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)

sample38.0ms (0.5%)

Algorithm

1×

intervals

Results

26.0ms	256×	body	128	valid
3.0ms	256×	pre	128	true

Compiler

Compiled 137 to 65 computations (52.6% saved)

simplify116.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (110.0ms)

Iter	Nodes	Cost
0	5202	47

prune6.0ms (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 (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.1b	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite52.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

52×	`pow1_binary64`
35×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
18×	`cbrt-unprod_binary64` `prod-exp_binary64`
17×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
14×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
12×	`pow-prod-down_binary64` `pow-prod-up_binary64` `pow-plus_binary64`
9×	`times-frac_binary64`
7×	`associate-r_binary64`
4×	`add-log-exp_binary64` `pow-sqr_binary64` `pow2_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64` `sqrt-prod_binary64` `*-commutative_binary64`
2×	`unswap-sqr_binary64` `pow3_binary64`
1×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `associate-*l/_binary64`

Counts

4 → 107

Calls

4 calls:

12.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
7.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
1.0ms	(sqrt.f64 PI.f64)

series157.0ms (2.1%)

Counts

4 → 10

Calls

4 calls:

65.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
47.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
45.0ms	(.f64 (.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x))
0.0ms	(sqrt.f64 PI.f64)

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4999	954
1	4999	954

prune291.0ms (3.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	116	3	119

Merged error: 0.0b

Counts

119 → 3

Compiler

Compiled 7808 to 3086 computations (60.5% saved)

localize34.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (pow.f64 (fabs.f64 x) 2) (sqrt.f64 (fabs.f64 x)))
0.2b	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
0.2b	(.f64 (.f64 (pow.f64 (fabs.f64 x) 2) (sqrt.f64 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
1.0b	(sqrt.f64 PI.f64)

rewrite56.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-exp-log_binary64`
32×	`add-cbrt-cube_binary64`
31×	`add-sqr-sqrt_binary64`
22×	`associate-l_binary64` `prod-exp_binary64`
21×	`pow1_binary64`
18×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`cbrt-unprod_binary64`
13×	`associate-r_binary64` `sqrt-prod_binary64`
10×	`pow-prod-up_binary64`
9×	`times-frac_binary64`
8×	`unswap-sqr_binary64`
7×	`pow-prod-down_binary64`
6×	`pow1/2_binary64` `sqrt-pow1_binary64`
5×	`unpow-prod-down_binary64`
4×	`add-log-exp_binary64`
3×	`unpow2_binary64` `cbrt-undiv_binary64` `sqr-pow_binary64` `div-exp_binary64` `*-commutative_binary64`
2×	`pow-to-exp_binary64` `pow-exp_binary64`
1×	`rem-sqrt-square_binary64` `div-inv_binary64` `associate-*l/_binary64`

Counts

4 → 113

Calls

4 calls:

13.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
10.0ms	(.f64 (.f64 (pow.f64 (fabs.f64 x) 2) (sqrt.f64 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
8.0ms	(*.f64 (pow.f64 (fabs.f64 x) 2) (sqrt.f64 (fabs.f64 x)))
1.0ms	(sqrt.f64 PI.f64)

series252.0ms (3.4%)

Counts

4 → 10

Calls

4 calls:

129.0ms	(*.f64 (pow.f64 (fabs.f64 x) 2) (sqrt.f64 (fabs.f64 x)))
70.0ms	(.f64 (/.f64 2 3) (.f64 (*.f64 (fabs.f64 x) (fabs.f64 x)) (fabs.f64 x)))
53.0ms	(.f64 (.f64 (pow.f64 (fabs.f64 x) 2) (sqrt.f64 (fabs.f64 x))) (sqrt.f64 (fabs.f64 x)))
0.0ms	(sqrt.f64 PI.f64)

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4870	1226
1	4870	1226

prune358.0ms (4.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

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

Merged error: 0.0b

Counts

126 → 3

Compiler

Compiled 8681 to 3832 computations (55.9% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
0.2b	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.3b	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 PI.f64))
1.0b	(sqrt.f64 PI.f64)

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`add-sqr-sqrt_binary64`
27×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
19×	`associate-r_binary64`
18×	`times-frac_binary64`
16×	`add-exp-log_binary64`
15×	`sqrt-prod_binary64`
10×	`add-cbrt-cube_binary64`
8×	`unpow-prod-down_binary64`
7×	`unswap-sqr_binary64`
6×	`associate-/r_binary64` `associate-l*_binary64` `prod-exp_binary64`
5×	`pow1_binary64`
4×	`add-log-exp_binary64` `sqr-pow_binary64` `cube-prod_binary64`
3×	`associate-/l*_binary64`
2×	`pow-to-exp_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`flip3-+_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` `flip-+_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 110

Calls

4 calls:

18.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 PI.f64))
7.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
6.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
1.0ms	(sqrt.f64 PI.f64)

series713.0ms (9.5%)

Counts

4 → 10

Calls

4 calls:

552.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 PI.f64))
96.0ms	(*.f64 1/5 (pow.f64 (fabs.f64 x) 5))
64.0ms	(*.f64 2/3 (pow.f64 (fabs.f64 x) 3))
0.0ms	(sqrt.f64 PI.f64)

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5574	3850

prune251.0ms (3.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	120	3	123

Merged error: 0b

Counts

123 → 3

Compiler

Compiled 4765 to 3153 computations (33.8% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (sqrt.f64 PI.f64)))
0.3b	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (sqrt.f64 PI.f64)))
1.0b	(sqrt.f64 PI.f64)
1.0b	(sqrt.f64 PI.f64)

rewrite154.0ms (2%)

Algorithm

1×	rewrite-expression-head

Rules

600×	`sqrt-prod_binary64`
576×	`times-frac_binary64`
316×	`add-sqr-sqrt_binary64`
314×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
34×	`associate-/l*_binary64`
18×	`associate-/r*_binary64`
12×	`div-inv_binary64`
11×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
6×	`pow1_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`associate-/l/_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `flip-+_binary64`

Counts

4 → 413

Calls

4 calls:

30.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (sqrt.f64 PI.f64)))
18.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (sqrt.f64 PI.f64)))
1.0ms	(sqrt.f64 PI.f64)
1.0ms	(sqrt.f64 PI.f64)

series1.2s (16.4%)

Counts

4 → 8

Calls

4 calls:

675.0ms	(/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (sqrt.f64 PI.f64)))
553.0ms	(/.f64 (/.f64 (+.f64 (+.f64 (+.f64 (.f64 2 (fabs.f64 x)) (.f64 2/3 (pow.f64 (fabs.f64 x) 3))) (.f64 1/5 (pow.f64 (fabs.f64 x) 5))) (.f64 1/21 (pow.f64 (fabs.f64 x) 7))) (sqrt.f64 (sqrt.f64 PI.f64))) (sqrt.f64 (sqrt.f64 PI.f64)))
0.0ms	(sqrt.f64 PI.f64)
0.0ms	(sqrt.f64 PI.f64)

simplify344.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

421 → 421

Iterations

Useful iterations: 0 (72.0ms)

Iter	Nodes	Cost
0	4964	37837
1	4964	37837

prune1.9s (25.8%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	421	0	421
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	421	3	424

Merged error: 0b

Counts

424 → 3

Compiler

Compiled 26139 to 15878 computations (39.3% saved)

regimes31.0ms (0.4%)

Compiler: Compiled 274 to 178 computations (35% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	52	108
1	52	108

end0.0ms (0%)

sample1.2s (15.4%)

Algorithm

1×

intervals

Results

755.0ms	8000×	body	128	valid
99.0ms	8000×	pre	128	true

Compiler

Compiled 269 to 152 computations (43.5% saved)

Details

analyze6.0ms (0.1%)

sample38.0ms (0.5%)

simplify116.0ms (1.5%)

prune6.0ms (0.1%)

localize25.0ms (0.3%)

rewrite52.0ms (0.7%)

series157.0ms (2.1%)

simplify68.0ms (0.9%)

prune291.0ms (3.9%)

localize34.0ms (0.5%)

rewrite56.0ms (0.7%)

series252.0ms (3.4%)

simplify82.0ms (1.1%)

prune358.0ms (4.8%)

localize18.0ms (0.2%)

rewrite47.0ms (0.6%)

series713.0ms (9.5%)

simplify70.0ms (0.9%)

prune251.0ms (3.3%)

localize19.0ms (0.3%)

rewrite154.0ms (2%)

series1.2s (16.4%)

simplify344.0ms (4.6%)

prune1.9s (25.8%)

regimes31.0ms (0.4%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample1.2s (15.4%)

Profiling