Details

analyze8.0ms (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)

sample64.0ms (0.9%)

Algorithm

1×

intervals

Results

53.0ms	256×	body	80	valid
3.0ms	258×	pre	80	true
0.0ms	2×	body	80	invalid

Compiler

Compiled 209 to 141 computations (32.5% saved)

simplify157.0ms (2.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (144.0ms)

Iter	Nodes	Cost
0	5069	55

prune8.0ms (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)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
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))))
1.0b	(sqrt.f64 PI.f64)
2.5b	(exp.f64 (pow.f64 (fabs.f64 x) 2))

rewrite84.0ms (1.2%)

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`
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 → 131

Calls

4 calls:

67.0ms	(*.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))))
7.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
3.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))
1.0ms	(sqrt.f64 PI.f64)

series129.0ms (1.9%)

Counts

4 → 10

Calls

4 calls:

105.0ms	(*.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))))
16.0ms	(/.f64 (exp.f64 (pow.f64 (fabs.f64 x) 2)) (sqrt.f64 PI.f64))
8.0ms	(exp.f64 (pow.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)

simplify119.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

141 → 141

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	5618	6120

prune332.0ms (4.9%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	124	17	141
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	126	17	143

Merged error: 0.7b

Counts

143 → 17

Compiler

Compiled 7827 to 5153 computations (34.2% saved)

localize29.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
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))))
1.0b	(sqrt.f64 PI.f64)
1.0b	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))

rewrite89.0ms (1.3%)

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`
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 → 195

Calls

4 calls:

68.0ms	(*.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)

series172.0ms (2.5%)

Counts

4 → 10

Calls

4 calls:

117.0ms	(*.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))))
28.0ms	(/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (sqrt.f64 PI.f64))
27.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify125.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

205 → 205

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5477	9229

prune482.0ms (7.1%)

Pruning

29 alts after pruning (28 fresh and 1 done)

	Pruned	Kept	Total
New	185	20	205
Fresh	8	8	16
Picked	0	1	1
Done	0	0	0
Total	193	29	222

Merged error: 0.3b

Counts

222 → 29

Compiler

Compiled 11515 to 6765 computations (41.3% saved)

localize36.0ms (0.5%)

Local error

Found 4 expressions with local error:

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

rewrite84.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
23×	`add-exp-log_binary64`
22×	`add-sqr-sqrt_binary64`
18×	`frac-add_binary64`
14×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64` `add-cbrt-cube_binary64`
12×	`distribute-lft-out_binary64`
11×	`associate-l_binary64`
10×	`prod-exp_binary64`
9×	`pow1_binary64`
8×	`associate-r_binary64`
7×	`associate-*r/_binary64` `unpow-prod-down_binary64` `frac-times_binary64`
6×	`flip3-+_binary64` `div-exp_binary64` `sqrt-prod_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `pow-pow_binary64` `unswap-sqr_binary64`
3×	`pow-to-exp_binary64` `pow-unpow_binary64` `sqr-pow_binary64` `pow-exp_binary64` `exp-prod_binary64`
2×	`pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-l/_binary64` `-commutative_binary64`

Counts

4 → 105

Calls

4 calls:

72.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (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))))
4.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series146.0ms (2.1%)

Counts

4 → 8

Calls

4 calls:

123.0ms	(.f64 (/.f64 (pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x)) (.f64 (sqrt.f64 (sqrt.f64 PI.f64)) (sqrt.f64 (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))))
23.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify93.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5237	4979

prune252.0ms (3.7%)

Pruning

28 alts after pruning (26 fresh and 2 done)

	Pruned	Kept	Total
New	110	3	113
Fresh	4	23	27
Picked	0	1	1
Done	0	1	1
Total	114	28	142

Merged error: 0.2b

Counts

142 → 28

Compiler

Compiled 7181 to 4299 computations (40.1% saved)

localize33.0ms (0.5%)

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)

rewrite15.0ms (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`
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 → 86

Calls

4 calls:

5.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
5.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
2.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series52.0ms (0.8%)

Counts

4 → 8

Calls

4 calls:

27.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
25.0ms	(pow.f64 (exp.f64 (fabs.f64 x)) (/.f64 (fabs.f64 x) 2))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify73.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

94 → 94

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	4988	1266
1	4988	1266

prune154.0ms (2.3%)

Pruning

32 alts after pruning (29 fresh and 3 done)

	Pruned	Kept	Total
New	88	6	94
Fresh	2	23	25
Picked	0	1	1
Done	0	2	2
Total	90	32	122

Merged error: 0.2b

Counts

122 → 32

Compiler

Compiled 5172 to 2845 computations (45% saved)

regimes242.0ms (3.5%)

Compiler: Compiled 3466 to 2258 computations (34.9% saved)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	34	67
1	34	67

end0.0ms (0%)

sample3.8s (55.9%)

Algorithm

1×

intervals

Results

1.7s	8000×	body	80	valid
93.0ms	8117×	pre	80	true
24.0ms	117×	body	80	invalid

Compiler

Compiled 1876 to 1225 computations (34.7% saved)

Details

analyze8.0ms (0.1%)

sample64.0ms (0.9%)

simplify157.0ms (2.3%)

prune8.0ms (0.1%)

localize26.0ms (0.4%)

rewrite84.0ms (1.2%)

series129.0ms (1.9%)

simplify119.0ms (1.7%)

prune332.0ms (4.9%)

localize29.0ms (0.4%)

rewrite89.0ms (1.3%)

series172.0ms (2.5%)

simplify125.0ms (1.8%)

prune482.0ms (7.1%)

localize36.0ms (0.5%)

rewrite84.0ms (1.2%)

series146.0ms (2.1%)

simplify93.0ms (1.4%)

prune252.0ms (3.7%)

localize33.0ms (0.5%)

rewrite15.0ms (0.2%)

series52.0ms (0.8%)

simplify73.0ms (1.1%)

prune154.0ms (2.3%)

regimes242.0ms (3.5%)

bsearch0.0ms (0%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample3.8s (55.9%)

Profiling