Details

analyze262.0ms (4.6%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample72.0ms (1.3%)

Algorithm

1×

intervals

Results

36.0ms	76×	body	1280	valid
12.0ms	46×	body	640	valid
9.0ms	28×	body	2560	valid
4.0ms	26×	body	320	valid
3.0ms	67×	body	80	valid
1.0ms	13×	body	160	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify22.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	12	14
1	12	14

prune2.0ms (0%)

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: 53.2b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

1.4b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.3b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
14.5b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`*-un-lft-identity_binary64`
6×	`add-sqr-sqrt_binary64`
5×	`add-log-exp_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
4×	`log-prod_binary64` `add-exp-log_binary64`
3×	`flip3-+_binary64` `add-cbrt-cube_binary64` `insert-posit16` `sqrt-prod_binary64` `flip-+_binary64`
2×	`distribute-lft-out_binary64` `log-div_binary64` `sqrt-div_binary64`
1×	`pow1/2_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `sum-log_binary64`

Counts

3 → 45

Calls

3 calls:

8.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
8.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
6.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

series198.0ms (3.5%)

Counts

3 → 9

Calls

3 calls:

95.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
64.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
39.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

simplify160.0ms (2.8%)

Algorithm

1×	egg-herbie

Counts

54 → 54

Iterations

Useful iterations: 0 (138.0ms)

Iter	Nodes	Cost
0	5390	903

prune71.0ms (1.3%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	50	4	54
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	51	4	55

Merged error: 0.0b

Counts

55 → 4

Compiler

Compiled 845 to 559 computations (33.8% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.1b	(*.f64 3/40 (pow.f64 x 5))
0.1b	(*.f64 (pow.f64 x 3) 1/6)
18.8b	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-sqr-sqrt_binary64`
15×	`associate-l_binary64`
13×	`add-exp-log_binary64`
10×	`-un-lft-identity_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64`
8×	`add-log-exp_binary64` `unpow-prod-down_binary64`
7×	`add-cbrt-cube_binary64` `unswap-sqr_binary64`
6×	`prod-exp_binary64`
4×	`sqr-pow_binary64` `cube-prod_binary64`
3×	`pow1_binary64` `insert-posit16`
2×	`pow-to-exp_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `pow-exp_binary64` `*-commutative_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `flip--_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `cube-mult_binary64`

Counts

3 → 72

Calls

3 calls:

8.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
8.0ms	(*.f64 (pow.f64 x 3) 1/6)
7.0ms	(*.f64 3/40 (pow.f64 x 5))

series185.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

67.0ms	(*.f64 3/40 (pow.f64 x 5))
64.0ms	(-.f64 (+.f64 x (.f64 3/40 (pow.f64 x 5))) (.f64 (pow.f64 x 3) 1/6))
54.0ms	(*.f64 (pow.f64 x 3) 1/6)

simplify142.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

81 → 81

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4850	1038
1	4850	1038

prune89.0ms (1.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	81	4	85

Merged error: 0.0b

Counts

85 → 4

Compiler

Compiled 1482 to 1149 computations (22.5% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1/16 (pow.f64 x 5))
0.2b	(/.f64 1/8 (pow.f64 x 3))
10.5b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
19.9b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite122.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Rules

72×	`add-sqr-sqrt_binary64`
71×	`times-frac_binary64`
68×	`*-un-lft-identity_binary64`
46×	`add-cube-cbrt_binary64`
26×	`unpow-prod-down_binary64`
19×	`associate-/r*_binary64`
15×	`add-exp-log_binary64`
14×	`cube-prod_binary64`
11×	`log-prod_binary64`
10×	`sqr-pow_binary64` `difference-of-squares_binary64`
9×	`add-log-exp_binary64`
8×	`add-cbrt-cube_binary64`
6×	`associate-/l*_binary64` `distribute-lft-out--_binary64` `div-exp_binary64` `frac-sub_binary64`
5×	`pow1_binary64` `log-div_binary64`
4×	`distribute-lft-out_binary64` `insert-posit16` `unpow3_binary64` `cube-mult_binary64`
2×	`pow-to-exp_binary64` `flip3-+_binary64` `flip3--_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `frac-add_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `flip--_binary64` `flip-+_binary64` `pow-exp_binary64`
1×	`sub-neg_binary64` `associate--r+_binary64` `rem-log-exp_binary64` `log-pow_binary64` `sum-log_binary64`

Counts

4 → 163

Calls

4 calls:

51.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
50.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
7.0ms	(/.f64 1/8 (pow.f64 x 3))
6.0ms	(/.f64 1/16 (pow.f64 x 5))

series242.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

74.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
62.0ms	(/.f64 1/16 (pow.f64 x 5))
53.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
52.0ms	(/.f64 1/8 (pow.f64 x 3))

simplify90.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4935	3673
1	4935	3673

prune276.0ms (4.9%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	174	1	175
Fresh	0	2	2
Picked	1	0	1
Done	0	1	1
Total	175	4	179

Merged error: 0b

Counts

179 → 4

Compiler

Compiled 4199 to 3344 computations (20.4% saved)

localize15.0ms (0.3%)

Local error

Found 4 expressions with local error:

2.9b	(sqrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
10.5b	(log.f64 (*.f64 (sqrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))) (sqrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))))
19.9b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
19.9b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite274.0ms (4.9%)

Algorithm

1×	rewrite-expression-head

Rules

65×	`sqrt-div_binary64`
45×	`add-sqr-sqrt_binary64` `frac-sub_binary64`
38×	`*-un-lft-identity_binary64`
35×	`log-div_binary64`
25×	`frac-times_binary64`
21×	`pow1_binary64` `times-frac_binary64`
15×	`flip3-+_binary64` `flip3--_binary64` `frac-add_binary64` `difference-of-squares_binary64` `flip--_binary64` `flip-+_binary64`
14×	`add-log-exp_binary64` `log-pow_binary64`
11×	`sqrt-prod_binary64`
9×	`pow1/2_binary64` `sqrt-pow1_binary64` `distribute-lft-out--_binary64`
7×	`add-exp-log_binary64`
6×	`distribute-lft-out_binary64`
5×	`pow-prod-up_binary64` `associate-r/_binary64` `add-cube-cbrt_binary64` `associate-l/_binary64`
4×	`diff-log_binary64` `add-cbrt-cube_binary64` `insert-posit16`
3×	`pow-prod-down_binary64` `sqr-pow_binary64` `unpow-prod-down_binary64` `cube-prod_binary64` `pow-sqr_binary64`
2×	`sub-neg_binary64` `associate--r+_binary64` `rem-log-exp_binary64` `sum-log_binary64`
1×	`log-prod_binary64` `pow-plus_binary64` `rem-sqrt-square_binary64` `prod-exp_binary64` `pow2_binary64`

Counts

4 → 137

Calls

4 calls:

108.0ms	(log.f64 (*.f64 (sqrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))) (sqrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))))
52.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
51.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
47.0ms	(sqrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))

series241.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

89.0ms	(log.f64 (*.f64 (sqrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))) (sqrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))))
57.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
52.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
43.0ms	(sqrt.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))

simplify116.0ms (2%)

Algorithm

1×	egg-herbie

Counts

149 → 149

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	4925	7930
1	4925	7930

prune537.0ms (9.5%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	149	0	149
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	149	4	153

Merged error: 0b

Counts

153 → 4

Compiler

Compiled 7326 to 5977 computations (18.4% saved)

regimes22.0ms (0.4%)

Compiler: Compiled 74 to 62 computations (16.2% saved)

bsearch46.0ms (0.8%)

Steps

Iters	Range		Point
9	0.0009110224086517436	4885.406804286417	0.9586315978757838
10	-39.70457242444396	-1.378587027312169e-10	-1.0563034297515377

Compiler

Compiled 1 to 1 computations (0% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	119	104
1	119	104

end0.0ms (0%)

sample2.4s (42.1%)

Algorithm

1×

intervals

Results

1.1s	2285×	body	1280	valid
419.0ms	1526×	body	640	valid
264.0ms	802×	body	2560	valid
139.0ms	822×	body	320	valid
95.0ms	2135×	body	80	valid
45.0ms	430×	body	160	valid

Compiler

Compiled 175 to 141 computations (19.4% saved)

Details

analyze262.0ms (4.6%)

sample72.0ms (1.3%)

simplify22.0ms (0.4%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite23.0ms (0.4%)

series198.0ms (3.5%)

simplify160.0ms (2.8%)

prune71.0ms (1.3%)

localize11.0ms (0.2%)

rewrite25.0ms (0.4%)

series185.0ms (3.3%)

simplify142.0ms (2.5%)

prune89.0ms (1.6%)

localize12.0ms (0.2%)

rewrite122.0ms (2.2%)

series242.0ms (4.3%)

simplify90.0ms (1.6%)

prune276.0ms (4.9%)

localize15.0ms (0.3%)

rewrite274.0ms (4.9%)

series241.0ms (4.3%)

simplify116.0ms (2%)

prune537.0ms (9.5%)

regimes22.0ms (0.4%)

bsearch46.0ms (0.8%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample2.4s (42.1%)

Profiling