Details

analyze1.3s (28.4%)

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
3.5%	96.2%	0.2%	10
9.5%	90.2%	0.2%	11
14.3%	85.4%	0.2%	12
16.5%	83.2%	0.2%	13
25.9%	73.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.1s (25.5%)

Results

978.0ms	8255×	body	128	valid
84.0ms	726×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify112.0ms (2.5%)

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 (0.1%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	1.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	10.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	1.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series64.0ms (1.5%)

Counts

2 → 84

Calls

2 calls:

40.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
25.0ms	(/.f64 t (-.f64 a z))

rewrite9.0ms (0.2%)

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:

6.0ms	(/.f64 t (-.f64 a z))
0.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

simplify76.0ms (1.7%)

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

prune66.0ms (1.5%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	106	2	108
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	106	4	110

Error

0.0b

Counts

110 → 4

Alt Table

Status	Error	Program
	41.6b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x) (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)) (fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)))
✓	1.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	37.5b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
▶	10.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 2405 to 739 computations (69.3% saved)

localize8.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 y z) t)
✓	10.0b	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

series43.0ms (1%)

Counts

2 → 84

Calls

2 calls:

36.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
7.0ms	(*.f64 (-.f64 y z) t)

rewrite14.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 55

Calls

2 calls:

8.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
4.0ms	(*.f64 (-.f64 y z) t)

simplify90.0ms (2%)

Algorithm

1×	egg-herbie

Rules

592×	`fma-def_binary64`
310×	`associate-/l/_binary64`
309×	`cancel-sign-sub-inv_binary64`
267×	`distribute-rgt-in_binary64`
239×	`distribute-lft-in_binary64`

Counts

139 → 125

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	184	2883
1	524	2478
2	1984	2217
3	4866	2212
4	4984	2212

prune78.0ms (1.8%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	123	2	125
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	124	5	129

Error

Counts

129 → 5

Alt Table

Status	Error	Program
▶	10.3b	(+.f64 x (.f64 (.f64 (-.f64 y z) t) (/.f64 1 (-.f64 a z))))
✓	1.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	19.1b	(+.f64 x (cbrt.f64 (pow.f64 (*.f64 (/.f64 t (-.f64 a z)) (-.f64 y z)) 3)))
	37.5b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
✓	10.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 2791 to 896 computations (67.9% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(*.f64 (-.f64 y z) t)
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	10.1b	(.f64 (.f64 (-.f64 y z) t) (/.f64 1 (-.f64 a z)))

series47.0ms (1.1%)

Counts

2 → 72

Calls

2 calls:

36.0ms	(.f64 (.f64 (-.f64 y z) t) (/.f64 1 (-.f64 a z)))
10.0ms	(/.f64 1 (-.f64 a z))

rewrite24.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
30×	`times-frac_binary64`
28×	`add-exp-log_binary64`
21×	`associate-r_binary64`

Counts

2 → 95

Calls

2 calls:

11.0ms	(.f64 (.f64 (-.f64 y z) t) (/.f64 1 (-.f64 a z)))
4.0ms	(/.f64 1 (-.f64 a z))

simplify130.0ms (3%)

Algorithm

1×	egg-herbie

Rules

873×	`times-frac_binary64`
663×	`fma-def_binary64`
518×	`fma-neg_binary64`
314×	`cancel-sign-sub-inv_binary64`
183×	`associate-l_binary64`

Counts

167 → 167

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	211	3622
1	579	3436
2	2107	2992
3	4544	2990
4	4985	2990
5	4967	2990

prune134.0ms (3.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	209	0	209
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	209	5	214

Error

Counts

214 → 5

Alt Table

Status	Error	Program
✓	10.3b	(+.f64 x (.f64 (.f64 (-.f64 y z) t) (/.f64 1 (-.f64 a z))))
✓	1.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
▶	19.1b	(+.f64 x (cbrt.f64 (pow.f64 (*.f64 (/.f64 t (-.f64 a z)) (-.f64 y z)) 3)))
	37.5b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
✓	10.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 4765 to 1765 computations (63% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(/.f64 t (-.f64 a z))
✓	0.1b	(pow.f64 (*.f64 (/.f64 t (-.f64 a z)) (-.f64 y z)) 3)
✓	9.0b	(*.f64 (/.f64 t (-.f64 a z)) (-.f64 y z))
✓	34.5b	(cbrt.f64 (pow.f64 (*.f64 (/.f64 t (-.f64 a z)) (-.f64 y z)) 3))

series269.0ms (6.1%)

Counts

3 → 144

Calls

3 calls:

161.0ms	(pow.f64 (*.f64 (/.f64 t (-.f64 a z)) (-.f64 y z)) 3)
73.0ms	(cbrt.f64 (pow.f64 (*.f64 (/.f64 t (-.f64 a z)) (-.f64 y z)) 3))
34.0ms	(*.f64 (/.f64 t (-.f64 a z)) (-.f64 y z))

rewrite34.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

42×	`add-sqr-sqrt_binary64`
37×	`*-un-lft-identity_binary64`
29×	`add-cube-cbrt_binary64`
21×	`associate-l_binary64`
18×	`prod-diff_binary64`

Counts

3 → 129

Calls

3 calls:

11.0ms	(*.f64 (/.f64 t (-.f64 a z)) (-.f64 y z))
8.0ms	(pow.f64 (*.f64 (/.f64 t (-.f64 a z)) (-.f64 y z)) 3)
2.0ms	(cbrt.f64 (pow.f64 (*.f64 (/.f64 t (-.f64 a z)) (-.f64 y z)) 3))

simplify153.0ms (3.5%)

Algorithm

1×	egg-herbie

Rules

706×	`times-frac_binary64`
511×	`associate-/l*_binary64`
369×	`fma-def_binary64`
181×	`*-commutative_binary64`
133×	`+-commutative_binary64`

Counts

273 → 267

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	615	10092
1	1833	9931
2	5011	9931

prune256.0ms (5.8%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	321	0	321
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	321	5	326

Error

Counts

326 → 5

Alt Table

Status	Error	Program
✓	10.3b	(+.f64 x (.f64 (.f64 (-.f64 y z) t) (/.f64 1 (-.f64 a z))))
✓	1.4b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	19.1b	(+.f64 x (cbrt.f64 (pow.f64 (*.f64 (/.f64 t (-.f64 a z)) (-.f64 y z)) 3)))
	37.5b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
✓	10.3b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 11457 to 5433 computations (52.6% saved)

regimes311.0ms (7.1%)

Accuracy

Total 0.2b remaining (94.4%)

Threshold costs 0.2b (94.4%)

Counts

41 → 3

Compiler

Compiled 4750 to 2911 computations (38.7% saved)

bsearch1.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	23	82
1	29	82
2	35	82
3	37	82
4	38	82
5	38	82

end73.0ms (1.7%)

Compiler: Compiled 208 to 96 computations (53.8% saved)

Details

analyze1.3s (28.4%)

sample1.1s (25.5%)

simplify112.0ms (2.5%)

prune3.0ms (0.1%)

localize8.0ms (0.2%)

series64.0ms (1.5%)

rewrite9.0ms (0.2%)

simplify76.0ms (1.7%)

prune66.0ms (1.5%)

localize8.0ms (0.2%)

series43.0ms (1%)

rewrite14.0ms (0.3%)

simplify90.0ms (2%)

prune78.0ms (1.8%)

localize8.0ms (0.2%)

series47.0ms (1.1%)

rewrite24.0ms (0.5%)

simplify130.0ms (3%)

prune134.0ms (3.1%)

localize9.0ms (0.2%)

series269.0ms (6.1%)

rewrite34.0ms (0.8%)

simplify153.0ms (3.5%)

prune256.0ms (5.8%)

regimes311.0ms (7.1%)

bsearch1.0ms (0%)

simplify4.0ms (0.1%)

end73.0ms (1.7%)

Profiling