Details

analyze1.2s (23.4%)

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
0%	99.8%	0.2%	10
10.1%	89.6%	0.2%	11
15.2%	84.6%	0.2%	12
20.5%	79.3%	0.2%	13
21.6%	77.1%	1.3%	14

Compiler

Compiled 15 to 10 computations (33.3% saved)

sample1.4s (28.7%)

Results

1.1s	8256×	body	128	valid
334.0ms	2637×	body	128	invalid

Compiler

Compiled 44 to 29 computations (34.1% saved)

simplify53.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

944×	`fma-def_binary64`
719×	`fma-neg_binary64`
235×	`cancel-sign-sub-inv_binary64`
165×	`distribute-rgt-in_binary64`
116×	`distribute-lft-in_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	13
1	16	13
2	31	11
3	65	11
4	151	11
5	315	11
6	546	11
7	973	11
8	1854	11
9	2736	11
10	3572	11
11	3748	11
12	3793	11
13	3838	11
14	3838	11

Stop Event

1×

saturated

Counts

1 → 2

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	6.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
▶	3.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))

Compiler

Compiled 76 to 45 computations (40.8% saved)

localize6.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	0.0b	(*.f64 y (-.f64 z t))
✓	4.7b	(/.f64 (*.f64 y (-.f64 z t)) a)

series83.0ms (1.7%)

Counts

3 → 144

Calls

3 calls:

59.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
19.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)
6.0ms	(*.f64 y (-.f64 z t))

rewrite61.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

370×	`fma-def_binary64`
218×	`expm1-udef_binary64`
218×	`log1p-udef_binary64`
199×	`fma-neg_binary64`
190×	`log-pow_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	10	30
1	225	30
2	3394	28

Stop Event

1×	node limit

Counts

3 → 132

Calls

3 calls:

59.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
59.0ms	(*.f64 y (-.f64 z t))
59.0ms	(/.f64 (*.f64 y (-.f64 z t)) a)

simplify171.0ms (3.4%)

Algorithm

1×	egg-herbie

Rules

707×	`fma-neg_binary64`
576×	`fma-def_binary64`
227×	`cancel-sign-sub-inv_binary64`
147×	`distribute-rgt-in_binary64`
140×	`unsub-neg_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	32	1660
1	81	1390
2	187	1388
3	442	1298
4	921	1298
5	1647	1298
6	2778	1298
7	3392	1298
8	3513	1298
9	3536	1298
10	3541	1298
11	3545	1298

Stop Event

1×

saturated

Counts

276 → 156

prune111.0ms (2.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	151	5	156
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	151	7	158

Error

0.0b

Counts

158 → 7

Alt Table

Status	Error	Program
	3.7b	(fma.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a) x)
	5.5b	(+.f64 x (pow.f64 (/.f64 (/.f64 a (-.f64 z t)) y) -1))
✓	3.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
▶	2.1b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	4.6b	(+.f64 x (*.f64 (/.f64 (-.f64 z t) (pow.f64 (cbrt.f64 a) 2)) (/.f64 y (cbrt.f64 a))))
	6.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	4.2b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 y (-.f64 z t))) 2) (.f64 (cbrt.f64 (*.f64 y (-.f64 z t))) (/.f64 1 a)) x)

Compiler

Compiled 2430 to 767 computations (68.4% saved)

localize6.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(fma.f64 (/.f64 y a) (-.f64 z t) x)

series35.0ms (0.7%)

Counts

1 → 60

Calls

1 calls:

35.0ms

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

rewrite77.0ms (1.5%)

Algorithm

1×	batch-egg-rewrite

Rules

499×	`log-prod_binary64`
446×	`prod-diff_binary64`
202×	`fma-def_binary64`
188×	`expm1-udef_binary64`
188×	`log1p-udef_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	11
1	194	11
2	2698	11

Stop Event

1×	node limit

Counts

1 → 29

Calls

1 calls:

76.0ms

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

simplify76.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
690×	`fma-neg_binary64`
199×	`cancel-sign-sub-inv_binary64`
102×	`div-sub_binary64`
93×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	964
1	58	694
2	135	680
3	311	590
4	620	590
5	1070	590
6	1844	590
7	2933	590
8	3274	590
9	3310	590
10	3340	590
11	3345	590
12	3345	590

Stop Event

1×

saturated

Counts

89 → 45

prune28.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	45	0	45
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	45	7	52

Error

0.0b

Counts

52 → 7

Alt Table

Status	Error	Program
▶	3.7b	(fma.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a) x)
	5.5b	(+.f64 x (pow.f64 (/.f64 (/.f64 a (-.f64 z t)) y) -1))
✓	3.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	2.1b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	4.6b	(+.f64 x (*.f64 (/.f64 (-.f64 z t) (pow.f64 (cbrt.f64 a) 2)) (/.f64 y (cbrt.f64 a))))
	6.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
	4.2b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 y (-.f64 z t))) 2) (.f64 (cbrt.f64 (*.f64 y (-.f64 z t))) (/.f64 1 a)) x)

Compiler

Compiled 759 to 255 computations (66.4% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
	0.0b	(*.f64 y (-.f64 z t))
✓	3.5b	(fma.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a) x)

series30.0ms (0.6%)

Counts

1 → 60

Calls

1 calls:

30.0ms

(fma.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a) x)

rewrite44.0ms (0.9%)

Algorithm

1×	batch-egg-rewrite

Rules

433×	`prod-diff_binary64`
210×	`fma-def_binary64`
206×	`expm1-udef_binary64`
206×	`log1p-udef_binary64`
185×	`log-pow_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	14
1	227	13
2	2899	13

Stop Event

1×	node limit

Counts

1 → 26

Calls

1 calls:

43.0ms

(fma.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a) x)

simplify75.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

704×	`fma-def_binary64`
690×	`fma-neg_binary64`
200×	`cancel-sign-sub-inv_binary64`
102×	`div-sub_binary64`
94×	`associate-r_binary64`

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	25	964
1	58	694
2	135	680
3	311	590
4	620	590
5	1074	590
6	1853	590
7	2937	590
8	3277	590
9	3313	590
10	3343	590
11	3348	590
12	3348	590

Stop Event

1×

saturated

Counts

86 → 42

prune45.0ms (0.9%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	71	0	71
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	71	7	78

Error

0.0b

Counts

78 → 7

Alt Table

Status	Error	Program
✓	3.7b	(fma.f64 (*.f64 y (-.f64 z t)) (/.f64 1 a) x)
	5.5b	(+.f64 x (pow.f64 (/.f64 (/.f64 a (-.f64 z t)) y) -1))
✓	3.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	2.1b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	4.6b	(+.f64 x (*.f64 (/.f64 (-.f64 z t) (pow.f64 (cbrt.f64 a) 2)) (/.f64 y (cbrt.f64 a))))
	6.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
▶	4.2b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 y (-.f64 z t))) 2) (.f64 (cbrt.f64 (*.f64 y (-.f64 z t))) (/.f64 1 a)) x)

Compiler

Compiled 1085 to 405 computations (62.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (cbrt.f64 (.f64 y (-.f64 z t))) (/.f64 1 a))
✓	0.5b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 y (-.f64 z t))) 2) (.f64 (cbrt.f64 (*.f64 y (-.f64 z t))) (/.f64 1 a)) x)
✓	0.5b	(pow.f64 (cbrt.f64 (*.f64 y (-.f64 z t))) 2)
✓	6.7b	(cbrt.f64 (*.f64 y (-.f64 z t)))

series477.0ms (9.5%)

Counts

4 → 75

Calls

4 calls:

248.0ms	(fma.f64 (pow.f64 (cbrt.f64 (.f64 y (-.f64 z t))) 2) (.f64 (cbrt.f64 (*.f64 y (-.f64 z t))) (/.f64 1 a)) x)
104.0ms	(pow.f64 (cbrt.f64 (*.f64 y (-.f64 z t))) 2)
87.0ms	(.f64 (cbrt.f64 (.f64 y (-.f64 z t))) (/.f64 1 a))
39.0ms	(cbrt.f64 (*.f64 y (-.f64 z t)))

rewrite61.0ms (1.2%)

Algorithm

1×	batch-egg-rewrite

Rules

445×	`prod-diff_binary64`
260×	`log1p-udef_binary64`
151×	`add-sqr-sqrt_binary64`
143×	`log1p-expm1-u_binary64`
143×	`expm1-log1p-u_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	60
1	312	46
2	3844	46

Stop Event

1×	node limit

Counts

4 → 99

Calls

4 calls:

59.0ms	(.f64 (cbrt.f64 (.f64 y (-.f64 z t))) (/.f64 1 a))
59.0ms	(fma.f64 (pow.f64 (cbrt.f64 (.f64 y (-.f64 z t))) 2) (.f64 (cbrt.f64 (*.f64 y (-.f64 z t))) (/.f64 1 a)) x)
59.0ms	(pow.f64 (cbrt.f64 (*.f64 y (-.f64 z t))) 2)
59.0ms	(cbrt.f64 (*.f64 y (-.f64 z t)))

simplify59.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

506×	`cancel-sign-sub-inv_binary64`
392×	`times-frac_binary64`
293×	`unswap-sqr_binary64`
248×	`fma-neg_binary64`
234×	`associate-r_binary64`

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	247	2884
1	773	2698
2	2749	2697

Stop Event

1×	node limit

Counts

174 → 170

prune186.0ms (3.7%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	212	2	214
Fresh	1	2	3
Picked	0	1	1
Done	1	2	3
Total	214	7	221

Error

Counts

221 → 7

Alt Table

Status	Error	Program
✓	3.6b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) a))
✓	2.1b	(fma.f64 (/.f64 y a) (-.f64 z t) x)
	5.5b	(+.f64 x (/.f64 y (/.f64 a (-.f64 z t))))
	4.9b	(fma.f64 (pow.f64 (cbrt.f64 (*.f64 y (-.f64 z t))) 2) (/.f64 (cbrt.f64 y) (/.f64 a (cbrt.f64 (-.f64 z t)))) x)
	4.6b	(+.f64 x (*.f64 (/.f64 (-.f64 z t) (pow.f64 (cbrt.f64 a) 2)) (/.f64 y (cbrt.f64 a))))
	6.1b	(fma.f64 y (/.f64 (-.f64 z t) a) x)
✓	4.2b	(fma.f64 (pow.f64 (cbrt.f64 (.f64 y (-.f64 z t))) 2) (.f64 (cbrt.f64 (*.f64 y (-.f64 z t))) (/.f64 1 a)) x)

Compiler

Compiled 7258 to 3711 computations (48.9% saved)

regimes602.0ms (12%)

Accuracy

Total 1.2b remaining (99%)

Threshold costs 0b (0%)

Counts

47 → 3

Compiler

Compiled 6886 to 4484 computations (34.9% saved)

bsearch2.0ms (0%)

Compiler: Compiled 10 to 7 computations (30% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	25	66
1	32	66
2	36	66
3	38	66
4	39	66

Stop Event

1×

saturated

end95.0ms (1.9%)

Compiler: Compiled 223 to 122 computations (45.3% saved)

Details

analyze1.2s (23.4%)

sample1.4s (28.7%)

simplify53.0ms (1.1%)

prune3.0ms (0.1%)

localize6.0ms (0.1%)

series83.0ms (1.7%)

rewrite61.0ms (1.2%)

simplify171.0ms (3.4%)

prune111.0ms (2.2%)

localize6.0ms (0.1%)

series35.0ms (0.7%)

rewrite77.0ms (1.5%)

simplify76.0ms (1.5%)

prune28.0ms (0.6%)

localize7.0ms (0.1%)

series30.0ms (0.6%)

rewrite44.0ms (0.9%)

simplify75.0ms (1.5%)

prune45.0ms (0.9%)

localize12.0ms (0.2%)

series477.0ms (9.5%)

rewrite61.0ms (1.2%)

simplify59.0ms (1.2%)

prune186.0ms (3.7%)

regimes602.0ms (12%)

bsearch2.0ms (0%)

simplify4.0ms (0.1%)

end95.0ms (1.9%)

Profiling