Details

analyze1.2s (5.8%)

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
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
18.4%	81.3%	0.2%	13
29.5%	70.3%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample81.0ms (0.4%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
1.0ms	19×	body	128	invalid

Compiler

Compiled 38 to 26 computations (31.6% saved)

simplify114.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

1893×	`fma-neg_binary64`
867×	`div-sub_binary64`
749×	`fma-def_binary64`
696×	`distribute-rgt-in_binary64`
535×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	40	14
3	81	14
4	160	14
5	302	14
6	620	14
7	1528	14
8	2624	14
9	2858	14
10	3205	14
11	3392	14
12	3498	14
13	3533	14
14	5398	14

prune3.0ms (0%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Kept	Total
New	2	2
Fresh	1	1
Picked	0	0
Done	0	0
Total	3	3

Error

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	2.2b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	12.8b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	2.2b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series55.0ms (0.3%)

Counts

2 → 84

Calls

2 calls:

37.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
18.0ms	(/.f64 t (-.f64 a z))

rewrite6.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64`
20×	`add-sqr-sqrt_binary64`
15×	`times-frac_binary64`
12×	`add-cube-cbrt_binary64`
5×	`associate-/r*_binary64`

Counts

2 → 49

Calls

2 calls:

4.0ms	(/.f64 t (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

simplify70.0ms (0.3%)

Algorithm

1×	egg-herbie

Rules

690×	`times-frac_binary64`
633×	`fma-def_binary64`
620×	`associate-/l*_binary64`
272×	`cancel-sign-sub-inv_binary64`
175×	`associate-/l/_binary64`

Counts

133 → 108

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	198	3215
1	492	3156
2	1711	2520
3	5110	2520

prune100.0ms (0.5%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	104	4	108
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	106	4	110

Error

0.0b

Counts

110 → 4

Alt Table

Status	Error	Program
	2.3b	(fma.f64 (-.f64 y z) (*.f64 t (/.f64 1 (-.f64 a z))) x)
	2.2b	(+.f64 (*.f64 (-.f64 y z) (/.f64 t (-.f64 a z))) x)
▶	1.8b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
	12.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))

Compiler

Compiled 2396 to 754 computations (68.5% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
✓	0.0b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	0.0b	(/.f64 z (-.f64 a z))
✓	3.1b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

series122.0ms (0.6%)

Counts

4 → 147

Calls

4 calls:

45.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
44.0ms	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
23.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
9.0ms	(/.f64 z (-.f64 a z))

rewrite1.0s (4.9%)

Algorithm

1×	rewrite-expression-head

Rules

3320×	`*-un-lft-identity_binary64`
3302×	`add-sqr-sqrt_binary64`
3291×	`times-frac_binary64`
2205×	`prod-diff_binary64`
1964×	`add-cube-cbrt_binary64`

Counts

4 → 2457

Calls

4 calls:

89.0ms	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
50.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
37.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
4.0ms	(/.f64 z (-.f64 a z))

simplify3.1s (15%)

Algorithm

1×	egg-herbie

Rules

933×	`times-frac_binary64`
426×	`*-commutative_binary64`
366×	`distribute-rgt-in_binary64`
308×	`fma-udef_binary64`
262×	`distribute-lft-in_binary64`

Counts

2604 → 2821

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1501	146886
1	2683	107534
2	4549	94985
3	4492	94985
4	5169	94985

prune2.3s (11%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	2818	3	2821
Fresh	1	2	3
Picked	1	0	1
Done	0	0	0
Total	2820	5	2825

Error

Counts

2825 → 5

Alt Table

Status	Error	Program
▶	1.9b	(+.f64 (.f64 t (.f64 (/.f64 1 (-.f64 a z)) (-.f64 y z))) x)
	13.8b	(+.f64 (/.f64 (.f64 t (-.f64 (.f64 (/.f64 y (-.f64 a z)) (/.f64 y (-.f64 a z))) (*.f64 (/.f64 z (-.f64 a z)) (/.f64 z (-.f64 a z))))) (+.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
	2.1b	(+.f64 (.f64 (.f64 t (/.f64 1 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (-.f64 (/.f64 y (cbrt.f64 (-.f64 a z))) (/.f64 z (cbrt.f64 (-.f64 a z))))) x)
	2.2b	(+.f64 (*.f64 (-.f64 y z) (/.f64 t (-.f64 a z))) x)
	12.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))

Compiler

Compiled 162232 to 28074 computations (82.7% saved)

localize10.0ms (0%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (.f64 t (.f64 (/.f64 1 (-.f64 a z)) (-.f64 y z))) x)
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	0.2b	(*.f64 (/.f64 1 (-.f64 a z)) (-.f64 y z))
✓	3.1b	(.f64 t (.f64 (/.f64 1 (-.f64 a z)) (-.f64 y z)))

series108.0ms (0.5%)

Counts

4 → 168

Calls

4 calls:

47.0ms	(+.f64 (.f64 t (.f64 (/.f64 1 (-.f64 a z)) (-.f64 y z))) x)
33.0ms	(.f64 t (.f64 (/.f64 1 (-.f64 a z)) (-.f64 y z)))
20.0ms	(*.f64 (/.f64 1 (-.f64 a z)) (-.f64 y z))
8.0ms	(/.f64 1 (-.f64 a z))

rewrite81.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

118×	`add-sqr-sqrt_binary64`
117×	`distribute-lft-in_binary64`
117×	`distribute-rgt-in_binary64`
112×	`*-un-lft-identity_binary64`
95×	`add-cube-cbrt_binary64`

Counts

4 → 267

Calls

4 calls:

19.0ms	(*.f64 (/.f64 1 (-.f64 a z)) (-.f64 y z))
18.0ms	(+.f64 (.f64 t (.f64 (/.f64 1 (-.f64 a z)) (-.f64 y z))) x)
11.0ms	(.f64 t (.f64 (/.f64 1 (-.f64 a z)) (-.f64 y z)))
4.0ms	(/.f64 1 (-.f64 a z))

simplify241.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

369×	`fma-neg_binary64`
327×	`associate-r_binary64`
325×	`associate-l_binary64`
261×	`+-commutative_binary64`
246×	`times-frac_binary64`

Counts

435 → 483

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	525	10036
1	1153	8906
2	4325	8744
3	4941	8744
4	4975	8744

prune424.0ms (2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	483	0	483
Fresh	0	4	4
Picked	0	1	1
Done	0	0	0
Total	483	5	488

Error

Counts

488 → 5

Alt Table

Status	Error	Program
✓	1.9b	(+.f64 (.f64 t (.f64 (/.f64 1 (-.f64 a z)) (-.f64 y z))) x)
	13.8b	(+.f64 (/.f64 (.f64 t (-.f64 (.f64 (/.f64 y (-.f64 a z)) (/.f64 y (-.f64 a z))) (*.f64 (/.f64 z (-.f64 a z)) (/.f64 z (-.f64 a z))))) (+.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
▶	2.1b	(+.f64 (.f64 (.f64 t (/.f64 1 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (-.f64 (/.f64 y (cbrt.f64 (-.f64 a z))) (/.f64 z (cbrt.f64 (-.f64 a z))))) x)
	2.2b	(+.f64 (*.f64 (-.f64 y z) (/.f64 t (-.f64 a z))) x)
	12.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))

Compiler

Compiled 13839 to 4840 computations (65% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 z (cbrt.f64 (-.f64 a z)))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
✓	0.6b	(cbrt.f64 (-.f64 a z))
✓	7.0b	(.f64 (.f64 t (/.f64 1 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (-.f64 (/.f64 y (cbrt.f64 (-.f64 a z))) (/.f64 z (cbrt.f64 (-.f64 a z)))))

series1.6s (7.9%)

Counts

4 → 120

Calls

4 calls:

1.5s	(.f64 (.f64 t (/.f64 1 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (-.f64 (/.f64 y (cbrt.f64 (-.f64 a z))) (/.f64 z (cbrt.f64 (-.f64 a z)))))
43.0ms	(/.f64 z (cbrt.f64 (-.f64 a z)))
39.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
30.0ms	(cbrt.f64 (-.f64 a z))

rewrite1.1s (5.2%)

Algorithm

1×	rewrite-expression-head

Rules

2984×	`times-frac_binary64`
2657×	`add-sqr-sqrt_binary64`
2653×	`*-un-lft-identity_binary64`
1903×	`cbrt-prod_binary64`
1865×	`add-cube-cbrt_binary64`

Counts

4 → 2053

Calls

4 calls:

101.0ms	(.f64 (.f64 t (/.f64 1 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (-.f64 (/.f64 y (cbrt.f64 (-.f64 a z))) (/.f64 z (cbrt.f64 (-.f64 a z)))))
11.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
5.0ms	(/.f64 z (cbrt.f64 (-.f64 a z)))
2.0ms	(cbrt.f64 (-.f64 a z))

simplify3.6s (17.5%)

Algorithm

1×	egg-herbie

Rules

660×	`associate-l_binary64`
552×	`fma-udef_binary64`
79×	`associate-*r/_binary64`
66×	`fma-def_binary64`
65×	`neg-mul-1_binary64`

Counts

2173 → 2888

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	2519	266485
1	5053	266485

prune2.7s (13%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	3038	0	3038
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	3038	5	3043

Error

Counts

3043 → 5

Alt Table

Status	Error	Program
✓	1.9b	(+.f64 (.f64 t (.f64 (/.f64 1 (-.f64 a z)) (-.f64 y z))) x)
	13.8b	(+.f64 (/.f64 (.f64 t (-.f64 (.f64 (/.f64 y (-.f64 a z)) (/.f64 y (-.f64 a z))) (*.f64 (/.f64 z (-.f64 a z)) (/.f64 z (-.f64 a z))))) (+.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	2.1b	(+.f64 (.f64 (.f64 t (/.f64 1 (*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (-.f64 (/.f64 y (cbrt.f64 (-.f64 a z))) (/.f64 z (cbrt.f64 (-.f64 a z))))) x)
	2.2b	(+.f64 (*.f64 (-.f64 y z) (/.f64 t (-.f64 a z))) x)
	12.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))

Compiler

Compiled 274252 to 45041 computations (83.6% saved)

regimes1.8s (8.5%)

Accuracy

Total 0.9b remaining (98.5%)

Threshold costs 0.9b (98.5%)

Counts

164 → 3

Compiler

Compiled 25741 to 15220 computations (40.9% saved)

bsearch40.0ms (0.2%)

Steps

Iters	Range		Point
10	2.6671257174486996e-140	6.352466918856919e-124	1.0616679928509863e-130
6	-7.855350025474898e-58	-5.249681254409062e-59	-5.615091370569311e-59

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

11×	`+-commutative_binary64`
8×	`sub-neg_binary64`
5×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	33	102
1	46	102
2	61	102
3	67	102
4	70	102
5	70	102

end1.0ms (0%)

Compiler: Compiled 73 to 31 computations (57.5% saved)

sample857.0ms (4.1%)

Algorithm

1×

intervals

Results

392.0ms	7998×	body	128	valid
35.0ms	749×	body	128	invalid
0.0ms	1×	body	1024	valid
0.0ms	1×	body	512	valid

Compiler

Compiled 229 to 112 computations (51.1% saved)

Details

analyze1.2s (5.8%)

sample81.0ms (0.4%)

simplify114.0ms (0.6%)

prune3.0ms (0%)

localize7.0ms (0%)

series55.0ms (0.3%)

rewrite6.0ms (0%)

simplify70.0ms (0.3%)

prune100.0ms (0.5%)

localize10.0ms (0%)

series122.0ms (0.6%)

rewrite1.0s (4.9%)

simplify3.1s (15%)

prune2.3s (11%)

localize10.0ms (0%)

series108.0ms (0.5%)

rewrite81.0ms (0.4%)

simplify241.0ms (1.2%)

prune424.0ms (2%)

localize13.0ms (0.1%)

series1.6s (7.9%)

rewrite1.1s (5.2%)

simplify3.6s (17.5%)

prune2.7s (13%)

regimes1.8s (8.5%)

bsearch40.0ms (0.2%)

simplify5.0ms (0%)

end1.0ms (0%)

sample857.0ms (4.1%)

Profiling