Details

analyze228.0ms (5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	87.4%	12.6%	6
20.3%	59.3%	20.4%	7
21.1%	51.5%	27.4%	8
35.5%	30.4%	34%	9
35.7%	26.1%	38.1%	10
42.8%	15.4%	41.8%	11
42.9%	13.2%	44%	12
46.4%	7.8%	45.8%	13
46.4%	6.6%	47%	14

Compiler

Compiled 30 to 26 computations (13.3% saved)

sample73.0ms (1.6%)

Algorithm

1×

intervals

Results

33.0ms	58×	body	1280	valid
15.0ms	45×	body	640	valid
9.0ms	118×	body	80	valid
5.0ms	23×	body	320	valid
2.0ms	12×	body	160	valid
1.0ms	9×	body	80	invalid
0.0ms	5×	body	80	overflowed
0.0ms	1×	body	640	invalid
0.0ms	1×	body	160	invalid

Compiler

Compiled 59 to 53 computations (10.2% saved)

simplify98.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5354	41

prune6.0ms (0.1%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 32.4b

Counts

2 → 1

Compiler

Compiled 56 to 48 computations (14.3% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 1 eps) x)
0.0b	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
0.0b	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
2.2b	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))

rewrite46.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

81×	`frac-sub_binary64`
74×	`exp-neg_binary64`
72×	`frac-times_binary64`
56×	`neg-sub0_binary64` `exp-diff_binary64`
38×	`associate-*l/_binary64`
36×	`associate-*r/_binary64`
28×	`flip3-+_binary64` `flip3--_binary64` `flip--_binary64` `flip-+_binary64`
18×	`un-div-inv_binary64`
12×	`exp-prod_binary64`
10×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
8×	`add-cube-cbrt_binary64`
6×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`associate-l_binary64` `rem-exp-log_binary64`
3×	`associate-r_binary64`
2×	`neg-mul-1_binary64` `distribute-lft-neg-in_binary64` `distribute-rgt-neg-in_binary64` `neg-log_binary64`
1×	`pow-prod-down_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `*-commutative_binary64`

Counts

4 → 147

Calls

4 calls:

22.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
7.0ms	(*.f64 (+.f64 1 eps) x)
4.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
3.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))

series47.0ms (1%)

Counts

4 → 12

Calls

4 calls:

32.0ms	(-.f64 (.f64 (+.f64 1 (/.f64 1 eps)) (exp.f64 (neg.f64 (.f64 (-.f64 1 eps) x)))) (.f64 (-.f64 (/.f64 1 eps) 1) (exp.f64 (neg.f64 (.f64 (+.f64 1 eps) x)))))
6.0ms	(exp.f64 (neg.f64 (*.f64 (+.f64 1 eps) x)))
5.0ms	(exp.f64 (neg.f64 (*.f64 (-.f64 1 eps) x)))
4.0ms	(*.f64 (+.f64 1 eps) x)

simplify113.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

159 → 159

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5440	8105

prune378.0ms (8.3%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	156	3	159
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	157	3	160

Merged error: 0.7b

Counts

160 → 3

Compiler

Compiled 7475 to 5809 computations (22.3% saved)

localize10.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(*.f64 (pow.f64 x 3) 2/3)
6.4b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

rewrite16.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`associate-l_binary64`
7×	`add-log-exp_binary64` `add-exp-log_binary64`
6×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
4×	`add-cbrt-cube_binary64` `unswap-sqr_binary64` `unpow-prod-down_binary64` `cube-prod_binary64`
3×	`associate-r_binary64` `prod-exp_binary64`
2×	`pow1_binary64` `diff-log_binary64` `sqr-pow_binary64`
1×	`pow-to-exp_binary64` `sub-neg_binary64` `flip3--_binary64` `cbrt-unprod_binary64` `difference-of-squares_binary64` `flip--_binary64` `pow-exp_binary64` `unpow3_binary64` `associate--l+_binary64` `sum-log_binary64` `*-commutative_binary64` `cube-mult_binary64`

Counts

2 → 45

Calls

2 calls:

9.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
6.0ms	(*.f64 (pow.f64 x 3) 2/3)

series9.0ms (0.2%)

Counts

2 → 6

Calls

2 calls:

4.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
4.0ms	(*.f64 (pow.f64 x 3) 2/3)

simplify70.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

51 → 51

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	4884	675
1	4884	675

prune53.0ms (1.2%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	48	3	51
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	49	5	54

Merged error: 0.7b

Counts

54 → 5

Compiler

Compiled 1059 to 791 computations (25.3% saved)

localize12.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.4b	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 x 3) 2/3)) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) 2) (.f64 x x))
43.6b	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
43.6b	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
43.6b	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))

rewrite29.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

9×	`add-log-exp_binary64`
5×	`add-sqr-sqrt_binary64`
4×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/3_binary64` `cbrt-prod_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `flip3--_binary64` `difference-of-squares_binary64` `flip--_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 41

Calls

4 calls:

16.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 x 3) 2/3)) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) 2) (.f64 x x))
4.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
4.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
4.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))

series25.0ms (0.6%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(-.f64 (+.f64 (.f64 (.f64 (cbrt.f64 (.f64 (pow.f64 x 3) 2/3)) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) (cbrt.f64 (.f64 (pow.f64 x 3) 2/3))) 2) (.f64 x x))
5.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
5.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))
5.0ms	(cbrt.f64 (*.f64 (pow.f64 x 3) 2/3))

simplify86.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

53 → 53

Iterations

Useful iterations: 0 (69.0ms)

Iter	Nodes	Cost
0	4824	701
1	4824	701

prune66.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	53	0	53
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	53	5	58

Merged error: 0.7b

Counts

58 → 5

Compiler

Compiled 1601 to 1266 computations (20.9% saved)

localize14.0ms (0.3%)

Local error

Found 4 expressions with local error:

6.4b	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
10.2b	(cbrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
10.2b	(cbrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
10.2b	(cbrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))

rewrite35.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`cbrt-prod_binary64`
11×	`add-sqr-sqrt_binary64`
9×	`add-log-exp_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`cbrt-div_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `difference-of-squares_binary64` `flip--_binary64`
3×	`pow1/3_binary64`
2×	`diff-log_binary64`
1×	`sub-neg_binary64` `associate--l+_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

9.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))
8.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
8.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
8.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))

series30.0ms (0.7%)

Counts

4 → 12

Calls

4 calls:

9.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
9.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
9.0ms	(cbrt.f64 (-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x)))
4.0ms	(-.f64 (+.f64 (.f64 (pow.f64 x 3) 2/3) 2) (.f64 x x))

simplify89.0ms (2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4876	1880
1	4876	1880

prune118.0ms (2.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	64	4	68
Fresh	1	2	3
Picked	1	0	1
Done	0	1	1
Total	66	7	73

Merged error: 0.7b

Counts

73 → 7

Compiler

Compiled 3364 to 2439 computations (27.5% saved)

regimes107.0ms (2.4%)

Compiler: Compiled 604 to 490 computations (18.9% saved)

bsearch59.0ms (1.3%)

Steps

Iters	Range		Point
8	319.7062364387002	1477888.5243037215	337.94709420177713

Compiler

Compiled 1 to 2 computations (-100% saved)

simplify8.0ms (0.2%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (5.0ms)

Iter	Nodes	Cost
0	255	92
1	255	92

end0.0ms (0%)

sample2.7s (59.4%)

Algorithm

1×

intervals

Results

947.0ms	1770×	body	1280	valid
414.0ms	1217×	body	640	valid
320.0ms	4083×	body	80	valid
142.0ms	607×	body	320	valid
49.0ms	323×	body	160	valid
18.0ms	227×	body	80	invalid
15.0ms	175×	body	80	overflowed
8.0ms	16×	body	1280	invalid
7.0ms	19×	body	640	invalid
4.0ms	16×	body	320	invalid
0.0ms	2×	body	160	invalid

Compiler

Compiled 390 to 319 computations (18.2% saved)

Details

analyze228.0ms (5%)

sample73.0ms (1.6%)

simplify98.0ms (2.2%)

prune6.0ms (0.1%)

localize17.0ms (0.4%)

rewrite46.0ms (1%)

series47.0ms (1%)

simplify113.0ms (2.5%)

prune378.0ms (8.3%)

localize10.0ms (0.2%)

rewrite16.0ms (0.4%)

series9.0ms (0.2%)

simplify70.0ms (1.5%)

prune53.0ms (1.2%)

localize12.0ms (0.3%)

rewrite29.0ms (0.6%)

series25.0ms (0.6%)

simplify86.0ms (1.9%)

prune66.0ms (1.5%)

localize14.0ms (0.3%)

rewrite35.0ms (0.8%)

series30.0ms (0.7%)

simplify89.0ms (2%)

prune118.0ms (2.6%)

regimes107.0ms (2.4%)

bsearch59.0ms (1.3%)

simplify8.0ms (0.2%)

end0.0ms (0%)

sample2.7s (59.4%)

Profiling