample72.0ms (0.7%)

Algorithm

1×

intervals

Results

52.0ms	256×	body	80	valid
7.0ms	258×	pre	80	true
0.0ms	2×	body	80	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify241.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (226.0ms)

Iter	Nodes	Cost
0	4938	55
1	4938	55

prune10.0ms (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: 2.6b

Counts

2 → 2

Compiler

Compiled 171 to 121 computations (29.2% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.4b	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
2.6b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite96.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`*-un-lft-identity_binary64`
45×	`add-sqr-sqrt_binary64`
42×	`times-frac_binary64`
36×	`add-cube-cbrt_binary64`
25×	`sqrt-prod_binary64`
22×	`associate-l_binary64`
18×	`frac-add_binary64`
12×	`distribute-lft-out_binary64`
11×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`associate-r_binary64` `exp-prod_binary64`
7×	`pow1_binary64` `associate-*r/_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `flip-+_binary64`
5×	`add-log-exp_binary64`
4×	`insert-posit16`
3×	`unswap-sqr_binary64` `unpow-prod-down_binary64` `associate-/l*_binary64` `div-inv_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `unpow2_binary64` `sqr-pow_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `rem-exp-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 135

Calls

4 calls:

76.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
8.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
4.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))
1.0ms	(sqrt.f64 PI.f64)

series1.1s (11.2%)

Counts

4 → 10

Calls

4 calls:

910.0ms	(*.f64 (/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
153.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
67.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)

simplify159.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

145 → 145

Iterations

Useful iterations: 0 (99.0ms)

Iter	Nodes	Cost
0	5044	6171

prune495.0ms (4.9%)

Pruning

21 alts after pruning (21 fresh and 0 done)

	Pruned	Kept	Total
New	124	21	145
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	126	21	147

Merged error: 0.7b

Counts

147 → 21

Compiler

Compiled 8158 to 5381 computations (34% saved)

localize27.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
0.4b	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
1.2b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite103.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`times-frac_binary64`
86×	`*-un-lft-identity_binary64`
85×	`add-sqr-sqrt_binary64`
66×	`add-cube-cbrt_binary64`
51×	`sqrt-prod_binary64`
46×	`associate-l_binary64`
44×	`unpow-prod-down_binary64`
18×	`frac-add_binary64`
17×	`add-exp-log_binary64`
16×	`sqr-pow_binary64`
12×	`distribute-lft-out_binary64`
11×	`add-cbrt-cube_binary64`
8×	`pow1_binary64` `associate-r_binary64`
7×	`associate-r/_binary64` `unswap-sqr_binary64` `associate-/l_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `associate-/r*_binary64` `div-exp_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `prod-exp_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `div-inv_binary64` `pow-exp_binary64` `exp-prod_binary64`
2×	`cbrt-unprod_binary64` `cbrt-undiv_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 199

Calls

4 calls:

79.0ms	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
7.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 PI.f64)

series1.5s (15%)

Counts

4 → 10

Calls

4 calls:

1.0s	(*.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (/.f64 1 (fabs.f64 x)) (/.f64 1/2 (pow.f64 (fabs.f64 x) 3))) (/.f64 3/4 (pow.f64 (fabs.f64 x) 5))) (/.f64 15/8 (pow.f64 (fabs.f64 x) 7))))
270.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
202.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify153.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

209 → 209

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5482	9318

prune689.0ms (6.8%)

Pruning

28 alts after pruning (28 fresh and 0 done)

	Pruned	Kept	Total
New	189	20	209
Fresh	12	8	20
Picked	1	0	1
Done	0	0	0
Total	202	28	230

Merged error: 0.3b

Counts

230 → 28

Compiler

Compiled 11792 to 6947 computations (41.1% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.2b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`add-exp-log_binary64` `add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
9×	`add-cbrt-cube_binary64` `unpow-prod-down_binary64`
7×	`pow1_binary64` `associate-/l*_binary64` `times-frac_binary64`
6×	`div-exp_binary64` `sqrt-prod_binary64`
4×	`add-log-exp_binary64` `pow-pow_binary64` `insert-posit16`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `prod-exp_binary64` `pow-exp_binary64` `exp-prod_binary64`
2×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`associate-/r*_binary64` `cbrt-unprod_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 83

Calls

4 calls:

14.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series474.0ms (4.7%)

Counts

4 → 8

Calls

4 calls:

272.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (*.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (sqrt.f64 PI.f64))))
201.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify114.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5035	1194

prune259.0ms (2.6%)

Pruning

30 alts after pruning (29 fresh and 1 done)

	Pruned	Kept	Total
New	86	5	91
Fresh	3	24	27
Picked	0	1	1
Done	0	0	0
Total	89	30	119

Merged error: 0.3b

Counts

119 → 30

Compiler

Compiled 5476 to 3223 computations (41.1% saved)

localize36.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.7b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.7b	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`pow-unpow_binary64` `add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
18×	`times-frac_binary64`
8×	`pow1_binary64` `pow-pow_binary64`
6×	`unpow-prod-down_binary64` `sqrt-prod_binary64` `exp-prod_binary64`
4×	`add-log-exp_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
2×	`pow-to-exp_binary64` `pow1/2_binary64` `sqr-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `pow-exp_binary64`

Counts

4 → 90

Calls

4 calls:

6.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
6.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series453.0ms (4.5%)

Counts

4 → 8

Calls

4 calls:

226.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
226.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify134.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (107.0ms)

Iter	Nodes	Cost
0	4911	1274
1	4911	1274

prune252.0ms (2.5%)

Pruning

33 alts after pruning (31 fresh and 2 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	3	25	28
Picked	0	1	1
Done	0	1	1
Total	95	33	128

Merged error: 0.3b

Counts

128 → 33

Compiler

Compiled 5394 to 2994 computations (44.5% saved)

regimes278.0ms (2.8%)

Compiler: Compiled 3808 to 2500 computations (34.3% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	67
1	34	67

end0.0ms (0%)

sample3.3s (32.7%)

Algorithm

1×

intervals

Results

1.6s	8000×	body	80	valid
104.0ms	8127×	pre	80	true
26.0ms	127×	body	80	invalid

Compiler

Compiled 2047 to 1346 computations (34.2% saved)

Details

analyze9.0ms (0.1%)

sample72.0ms (0.7%)

simplify241.0ms (2.4%)

prune10.0ms (0.1%)

localize27.0ms (0.3%)

rewrite96.0ms (1%)

series1.1s (11.2%)

simplify159.0ms (1.6%)

prune495.0ms (4.9%)

localize27.0ms (0.3%)

rewrite103.0ms (1%)

series1.5s (15%)

simplify153.0ms (1.5%)

prune689.0ms (6.8%)

localize31.0ms (0.3%)

rewrite24.0ms (0.2%)

series474.0ms (4.7%)

simplify114.0ms (1.1%)

prune259.0ms (2.6%)

localize36.0ms (0.4%)

rewrite18.0ms (0.2%)

series453.0ms (4.5%)

simplify134.0ms (1.3%)

prune252.0ms (2.5%)

regimes278.0ms (2.8%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample3.3s (32.7%)

Profiling