Details

analyze1.2s (17%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
0%	99.9%	0.1%	7
0%	99.9%	0.1%	8
2.3%	91.3%	6.4%	9
3.5%	87%	9.5%	10
4.1%	86.4%	9.5%	11
18.4%	66.6%	15%	12
20.5%	61.8%	17.7%	13
21.9%	60.4%	17.7%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample2.4s (34.4%)

Results

965.0ms	6426×	body	128	valid
589.0ms	962×	body	1024	valid
252.0ms	558×	body	512	valid
180.0ms	1453×	body	128	invalid
117.0ms	197×	body	1024	invalid
93.0ms	232×	body	512	invalid
84.0ms	307×	body	256	valid
46.0ms	176×	body	256	invalid
3.0ms	3×	body	2048	valid

Compiler

Compiled 50 to 32 computations (36% saved)

simplify54.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

851×	`fma-def_binary64`
522×	`unswap-sqr_binary64`
335×	`fma-neg_binary64`
256×	`associate-l_binary64`
216×	`associate-r_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	20
1	19	16
2	28	16
3	56	16
4	119	16
5	280	16
6	672	16
7	2284	16
8	4398	16
9	4953	16

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

6.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	6.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))

Compiler

Compiled 55 to 31 computations (43.6% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
✓	0.0b	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
✓	0.0b	(/.f64 y (+.f64 y z))
✓	6.3b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series189.0ms (2.7%)

Counts

4 → 108

Calls

4 calls:

97.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
51.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
32.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
8.0ms	(/.f64 y (+.f64 y z))

rewrite51.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

138×	`times-frac_binary64`
122×	`*-un-lft-identity_binary64`
90×	`unpow-prod-down_binary64`
82×	`add-sqr-sqrt_binary64`
82×	`add-cube-cbrt_binary64`

Counts

4 → 195

Calls

4 calls:

17.0ms	(+.f64 x (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
11.0ms	(/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)
5.0ms	(pow.f64 (/.f64 y (+.f64 y z)) y)
3.0ms	(/.f64 y (+.f64 y z))

simplify157.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

385×	`fma-def_binary64`
358×	`times-frac_binary64`
355×	`associate-/l*_binary64`
264×	`associate-/r*_binary64`
248×	`associate-r_binary64`

Counts

303 → 430

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	612	9531
1	1653	9295
2	5034	9295

prune284.0ms (4%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	426	4	430
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	427	4	431

Error

Counts

431 → 4

Alt Table

Status	Error	Program
	6.5b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))
	40.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) y)
	10.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
▶	1.9b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 12615 to 4727 computations (62.5% saved)

localize3.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 1 y))

series4.0ms (0.1%)

Counts

1 → 24

Calls

1 calls:

4.0ms

(+.f64 x (/.f64 1 y))

rewrite5.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`*-un-lft-identity_binary64`
3×	`add-log-exp_binary64`
3×	`fma-def_binary64`
2×	`distribute-lft-out_binary64`
2×	`add-sqr-sqrt_binary64`

Counts

1 → 18

Calls

1 calls:

4.0ms

(+.f64 x (/.f64 1 y))

simplify102.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

572×	`unswap-sqr_binary64`
448×	`fma-neg_binary64`
321×	`fma-def_binary64`
284×	`distribute-rgt-in_binary64`
282×	`associate-+l+_binary64`

Counts

42 → 28

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	30	322
1	88	302
2	189	299
3	419	299
4	1068	299
5	2246	299
6	3475	299
7	4871	299
8	4894	299
9	4906	299

prune15.0ms (0.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	28	0	28
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	28	4	32

Error

Counts

32 → 4

Alt Table

Status	Error	Program
▶	6.5b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))
	40.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) y)
	10.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	1.9b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 418 to 252 computations (39.7% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))
✓	0.4b	(*.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))
✓	0.5b	(cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))
	6.3b	(pow.f64 (/.f64 y (+.f64 y z)) y)

series248.0ms (3.5%)

Counts

3 → 72

Calls

3 calls:

126.0ms

(*.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))

75.0ms

(cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))

47.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))

rewrite268.0ms (3.8%)

Algorithm

1×	rewrite-expression-head

Rules

749×	`times-frac_binary64`
521×	`cbrt-prod_binary64`
494×	`*-un-lft-identity_binary64`
462×	`add-sqr-sqrt_binary64`
386×	`unpow-prod-down_binary64`

Counts

3 → 493

Calls

3 calls:

77.0ms

(*.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))

43.0ms

(*.f64 (*.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)))

7.0ms

(cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))

simplify435.0ms (6.2%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-def_binary64`
538×	`times-frac_binary64`
453×	`*-commutative_binary64`
176×	`sqr-pow_binary64`
146×	`+-commutative_binary64`

Counts

565 → 787

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	1264	29639
1	3129	28160
2	5053	28160

prune965.0ms (13.7%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	1372	0	1372
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	1372	4	1376

Error

Counts

1376 → 4

Alt Table

Status	Error	Program
✓	6.5b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))
	40.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) y)
▶	10.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	1.9b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 78159 to 21227 computations (72.8% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	0.2b	(/.f64 (exp.f64 (neg.f64 z)) y)

series17.0ms (0.2%)

Counts

2 → 44

Calls

2 calls:

10.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
7.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`
9×	`times-frac_binary64`
4×	`add-cbrt-cube_binary64`

Counts

2 → 48

Calls

2 calls:

6.0ms	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
3.0ms	(/.f64 (exp.f64 (neg.f64 z)) y)

simplify90.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

559×	`associate-/l*_binary64`
517×	`fma-neg_binary64`
466×	`fma-def_binary64`
340×	`associate-/l/_binary64`
311×	`associate-*l/_binary64`

Counts

92 → 81

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	105	1172
1	240	1134
2	585	1126
3	1543	1124
4	4396	1117
5	4890	1117
6	4978	1117

prune44.0ms (0.6%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	81	0	81
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	81	4	85

Error

Counts

85 → 4

Alt Table

Status	Error	Program
✓	6.5b	(+.f64 x (.f64 (.f64 (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y)) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))) (cbrt.f64 (/.f64 (pow.f64 (/.f64 y (+.f64 y z)) y) y))))
	40.0b	(/.f64 (pow.f64 (/.f64 y (+.f64 z y)) y) y)
✓	10.6b	(+.f64 x (/.f64 (exp.f64 (neg.f64 z)) y))
✓	1.9b	(+.f64 x (/.f64 1 y))

Compiler

Compiled 1182 to 394 computations (66.7% saved)

regimes366.0ms (5.2%)

Accuracy

Total 0.8b remaining (97.9%)

Threshold costs 0.8b (97.9%)

Counts

65 → 2

Compiler

Compiled 8712 to 4367 computations (49.9% saved)

bsearch23.0ms (0.3%)

Steps

Iters	Range		Point
6	1.0897341147356067e-10	1.2732691848043923e-5	1.0730363162252807e-5

Compiler

Compiled 4 to 3 computations (25% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	24
1	22	24
2	24	24
3	25	24
4	24	24

end54.0ms (0.8%)

Compiler: Compiled 105 to 57 computations (45.7% saved)

Details

analyze1.2s (17%)

sample2.4s (34.4%)

simplify54.0ms (0.8%)

prune3.0ms (0%)

localize7.0ms (0.1%)

series189.0ms (2.7%)

rewrite51.0ms (0.7%)

simplify157.0ms (2.2%)

prune284.0ms (4%)

localize3.0ms (0%)

series4.0ms (0.1%)

rewrite5.0ms (0.1%)

simplify102.0ms (1.5%)

prune15.0ms (0.2%)

localize10.0ms (0.1%)

series248.0ms (3.5%)

rewrite268.0ms (3.8%)

simplify435.0ms (6.2%)

prune965.0ms (13.7%)

localize5.0ms (0.1%)

series17.0ms (0.2%)

rewrite11.0ms (0.2%)

simplify90.0ms (1.3%)

prune44.0ms (0.6%)

regimes366.0ms (5.2%)

bsearch23.0ms (0.3%)

simplify2.0ms (0%)

end54.0ms (0.8%)

Profiling