Details

analyze1.0s (9.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.3%	0.2%	12
12.2%	87.5%	0.2%	13
21.9%	77.7%	0.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample27.0ms (0.3%)

Algorithm

1×

intervals

Results

8.0ms	211×	body	128	valid
2.0ms	17×	body	512	valid
2.0ms	11×	body	1024	valid
1.0ms	33×	body	128	invalid
1.0ms	5×	body	2048	valid
1.0ms	12×	body	256	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify98.0ms (1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	5088	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

Merged error: 15.9b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
3.0b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
5.8b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite51.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
27×	`add-cube-cbrt_binary64`
23×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `flip3--_binary64` `associate-l_binary64` `associate-/l_binary64` `flip--_binary64`
4×	`associate-/r/_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 119

Calls

3 calls:

26.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
9.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
4.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

series970.0ms (9.6%)

Counts

3 → 9

Calls

3 calls:

485.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
350.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
134.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

simplify65.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5636	2420

prune130.0ms (1.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	118	10	128
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	119	10	129

Merged error: 3.0b

Counts

129 → 10

Compiler

Compiled 2818 to 605 computations (78.5% saved)

localize20.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
0.8b	(.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
10.6b	(+.f64 x (.f64 (.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`add-exp-log_binary64`
17×	`add-sqr-sqrt_binary64`
16×	`cbrt-div_binary64`
14×	`*-un-lft-identity_binary64` `add-cbrt-cube_binary64`
13×	`associate-r_binary64`
10×	`flip3--_binary64` `flip--_binary64` `cbrt-prod_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64`
8×	`add-cube-cbrt_binary64` `associate-/r/_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `frac-times_binary64`
5×	`associate-l_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64` `associate-*l/_binary64`
3×	`associate-*r/_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64`
2×	`pow1/3_binary64` `unswap-sqr_binary64` `times-frac_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 85

Calls

4 calls:

30.0ms	(.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
5.0ms	(+.f64 x (.f64 (.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))
4.0ms	(cbrt.f64 (-.f64 a z))
4.0ms	(cbrt.f64 (-.f64 a z))

series2.0s (20%)

Counts

4 → 12

Calls

4 calls:

1.1s	(.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))))
511.0ms	(+.f64 x (.f64 (.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))
206.0ms	(cbrt.f64 (-.f64 a z))
204.0ms	(cbrt.f64 (-.f64 a z))

simplify72.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

97 → 97

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5048	2503

prune118.0ms (1.2%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	96	1	97
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	96	11	107

Merged error: 3.0b

Counts

107 → 11

Compiler

Compiled 4001 to 809 computations (79.8% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a z))
0.6b	(cbrt.f64 (-.f64 a z))
2.6b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
8.8b	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

rewrite78.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
59×	`*-un-lft-identity_binary64`
52×	`times-frac_binary64`
46×	`associate-r_binary64`
37×	`cbrt-prod_binary64`
27×	`add-cube-cbrt_binary64`
25×	`add-exp-log_binary64`
18×	`cbrt-div_binary64` `add-cbrt-cube_binary64`
17×	`associate-l_binary64`
16×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`associate-/r/_binary64`
9×	`flip3--_binary64` `flip--_binary64`
8×	`cbrt-unprod_binary64` `prod-exp_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
6×	`add-log-exp_binary64` `pow1_binary64` `unswap-sqr_binary64`
5×	`frac-times_binary64`
3×	`associate-r/_binary64` `associate-l/_binary64`
2×	`pow1/3_binary64` `div-inv_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

4 → 134

Calls

4 calls:

48.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
5.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
4.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))

series1.6s (16.1%)

Counts

4 → 12

Calls

4 calls:

719.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
501.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
215.0ms	(cbrt.f64 (-.f64 a z))
201.0ms	(cbrt.f64 (-.f64 a z))

simplify64.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (29.0ms)

Iter	Nodes	Cost
0	5309	3930

prune145.0ms (1.4%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	145	1	146
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	145	12	157

Merged error: 3.0b

Counts

157 → 12

Compiler

Compiled 4614 to 849 computations (81.6% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 (-.f64 a z) (-.f64 t x))
0.6b	(/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))
4.2b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))))
5.8b	(*.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))))

rewrite128.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

392×	`times-frac_binary64`
338×	`add-sqr-sqrt_binary64`
326×	`*-un-lft-identity_binary64`
158×	`add-cube-cbrt_binary64`
98×	`associate-r_binary64`
83×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
36×	`associate-/r*_binary64` `add-exp-log_binary64`
20×	`add-cbrt-cube_binary64`
18×	`associate-/r/_binary64`
15×	`div-exp_binary64`
11×	`flip3--_binary64` `flip--_binary64`
10×	`div-inv_binary64`
8×	`associate-/l*_binary64`
7×	`pow1_binary64` `cbrt-undiv_binary64` `prod-exp_binary64`
6×	`add-log-exp_binary64`
5×	`associate-l_binary64` `unswap-sqr_binary64`
4×	`1-exp_binary64` `rec-exp_binary64`
3×	`cbrt-unprod_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64` `frac-times_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `associate-r/_binary64` `div-sub_binary64` `inv-pow_binary64` `un-div-inv_binary64` `+-commutative_binary64` `pow-flip_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

4 → 344

Calls

4 calls:

47.0ms	(*.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))))
15.0ms	(/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))
9.0ms	(/.f64 (-.f64 a z) (-.f64 t x))
5.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))))

series1.7s (17.2%)

Counts

4 → 12

Calls

4 calls:

695.0ms	(*.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x))))
498.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))))
424.0ms	(/.f64 1 (/.f64 (-.f64 a z) (-.f64 t x)))
123.0ms	(/.f64 (-.f64 a z) (-.f64 t x))

simplify128.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

356 → 356

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4971	7621
1	4971	7621

prune308.0ms (3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	353	3	356
Fresh	3	6	9
Picked	1	0	1
Done	0	2	2
Total	357	11	368

Merged error: 2.8b

Counts

368 → 11

Compiler

Compiled 8517 to 2089 computations (75.5% saved)

regimes166.0ms (1.6%)

Compiler: Compiled 1120 to 805 computations (28.1% saved)

bsearch45.0ms (0.4%)

Steps

Iters	Range		Point
6	4.30725829499155e-187	6.222485622356145e-186	6.11279924812159e-186
6	-7.477889746351589e-125	-1.0397096663550005e-125	-1.757536018637735e-125

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	84
1	71	84

end0.0ms (0%)

sample1.0s (10%)

Algorithm

1×

intervals

Results

276.0ms	6706×	body	128	valid
57.0ms	383×	body	1024	valid
52.0ms	452×	body	512	valid
50.0ms	1191×	body	128	invalid
33.0ms	388×	body	256	valid
13.0ms	71×	body	2048	valid

Compiler

Compiled 292 to 196 computations (32.9% saved)

Details

analyze1.0s (9.9%)

sample27.0ms (0.3%)

simplify98.0ms (1%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite51.0ms (0.5%)

series970.0ms (9.6%)

simplify65.0ms (0.6%)

prune130.0ms (1.3%)

localize20.0ms (0.2%)

rewrite56.0ms (0.5%)

series2.0s (20%)

simplify72.0ms (0.7%)

prune118.0ms (1.2%)

localize13.0ms (0.1%)

rewrite78.0ms (0.8%)

series1.6s (16.1%)

simplify64.0ms (0.6%)

prune145.0ms (1.4%)

localize11.0ms (0.1%)

rewrite128.0ms (1.3%)

series1.7s (17.2%)

simplify128.0ms (1.3%)

prune308.0ms (3%)

regimes166.0ms (1.6%)

bsearch45.0ms (0.4%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.0s (10%)

Profiling