Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample22.0ms (0.3%)

Algorithm

1×

intervals

Results

6.0ms	53×	body	1024	valid
5.0ms	146×	body	128	valid
3.0ms	34×	body	512	valid
1.0ms	18×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify169.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	681	19
1	681	19

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

Error

27.8b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
3.0b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite76.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

148×	`*-un-lft-identity_binary64_2806`
88×	`times-frac_binary64_2812`
85×	`add-sqr-sqrt_binary64_2828`
37×	`add-cube-cbrt_binary64_2841`
34×	`cancel-sign-sub-inv_binary64_2772`
27×	`distribute-lft-out_binary64_2757`
22×	`distribute-lft-out--_binary64_2758` `difference-of-squares_binary64_2775`
11×	`associate-/r*_binary64_2750`
9×	`difference-of-sqr-1_binary64_2776`
7×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `associate-/l*_binary64_2751`
6×	`associate-/r/_binary64_2752`
5×	`add-log-exp_binary64_2845`
3×	`div-inv_binary64_2803` `flip3--_binary64_2810` `flip--_binary64_2781` `pow1_binary64_2867`
2×	`associate-/l/_binary64_2753` `div-exp_binary64_2857` `cbrt-undiv_binary64_2840` `flip-+_binary64_2780` `flip3-+_binary64_2809` `clear-num_binary64_2805` `frac-2neg_binary64_2817`
1×	`diff-log_binary64_2898` `sub-neg_binary64_2799` `frac-sub_binary64_2815`

Counts

3 → 147

Calls

3 calls:

44.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
5.0ms	(/.f64 x (+.f64 x 1))

series128.0ms (1.6%)

Counts

3 → 36

Calls

3 calls:

61.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
34.0ms	(/.f64 x (+.f64 x 1))
33.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))

Compiler

Compiled 545 to 467 computations (14.3% saved)

simplify79.0ms (1%)

Algorithm

1×	egg-herbie

Counts

183 → 183

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	4960	3142
1	4960	3142

prune230.0ms (2.9%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	180	3	183
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	181	3	184

Error

0.0b

Counts

184 → 3

Compiler

Compiled 3425 to 2415 computations (29.5% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 (-.f64 x 1) (sqrt.f64 (+.f64 x 1))))
0.1b	(/.f64 (-.f64 x 1) (sqrt.f64 (+.f64 x 1)))
8.8b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 (-.f64 x 1) (sqrt.f64 (+.f64 x 1)))))

rewrite612.0ms (7.8%)

Algorithm

1×	rewrite-expression-head

Rules

1597×	`times-frac_binary64_2812`
1396×	`*-un-lft-identity_binary64_2806`
1097×	`add-sqr-sqrt_binary64_2828`
906×	`sqrt-prod_binary64_2822`
590×	`add-cube-cbrt_binary64_2841`
390×	`cancel-sign-sub-inv_binary64_2772`
240×	`difference-of-squares_binary64_2775`
229×	`distribute-lft-out_binary64_2757`
116×	`distribute-lft-out--_binary64_2758`
113×	`difference-of-sqr-1_binary64_2776`
66×	`associate-/r*_binary64_2750`
36×	`associate-/r/_binary64_2752`
34×	`sqrt-div_binary64_2823`
19×	`div-inv_binary64_2803`
18×	`flip-+_binary64_2780` `flip3-+_binary64_2809`
17×	`associate-/l*_binary64_2751`
13×	`add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842`
6×	`add-log-exp_binary64_2845`
5×	`div-exp_binary64_2857` `cbrt-undiv_binary64_2840`
4×	`associate-/l/_binary64_2753` `pow1_binary64_2867`
3×	`clear-num_binary64_2805` `frac-2neg_binary64_2817`
2×	`flip3--_binary64_2810` `flip--_binary64_2781`
1×	`div-sub_binary64_2811` `diff-log_binary64_2898` `sub-neg_binary64_2799` `frac-sub_binary64_2815`

Counts

4 → 996

Calls

4 calls:

372.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 (-.f64 x 1) (sqrt.f64 (+.f64 x 1)))))
33.0ms	(/.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 (-.f64 x 1) (sqrt.f64 (+.f64 x 1))))
11.0ms	(/.f64 (-.f64 x 1) (sqrt.f64 (+.f64 x 1)))
6.0ms	(/.f64 x (+.f64 x 1))

series154.0ms (1.9%)

Counts

4 → 38

Calls

4 calls:

62.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 (-.f64 x 1) (sqrt.f64 (+.f64 x 1)))))
34.0ms	(/.f64 (sqrt.f64 (+.f64 x 1)) (/.f64 (-.f64 x 1) (sqrt.f64 (+.f64 x 1))))
32.0ms	(/.f64 (-.f64 x 1) (sqrt.f64 (+.f64 x 1)))
25.0ms	(/.f64 x (+.f64 x 1))

Compiler

Compiled 701 to 593 computations (15.4% saved)

simplify356.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

1034 → 1034

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	5443	38383

prune3.6s (45.3%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	1034	0	1034
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	1034	3	1037

Error

0.0b

Counts

1037 → 3

Compiler

Compiled 32193 to 24367 computations (24.3% saved)

localize4.0ms (0.1%)

Local error

Found 1 expressions with local error:

0.0b	(*.f64 x (+.f64 3 x))

rewrite8.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-sqr-sqrt_binary64_2828` `*-un-lft-identity_binary64_2806`
4×	`associate-r_binary64_2746`
3×	`associate-l_binary64_2747` `add-exp-log_binary64_2844` `add-cbrt-cube_binary64_2842` `add-cube-cbrt_binary64_2841` `pow1_binary64_2867`
2×	`associate-*r/_binary64_2748`
1×	`distribute-lft-out_binary64_2757` `*-commutative_binary64_2737` `distribute-lft-in_binary64_2755` `distribute-rgt-in_binary64_2756` `prod-exp_binary64_2855` `cbrt-unprod_binary64_2839` `flip-+_binary64_2780` `add-log-exp_binary64_2845` `flip3-+_binary64_2809` `pow-prod-down_binary64_2877` `unswap-sqr_binary64_2774`

Counts

1 → 23

Calls

1 calls:

7.0ms

(*.f64 x (+.f64 3 x))

series33.0ms (0.4%)

Counts

1 → 6

Calls

1 calls:

33.0ms

(*.f64 x (+.f64 3 x))

Compiler

Compiled 69 to 63 computations (8.7% saved)

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

29 → 29

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4803	245
1	4803	245

prune21.0ms (0.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	29	0	29
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	29	3	32

Error

0.0b

Counts

32 → 3

Compiler

Compiled 323 to 232 computations (28.2% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 1 (pow.f64 x 4))
0.1b	(/.f64 1 (*.f64 x x))
0.3b	(/.f64 3 (pow.f64 x 3))
9.4b	(+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4)))

rewrite88.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

62×	`times-frac_binary64_2812`
54×	`*-un-lft-identity_binary64_2806`
47×	`add-sqr-sqrt_binary64_2828` `add-cube-cbrt_binary64_2841`
29×	`add-exp-log_binary64_2844`
24×	`unpow-prod-down_binary64_2885`
20×	`associate-/r*_binary64_2750`
13×	`div-exp_binary64_2857` `add-cbrt-cube_binary64_2842`
12×	`cube-prod_binary64_2834` `pow1_binary64_2867`
9×	`associate-/l*_binary64_2751`
8×	`sqr-pow_binary64_2778`
7×	`pow-flip_binary64_2880`
6×	`add-log-exp_binary64_2845`
5×	`1-exp_binary64_2850` `rec-exp_binary64_2856`
4×	`pow-exp_binary64_2874` `div-inv_binary64_2803` `cbrt-undiv_binary64_2840` `unpow3_binary64_2872` `pow-to-exp_binary64_2875` `cube-mult_binary64_2836`
3×	`distribute-lft-out_binary64_2757` `prod-exp_binary64_2855` `clear-num_binary64_2805` `frac-2neg_binary64_2817`
2×	`inv-pow_binary64_2891`
1×	`pow-sqr_binary64_2779` `pow-prod-up_binary64_2876` `cbrt-unprod_binary64_2839` `flip-+_binary64_2780` `sum-log_binary64_2897` `frac-add_binary64_2814` `flip3-+_binary64_2809` `pow2_binary64_2887` `pow-prod-down_binary64_2877` `pow-plus_binary64_2869` `+-commutative_binary64_2736`

Counts

4 → 165

Calls

4 calls:

57.0ms	(+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4)))
6.0ms	(/.f64 3 (pow.f64 x 3))
6.0ms	(/.f64 1 (*.f64 x x))
5.0ms	(/.f64 1 (pow.f64 x 4))

series155.0ms (2%)

Counts

4 → 15

Calls

4 calls:

67.0ms	(+.f64 (/.f64 3 (pow.f64 x 3)) (/.f64 1 (pow.f64 x 4)))
36.0ms	(/.f64 3 (pow.f64 x 3))
30.0ms	(/.f64 1 (pow.f64 x 4))
22.0ms	(/.f64 1 (*.f64 x x))

Compiler

Compiled 561 to 462 computations (17.6% saved)

simplify72.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

180 → 180

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5123	2048

prune264.0ms (3.3%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	179	1	180
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	179	4	183

Error

0.0b

Counts

183 → 4

Compiler

Compiled 4498 to 3234 computations (28.1% saved)

regimes212.0ms (2.7%)

Accuracy

Total 0.2b remaining (92.1%)

Threshold costs 0.2b (92.1%)

Compiler

Compiled 2071 to 1606 computations (22.5% saved)

bsearch3.0ms (0%)

Compiler: Compiled 13 to 10 computations (23.1% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (3.0ms)

Iter	Nodes	Cost
0	160	84
1	160	84

end0.0ms (0%)

sample1.5s (19.3%)

Algorithm

1×

intervals

Results

241.0ms	1987×	body	1024	valid
138.0ms	4352×	body	128	valid
85.0ms	967×	body	512	valid
37.0ms	221×	body	2048	valid
29.0ms	473×	body	256	valid

Compiler

Compiled 1012 to 785 computations (22.4% saved)

Details

analyze4.0ms (0.1%)

sample22.0ms (0.3%)

simplify169.0ms (2.1%)

prune2.0ms (0%)

localize6.0ms (0.1%)

rewrite76.0ms (1%)

series128.0ms (1.6%)

simplify79.0ms (1%)

prune230.0ms (2.9%)

localize11.0ms (0.1%)

rewrite612.0ms (7.8%)

series154.0ms (1.9%)

simplify356.0ms (4.5%)

prune3.6s (45.3%)

localize4.0ms (0.1%)

rewrite8.0ms (0.1%)

series33.0ms (0.4%)

simplify68.0ms (0.9%)

prune21.0ms (0.3%)

localize13.0ms (0.2%)

rewrite88.0ms (1.1%)

series155.0ms (2%)

simplify72.0ms (0.9%)

prune264.0ms (3.3%)

regimes212.0ms (2.7%)

bsearch3.0ms (0%)

simplify5.0ms (0.1%)

end0.0ms (0%)

sample1.5s (19.3%)

Profiling