Details

analyze72.0ms (3.1%)

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
25%	74.9%	0.1%	5
37.5%	50%	12.6%	6
50%	37.5%	12.6%	7
56.2%	25%	18.8%	8
62.4%	18.7%	18.8%	9
65.6%	12.5%	22%	10
68.7%	9.4%	22%	11
70.2%	6.2%	23.5%	12
71.8%	4.7%	23.5%	13
72.6%	3.1%	24.3%	14

Compiler

Compiled 10 to 7 computations (30% saved)

sample46.0ms (2%)

Algorithm

1×

intervals

Results

7.0ms	256×	body	128	valid
0.0ms	5×	body	128	invalid

Compiler

Compiled 21 to 15 computations (28.6% saved)

simplify19.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

265×	`fma-def_binary64`
84×	`fma-neg_binary64`
35×	`distribute-rgt-in_binary64`
26×	`unsub-neg_binary64`
25×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

prune1.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

0.1b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

Compiler

Compiled 27 to 18 computations (33.3% saved)

localize4.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 1 (*.f64 x y))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))

series9.0ms (0.4%)

Counts

2 → 48

Calls

2 calls:

6.0ms	(.f64 x (-.f64 1 (.f64 x y)))
3.0ms	(-.f64 1 (*.f64 x y))

rewrite10.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`prod-diff_binary64`
8×	`*-un-lft-identity_binary64`
8×	`add-cube-cbrt_binary64`
5×	`distribute-lft-in_binary64`

Counts

2 → 52

Calls

2 calls:

5.0ms	(.f64 x (-.f64 1 (.f64 x y)))
2.0ms	(-.f64 1 (*.f64 x y))

simplify86.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

1016×	`fma-def_binary64`
587×	`unsub-neg_binary64`
328×	`associate-l_binary64`
293×	`unswap-sqr_binary64`
278×	`*-commutative_binary64`

Counts

100 → 81

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	81	1128
1	162	1037
2	490	982
3	1467	953
4	3061	953
5	4899	953
6	4821	953

prune65.0ms (2.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	75	6	81
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	7	82

Error

Counts

82 → 7

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	6.5b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	11.7b	(.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 1 (.f64 x y)) (-.f64 1 (.f64 x y))) (-.f64 1 (.f64 x y)))))
	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
▶	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	13.2b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))

Compiler

Compiled 1300 to 614 computations (52.8% saved)

localize13.0ms (0.5%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 1 1 (neg.f64 (*.f64 y x)))
✓	0.1b	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
✓	51.5b	(fma.f64 (neg.f64 y) x (*.f64 y x))

series19.0ms (0.8%)

Counts

3 → 72

Calls

3 calls:

9.0ms	(fma.f64 (neg.f64 y) x (*.f64 y x))
6.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
4.0ms	(fma.f64 1 1 (neg.f64 (*.f64 y x)))

rewrite5.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-sqr-sqrt_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-cube-cbrt_binary64`
5×	`add-cbrt-cube_binary64`
5×	`add-exp-log_binary64`

Counts

3 → 40

Calls

3 calls:

3.0ms	(.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x)
0.0ms	(fma.f64 (neg.f64 y) x (*.f64 y x))
0.0ms	(fma.f64 1 1 (neg.f64 (*.f64 y x)))

simplify98.0ms (4.2%)

Algorithm

1×	egg-herbie

Rules

820×	`fma-def_binary64`
640×	`distribute-rgt-in_binary64`
588×	`distribute-lft-in_binary64`
390×	`distribute-neg-out_binary64`
241×	`associate-l_binary64`

Counts

112 → 80

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	62	907
1	108	825
2	295	777
3	922	777
4	3226	777
5	4767	777
6	4999	777
7	4815	777

prune68.0ms (2.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	80	0	80
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	80	7	87

Error

Counts

87 → 7

Alt Table

Status	Error	Program
	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	6.5b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	11.7b	(.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 1 (.f64 x y)) (-.f64 1 (.f64 x y))) (-.f64 1 (.f64 x y)))))
▶	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	13.2b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))

Compiler

Compiled 2026 to 737 computations (63.6% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
✓	0.5b	(.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (*.f64 x y)))))
✓	0.6b	(cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))

series89.0ms (3.8%)

Counts

3 → 72

Calls

3 calls:

42.0ms

(*.f64 (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))) (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))))

29.0ms

(cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y))))

16.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))) (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y))))) (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))))

rewrite33.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`associate-*r/_binary64`
68×	`cbrt-div_binary64`
34×	`flip--_binary64`
34×	`flip3--_binary64`
32×	`frac-times_binary64`

Counts

3 → 115

Calls

3 calls:

8.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))) (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y))))) (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))))

5.0ms

(*.f64 (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))) (cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y)))))

3.0ms

(cbrt.f64 (*.f64 x (-.f64 1 (*.f64 x y))))

simplify143.0ms (6.1%)

Algorithm

1×	egg-herbie

Rules

734×	`cancel-sign-sub-inv_binary64`
304×	`associate-/r*_binary64`
208×	`associate-l_binary64`
192×	`sub-neg_binary64`
192×	`times-frac_binary64`

Counts

187 → 247

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	330	6638
1	922	6109
2	3303	5782
3	5086	5782

prune401.0ms (17.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	524	0	524
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	524	7	531

Error

Counts

531 → 7

Alt Table

Status	Error	Program
▶	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	6.5b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	11.7b	(.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 1 (.f64 x y)) (-.f64 1 (.f64 x y))) (-.f64 1 (.f64 x y)))))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	13.2b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))

Compiler

Compiled 21613 to 11942 computations (44.7% saved)

localize9.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
✓	0.3b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
✓	0.6b	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
✓	0.6b	(cbrt.f64 x)

series157.0ms (6.7%)

Counts

4 → 72

Calls

4 calls:

66.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
39.0ms	(cbrt.f64 x)
36.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
16.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))

rewrite29.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-sqr-sqrt_binary64`
25×	`distribute-lft-in_binary64`
25×	`distribute-rgt-in_binary64`
25×	`pow1_binary64`
23×	`cbrt-prod_binary64`

Counts

4 → 137

Calls

4 calls:

10.0ms	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
5.0ms	(.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y)))
4.0ms	(*.f64 (cbrt.f64 x) (cbrt.f64 x))
1.0ms	(cbrt.f64 x)

simplify137.0ms (5.8%)

Algorithm

1×	egg-herbie

Rules

500×	`exp-prod_binary64`
419×	`fma-neg_binary64`
398×	`fma-def_binary64`
345×	`associate-l_binary64`
291×	`distribute-rgt-in_binary64`

Counts

209 → 195

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	168	2627
1	348	2339
2	1356	2193
3	3351	2063
4	4202	1965
5	4737	1965
6	4598	1965

prune100.0ms (4.3%)

Pruning

7 alts after pruning (3 fresh and 4 done)

	Pruned	Kept	Total
New	231	0	231
Fresh	0	3	3
Picked	0	1	1
Done	0	3	3
Total	231	7	238

Error

Counts

238 → 7

Alt Table

Status	Error	Program
✓	1.4b	(.f64 (.f64 (cbrt.f64 x) (cbrt.f64 x)) (.f64 (cbrt.f64 x) (-.f64 1 (.f64 x y))))
	6.5b	(-.f64 x (*.f64 y (pow.f64 x 2)))
	11.7b	(.f64 x (cbrt.f64 (.f64 (.f64 (-.f64 1 (.f64 x y)) (-.f64 1 (.f64 x y))) (-.f64 1 (.f64 x y)))))
✓	1.4b	(.f64 (.f64 (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y))))) (cbrt.f64 (.f64 x (-.f64 1 (.f64 x y)))))
✓	0.1b	(.f64 x (-.f64 1 (.f64 x y)))
✓	0.1b	(+.f64 (.f64 (fma.f64 1 1 (neg.f64 (.f64 y x))) x) (.f64 (fma.f64 (neg.f64 y) x (.f64 y x)) x))
	13.2b	(.f64 (.f64 x (sqrt.f64 (-.f64 1 (.f64 x y)))) (sqrt.f64 (-.f64 1 (.f64 x y))))

Compiler

Compiled 4740 to 1712 computations (63.9% saved)

regimes222.0ms (9.4%)

Accuracy

Total 0.1b remaining (75.3%)

Threshold costs 0.1b (75.3%)

Counts

73 → 1

Compiler

Compiled 4276 to 2566 computations (40% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

6×	`*-commutative_binary64`
5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`distribute-rgt-neg-in_binary64`
4×	`neg-sub0_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	8	10
1	17	10
2	26	10
3	37	10
4	43	10
5	46	10
6	47	10
7	46	10

end0.0ms (0%)

Compiler: Compiled 9 to 5 computations (44.4% saved)

sample502.0ms (21.3%)

Algorithm

1×

intervals

Results

220.0ms	8000×	body	128	valid
2.0ms	91×	body	128	invalid

Compiler

Compiled 143 to 88 computations (38.5% saved)

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10

Details

analyze72.0ms (3.1%)

sample46.0ms (2%)

simplify19.0ms (0.8%)

prune1.0ms (0.1%)

localize4.0ms (0.2%)

series9.0ms (0.4%)

rewrite10.0ms (0.4%)

simplify86.0ms (3.7%)

prune65.0ms (2.8%)

localize13.0ms (0.5%)

series19.0ms (0.8%)

rewrite5.0ms (0.2%)

simplify98.0ms (4.2%)

prune68.0ms (2.9%)

localize9.0ms (0.4%)

series89.0ms (3.8%)

rewrite33.0ms (1.4%)

simplify143.0ms (6.1%)

prune401.0ms (17.1%)

localize9.0ms (0.4%)

series157.0ms (6.7%)

rewrite29.0ms (1.2%)

simplify137.0ms (5.8%)

prune100.0ms (4.3%)

regimes222.0ms (9.4%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample502.0ms (21.3%)

Profiling

Iter	Nodes	Cost
0	7	10
1	16	10
2	31	10
3	63	10
4	134	10
5	183	10
6	236	10
7	328	10
8	360	10
9	359	10
10	389	10
11	346	10