Details

analyze1.2s (22.9%)

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
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)

sample1.3s (23.8%)

Results

1.1s	8255×	body	128	valid
89.0ms	774×	body	128	invalid
0.0ms	1×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify112.0ms (2.1%)

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

prune5.0ms (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
	10.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
▶	3.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	3.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series52.0ms (1%)

Counts

2 → 84

Calls

2 calls:

39.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
13.0ms	(/.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)

simplify72.0ms (1.3%)

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

prune70.0ms (1.3%)

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
	35.6b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
▶	10.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
	22.7b	(fma.f64 (-.f64 y z) (.f64 (/.f64 t (-.f64 (.f64 a a) (*.f64 z z))) (+.f64 a z)) x)
✓	3.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 2375 to 741 computations (68.8% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
✓	0.0b	(*.f64 (-.f64 y z) t)
✓	11.1b	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

series130.0ms (2.4%)

Counts

3 → 144

Calls

3 calls:

81.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
39.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
10.0ms	(*.f64 (-.f64 y z) t)

rewrite25.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`*-un-lft-identity_binary64`
16×	`add-sqr-sqrt_binary64`
10×	`add-cbrt-cube_binary64`
10×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`

Counts

3 → 72

Calls

3 calls:

7.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
6.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
4.0ms	(*.f64 (-.f64 y z) t)

simplify144.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

898×	`fma-def_binary64`
587×	`cancel-sign-sub-inv_binary64`
313×	`sub-neg_binary64`
179×	`fma-neg_binary64`
159×	`associate-/l*_binary64`

Counts

216 → 188

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	248	5006
1	725	4379
2	2654	3966
3	4886	3964
4	5000	3964
5	4974	3964

prune117.0ms (2.2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	186	2	188
Fresh	1	1	2
Picked	0	1	1
Done	0	1	1
Total	187	5	192

Error

0.0b

Counts

192 → 5

Alt Table

Status	Error	Program
	21.2b	(+.f64 x (cbrt.f64 (pow.f64 (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))) 3)))
▶	2.3b	(+.f64 x (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))))
✓	10.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
	22.7b	(fma.f64 (-.f64 y z) (.f64 (/.f64 t (-.f64 (.f64 a a) (*.f64 z z))) (+.f64 a z)) x)
✓	3.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 4416 to 1274 computations (71.2% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))))
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
✓	2.5b	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))

series88.0ms (1.6%)

Counts

3 → 144

Calls

3 calls:

40.0ms	(+.f64 x (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))))
30.0ms	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
18.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

rewrite30.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

77×	`add-sqr-sqrt_binary64`
72×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
28×	`add-cube-cbrt_binary64`

Counts

3 → 122

Calls

3 calls:

11.0ms	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
6.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
4.0ms	(+.f64 x (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))))

simplify160.0ms (3%)

Algorithm

1×	egg-herbie

Rules

809×	`cancel-sign-sub-inv_binary64`
481×	`sub-neg_binary64`
214×	`associate--l+_binary64`
213×	`fma-neg_binary64`
205×	`+-commutative_binary64`

Counts

266 → 243

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	347	6572
1	979	6464
2	3690	6005
3	5272	6005

prune160.0ms (3%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	242	1	243
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	242	6	248

Error

Counts

248 → 6

Alt Table

Status	Error	Program
	21.2b	(+.f64 x (cbrt.f64 (pow.f64 (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))) 3)))
✓	2.3b	(+.f64 x (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))))
▶	6.7b	(+.f64 x (.f64 (.f64 t (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (-.f64 a z))))
✓	10.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
	22.7b	(fma.f64 (-.f64 y z) (.f64 (/.f64 t (-.f64 (.f64 a a) (*.f64 z z))) (+.f64 a z)) x)
✓	3.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 6303 to 1853 computations (70.6% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series183.0ms (3.4%)

Counts

4 → 132

Calls

4 calls:

61.0ms	(cbrt.f64 (-.f64 y z))
54.0ms	(/.f64 (cbrt.f64 (-.f64 y z)) (-.f64 a z))
38.0ms	(.f64 (.f64 t (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (-.f64 a z)))
30.0ms	(*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))

rewrite67.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

127×	`add-sqr-sqrt_binary64`
125×	`*-un-lft-identity_binary64`
88×	`cbrt-prod_binary64`
80×	`times-frac_binary64`
54×	`associate-r_binary64`

Counts

4 → 235

Calls

4 calls:

23.0ms	(.f64 (.f64 t (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (-.f64 a z)))
8.0ms	(*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))
7.0ms	(/.f64 (cbrt.f64 (-.f64 y z)) (-.f64 a z))
2.0ms	(cbrt.f64 (-.f64 y z))

simplify227.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

377×	`associate-/l*_binary64`
376×	`fma-def_binary64`
270×	`times-frac_binary64`
241×	`*-commutative_binary64`
189×	`associate-/r*_binary64`

Counts

367 → 442

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	697	11404
1	2026	10355
2	4918	10355
3	4982	10355

prune409.0ms (7.6%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	546	0	546
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	546	6	552

Error

Counts

552 → 6

Alt Table

Status	Error	Program
	21.2b	(+.f64 x (cbrt.f64 (pow.f64 (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))) 3)))
✓	2.3b	(+.f64 x (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))))
✓	6.7b	(+.f64 x (.f64 (.f64 t (*.f64 (cbrt.f64 (-.f64 y z)) (cbrt.f64 (-.f64 y z)))) (/.f64 (cbrt.f64 (-.f64 y z)) (-.f64 a z))))
✓	10.5b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
	22.7b	(fma.f64 (-.f64 y z) (.f64 (/.f64 t (-.f64 (.f64 a a) (*.f64 z z))) (+.f64 a z)) x)
✓	3.3b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

Compiler

Compiled 20751 to 7209 computations (65.3% saved)

regimes679.0ms (12.6%)

Accuracy

Total 0.5b remaining (96.7%)

Threshold costs 0.5b (96.7%)

Counts

68 → 3

Compiler

Compiled 8360 to 5140 computations (38.5% saved)

bsearch14.0ms (0.3%)

Steps

Iters	Range		Point
2	3.1361160382930215e-111	3.4672755202711913e-109	1.0453891552587748e-110
2	-6.892496748849379e-66	-7.234347480398853e-71	-1.2875828197469994e-69

Compiler

Compiled 6 to 5 computations (16.7% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	22	58
1	29	58
2	35	58
3	37	58
4	38	58
5	38	58

end89.0ms (1.6%)

Compiler: Compiled 206 to 108 computations (47.6% saved)

Details

analyze1.2s (22.9%)

sample1.3s (23.8%)

simplify112.0ms (2.1%)

prune5.0ms (0.1%)

localize7.0ms (0.1%)

series52.0ms (1%)

rewrite9.0ms (0.2%)

simplify72.0ms (1.3%)

prune70.0ms (1.3%)

localize7.0ms (0.1%)

series130.0ms (2.4%)

rewrite25.0ms (0.5%)

simplify144.0ms (2.7%)

prune117.0ms (2.2%)

localize11.0ms (0.2%)

series88.0ms (1.6%)

rewrite30.0ms (0.6%)

simplify160.0ms (3%)

prune160.0ms (3%)

localize11.0ms (0.2%)

series183.0ms (3.4%)

rewrite67.0ms (1.2%)

simplify227.0ms (4.2%)

prune409.0ms (7.6%)

regimes679.0ms (12.6%)

bsearch14.0ms (0.3%)

simplify4.0ms (0.1%)

end89.0ms (1.6%)

Profiling