Details

analyze6.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	74.9%	25.1%	0
0%	74.9%	25.1%	1
37.5%	37.5%	25.1%	2
37.5%	18.7%	43.8%	3
46.8%	9.4%	43.8%	4
51.5%	4.7%	43.8%	5
51.5%	2.3%	46.1%	6
52.7%	1.2%	46.1%	7
53.3%	0.6%	46.1%	8
53.3%	0.3%	46.4%	9
53.4%	0.1%	46.4%	10
53.5%	0.1%	46.4%	11
53.5%	0%	46.5%	12
53.5%	0%	46.5%	13
53.5%	0%	46.5%	14

Compiler

Compiled 70 to 33 computations (52.9% saved)

sample39.0ms (0.7%)

Algorithm

1×

intervals

Results

27.0ms	256×	body	80	valid
3.0ms	256×	pre	80	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify212.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (197.0ms)

Iter	Nodes	Cost
0	5204	47

prune7.0ms (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 → 2

Compiler

Compiled 125 to 77 computations (38.4% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
0.1b	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
0.1b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite94.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`add-exp-log_binary64`
76×	`prod-exp_binary64`
75×	`add-cbrt-cube_binary64`
48×	`associate-l_binary64`
46×	`add-sqr-sqrt_binary64`
44×	`cbrt-unprod_binary64`
40×	`times-frac_binary64`
36×	`pow1_binary64`
35×	`*-un-lft-identity_binary64`
33×	`add-cube-cbrt_binary64`
22×	`pow-prod-down_binary64`
15×	`div-exp_binary64` `associate-*l/_binary64`
14×	`sqrt-prod_binary64`
12×	`frac-add_binary64`
9×	`cbrt-undiv_binary64`
6×	`flip3-+_binary64` `1-exp_binary64` `associate-*r/_binary64` `rec-exp_binary64` `flip-+_binary64` `frac-times_binary64`
5×	`associate-r_binary64` `unswap-sqr_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`div-inv_binary64` `*-commutative_binary64`
1×	`pow1/2_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`

Counts

4 → 173

Calls

4 calls:

33.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
32.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
17.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
2.0ms	(sqrt.f64 PI.f64)

series728.0ms (12.7%)

Counts

4 → 10

Calls

4 calls:

528.0ms	(.f64 (/.f64 1 (sqrt.f64 PI.f64)) (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 (/.f64 2 3) (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))) (.f64 (/.f64 1 21) (.f64 (.f64 (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))))
115.0ms	(.f64 (/.f64 1 5) (.f64 (.f64 (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)) (fabs.f64 x)))
84.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

simplify225.0ms (3.9%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (150.0ms)

Iter	Nodes	Cost
0	4898	5483
1	4898	5483

prune581.0ms (10.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	180	3	183
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	181	4	185

Merged error: 0b

Counts

185 → 4

Compiler

Compiled 11339 to 5263 computations (53.6% saved)

localize18.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
0.1b	(.f64 (+.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x)))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.1b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

rewrite51.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
42×	`associate-r_binary64`
24×	`*-un-lft-identity_binary64`
23×	`add-cube-cbrt_binary64`
21×	`add-exp-log_binary64`
16×	`sqrt-prod_binary64`
14×	`unswap-sqr_binary64`
12×	`add-cbrt-cube_binary64` `associate-l_binary64` `unpow-prod-down_binary64`
11×	`times-frac_binary64`
10×	`prod-exp_binary64`
6×	`pow1_binary64` `sqr-pow_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `cube-prod_binary64` `insert-posit16` `*-commutative_binary64`
3×	`pow-to-exp_binary64` `pow-exp_binary64` `sqrt-div_binary64`
2×	`flip3-+_binary64` `flip-+_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `associate-*r/_binary64` `div-inv_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 124

Calls

4 calls:

25.0ms	(.f64 (+.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x)))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
8.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
7.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
6.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))

series824.0ms (14.3%)

Counts

4 → 12

Calls

4 calls:

511.0ms	(.f64 (+.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (.f64 2 (fabs.f64 x)))) (*.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (/.f64 1 PI.f64)))
127.0ms	(*.f64 1/21 (pow.f64 (fabs.f64 x) 7))
108.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
77.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))

simplify152.0ms (2.6%)

Algorithm

1×	egg-herbie

Counts

136 → 136

Iterations

Useful iterations: 0 (109.0ms)

Iter	Nodes	Cost
0	5273	3601

prune327.0ms (5.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	135	1	136
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	136	4	140

Merged error: 0b

Counts

140 → 4

Compiler

Compiled 5408 to 3855 computations (28.7% saved)

localize22.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(/.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 2 (fabs.f64 x)))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.0b	(/.f64 1/21 (sqrt.f64 PI.f64))

rewrite27.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`add-sqr-sqrt_binary64`
36×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `times-frac_binary64`
30×	`sqrt-prod_binary64`
12×	`associate-/r*_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64` `associate-/l*_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
2×	`associate-/l/_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`flip3-+_binary64` `flip-+_binary64`

Counts

4 → 110

Calls

4 calls:

15.0ms	(/.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 2 (fabs.f64 x)))) (sqrt.f64 PI.f64))
5.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series337.0ms (5.9%)

Counts

4 → 6

Calls

4 calls:

336.0ms	(/.f64 (+.f64 (.f64 1/5 (pow.f64 (fabs.f64 x) 5)) (+.f64 (.f64 2/3 (pow.f64 (fabs.f64 x) 3)) (*.f64 2 (fabs.f64 x)))) (sqrt.f64 PI.f64))
0.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5014	3230

prune251.0ms (4.4%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	115	1	116
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	116	4	120

Merged error: 0b

Counts

120 → 4

Compiler

Compiled 4787 to 3008 computations (37.2% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

1.0b	(/.f64 1/21 (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
22×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
21×	`sqrt-prod_binary64`
18×	`times-frac_binary64`
7×	`pow1_binary64`
6×	`associate-/r*_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `associate-/l*_binary64`
1×	`cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 82

Calls

4 calls:

5.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)
2.0ms	(sqrt.f64 PI.f64)

series0.0ms (0%)

Counts

4 → 4

Calls

4 calls:

0.0ms	(sqrt.f64 PI.f64)
0.0ms	(/.f64 1/21 (sqrt.f64 PI.f64))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify208.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

86 → 86

Iterations

Useful iterations: 0 (182.0ms)

Iter	Nodes	Cost
0	4714	966
1	4714	966

prune167.0ms (2.9%)

Pruning

4 alts after pruning (0 fresh and 4 done)

	Pruned	Kept	Total
New	86	0	86
Fresh	0	0	0
Picked	0	1	1
Done	0	3	3
Total	86	4	90

Merged error: 0b

Counts

90 → 4

Compiler

Compiled 3538 to 2028 computations (42.7% saved)

regimes114.0ms (2%)

Compiler: Compiled 1229 to 708 computations (42.4% saved)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	36	50
1	36	50

end0.0ms (0%)

sample1.2s (20.7%)

Algorithm

1×

intervals

Results

766.0ms	8000×	body	80	valid
101.0ms	8001×	pre	80	true
0.0ms	1×	body	80	invalid

Compiler

Compiled 268 to 165 computations (38.4% saved)

Details

analyze6.0ms (0.1%)

sample39.0ms (0.7%)

simplify212.0ms (3.7%)

prune7.0ms (0.1%)

localize25.0ms (0.4%)

rewrite94.0ms (1.6%)

series728.0ms (12.7%)

simplify225.0ms (3.9%)

prune581.0ms (10.1%)

localize18.0ms (0.3%)

rewrite51.0ms (0.9%)

series824.0ms (14.3%)

simplify152.0ms (2.6%)

prune327.0ms (5.7%)

localize22.0ms (0.4%)

rewrite27.0ms (0.5%)

series337.0ms (5.9%)

simplify98.0ms (1.7%)

prune251.0ms (4.4%)

localize24.0ms (0.4%)

rewrite13.0ms (0.2%)

series0.0ms (0%)

simplify208.0ms (3.6%)

prune167.0ms (2.9%)

regimes114.0ms (2%)

bsearch0.0ms (0%)

simplify6.0ms (0.1%)

end0.0ms (0%)

sample1.2s (20.7%)

Profiling