Details

analyze306.0ms (3.1%)

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
49.9%	49.9%	0.2%	6
49.9%	49.9%	0.2%	7
49.9%	49.9%	0.2%	8
49.9%	49.9%	0.2%	9
49.9%	49.9%	0.2%	10
74.8%	24.9%	0.2%	11
74.8%	24.9%	0.2%	12
74.8%	24.9%	0.2%	13
74.8%	24.9%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample855.0ms (8.6%)

Infinites

8.3% of outputs are infinite.

Results

778.0ms

8256×

body

128

valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify117.0ms (1.2%)

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

prune4.0ms (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
▶	2.7b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
	10.2b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 t (-.f64 a z))
✓	2.7b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)

series54.0ms (0.5%)

Counts

2 → 84

Calls

2 calls:

37.0ms	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
17.0ms	(/.f64 t (-.f64 a z))

rewrite6.0ms (0.1%)

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)

simplify75.0ms (0.8%)

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

prune83.0ms (0.8%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	106	4	110

Error

0.0b

Counts

110 → 4

Alt Table

Status	Error	Program
✓	2.7b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
▶	1.3b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
	10.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	41.5b	(fma.f64 (-.f64 y z) (.f64 (/.f64 t (-.f64 (pow.f64 a 3) (pow.f64 z 3))) (+.f64 (.f64 a a) (+.f64 (.f64 z z) (.f64 a z)))) x)

Compiler

Compiled 2407 to 759 computations (68.5% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	0.0b	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
✓	0.0b	(/.f64 y (-.f64 a z))
✓	2.1b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))

series133.0ms (1.3%)

Counts

4 → 147

Calls

4 calls:

46.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
45.0ms	(+.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)))
19.0ms	(/.f64 y (-.f64 a z))

rewrite961.0ms (9.7%)

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:

97.0ms	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
53.0ms	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
30.0ms	(-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))
4.0ms	(/.f64 y (-.f64 a z))

simplify2.9s (29.4%)

Algorithm

1×	egg-herbie

Rules

518×	`times-frac_binary64`
427×	`*-commutative_binary64`
366×	`distribute-rgt-in_binary64`
306×	`fma-udef_binary64`
263×	`fma-def_binary64`

Counts

2604 → 3060

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1518	160062
1	2701	110524
2	4557	110112
3	5230	110112

prune2.3s (23.5%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	3058	2	3060
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	3058	6	3064

Error

Counts

3064 → 6

Alt Table

Status	Error	Program
✓	2.7b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	1.3b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
▶	1.3b	(+.f64 (*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))) x)
	10.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	41.5b	(fma.f64 (-.f64 y z) (.f64 (/.f64 t (-.f64 (pow.f64 a 3) (pow.f64 z 3))) (+.f64 (.f64 a a) (+.f64 (.f64 z z) (.f64 a z)))) x)
	1.5b	(+.f64 (.f64 t (-.f64 (.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 a z))) (/.f64 z (-.f64 a z)))) x)

Compiler

Compiled 176840 to 29987 computations (83% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))) x)
✓	0.0b	(/.f64 1 (-.f64 a z))
✓	0.1b	(fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))
✓	2.1b	(*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z)))))

series129.0ms (1.3%)

Counts

4 → 168

Calls

4 calls:

50.0ms	(+.f64 (*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))) x)
47.0ms	(*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z)))))
24.0ms	(fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))
8.0ms	(/.f64 1 (-.f64 a z))

rewrite15.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64`
24×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
15×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

4 → 91

Calls

4 calls:

4.0ms	(/.f64 1 (-.f64 a z))
3.0ms	(+.f64 (*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))) x)
3.0ms	(*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z)))))
0.0ms	(fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))

simplify157.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

851×	`cancel-sign-sub-inv_binary64`
465×	`sub-neg_binary64`
280×	`fma-neg_binary64`
227×	`+-commutative_binary64`
215×	`associate--l+_binary64`

Counts

259 → 248

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	335	6890
1	874	6471
2	3121	6309
3	4971	6308
4	4995	6308

prune217.0ms (2.2%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	248	0	248
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	248	6	254

Error

Counts

254 → 6

Alt Table

Status	Error	Program
✓	2.7b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	1.3b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	1.3b	(+.f64 (*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))) x)
	10.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	41.5b	(fma.f64 (-.f64 y z) (.f64 (/.f64 t (-.f64 (pow.f64 a 3) (pow.f64 z 3))) (+.f64 (.f64 a a) (+.f64 (.f64 z z) (.f64 a z)))) x)
▶	1.5b	(+.f64 (.f64 t (-.f64 (.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 a z))) (/.f64 z (-.f64 a z)))) x)

Compiler

Compiled 7162 to 2483 computations (65.3% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 a z)))
✓	0.5b	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
✓	0.6b	(cbrt.f64 y)
✓	2.1b	(.f64 t (-.f64 (.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 a z))) (/.f64 z (-.f64 a z))))

series153.0ms (1.5%)

Counts

4 → 108

Calls

4 calls:

53.0ms	(.f64 t (-.f64 (.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 a z))) (/.f64 z (-.f64 a z))))
37.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
35.0ms	(cbrt.f64 y)
27.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 a z)))

rewrite68.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

119×	`add-sqr-sqrt_binary64`
104×	`*-un-lft-identity_binary64`
92×	`times-frac_binary64`
68×	`add-cube-cbrt_binary64`
45×	`associate-r_binary64`

Counts

4 → 226

Calls

4 calls:

20.0ms	(.f64 t (-.f64 (.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 a z))) (/.f64 z (-.f64 a z))))
13.0ms	(.f64 (.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 a z)))
5.0ms	(*.f64 (cbrt.f64 y) (cbrt.f64 y))
1.0ms	(cbrt.f64 y)

simplify140.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

687×	`associate-l_binary64`
529×	`associate-r_binary64`
317×	`associate-/l*_binary64`
254×	`associate-*r/_binary64`
189×	`*-commutative_binary64`

Counts

334 → 348

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	585	9442
1	1433	7366
2	5097	7366

prune304.0ms (3.1%)

Pruning

6 alts after pruning (2 fresh and 4 done)

	Pruned	Kept	Total
New	382	0	382
Fresh	0	2	2
Picked	0	1	1
Done	0	3	3
Total	382	6	388

Error

Counts

388 → 6

Alt Table

Status	Error	Program
✓	2.7b	(fma.f64 (-.f64 y z) (/.f64 t (-.f64 a z)) x)
✓	1.3b	(+.f64 (*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z)))) x)
✓	1.3b	(+.f64 (*.f64 t (fma.f64 y (/.f64 1 (-.f64 a z)) (neg.f64 (/.f64 z (-.f64 a z))))) x)
	10.8b	(-.f64 (+.f64 (/.f64 (.f64 y t) (-.f64 a z)) x) (/.f64 (.f64 t z) (-.f64 a z)))
	41.5b	(fma.f64 (-.f64 y z) (.f64 (/.f64 t (-.f64 (pow.f64 a 3) (pow.f64 z 3))) (+.f64 (.f64 a a) (+.f64 (.f64 z z) (.f64 a z)))) x)
✓	1.5b	(+.f64 (.f64 t (-.f64 (.f64 (*.f64 (cbrt.f64 y) (cbrt.f64 y)) (/.f64 (cbrt.f64 y) (-.f64 a z))) (/.f64 z (-.f64 a z)))) x)

Compiler

Compiled 13023 to 3045 computations (76.6% saved)

regimes779.0ms (7.8%)

Accuracy

Total 1.1b remaining (99%)

Threshold costs 0b (0%)

Counts

114 → 1

Compiler

Compiled 17649 to 9816 computations (44.4% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	15	20
2	24	20
3	28	20
4	30	20
5	30	20

end91.0ms (0.9%)

Compiler: Compiled 175 to 98 computations (44% saved)

Details

analyze306.0ms (3.1%)

sample855.0ms (8.6%)

simplify117.0ms (1.2%)

prune4.0ms (0%)

localize8.0ms (0.1%)

series54.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify75.0ms (0.8%)

prune83.0ms (0.8%)

localize9.0ms (0.1%)

series133.0ms (1.3%)

rewrite961.0ms (9.7%)

simplify2.9s (29.4%)

prune2.3s (23.5%)

localize10.0ms (0.1%)

series129.0ms (1.3%)

rewrite15.0ms (0.2%)

simplify157.0ms (1.6%)

prune217.0ms (2.2%)

localize13.0ms (0.1%)

series153.0ms (1.5%)

rewrite68.0ms (0.7%)

simplify140.0ms (1.4%)

prune304.0ms (3.1%)

regimes779.0ms (7.8%)

simplify3.0ms (0%)

end91.0ms (0.9%)

Profiling