Details

analyze1.7s (21.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
1.8%	98%	0.3%	13
2.4%	97.3%	0.3%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample38.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
6.0ms	120×	body	128	invalid

Compiler

Compiled 49 to 33 computations (32.7% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

89×	`fma-def_binary64`
24×	`associate-+l+_binary64`
22×	`associate-+r+_binary64`
19×	`+-commutative_binary64`
10×	`*-commutative_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	14	22
1	27	16
2	66	15
3	122	13
4	157	13
5	164	13
6	167	13
7	167	13

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	3.6b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
▶	2.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))

Compiler

Compiled 105 to 60 computations (42.9% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
✓	0.0b	(+.f64 x (*.f64 y z))
✓	0.0b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	6.0b	(.f64 (.f64 a z) b)

series54.0ms (0.7%)

Counts

4 → 204

Calls

4 calls:

24.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
14.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
11.0ms	(.f64 (.f64 a z) b)
5.0ms	(+.f64 x (*.f64 y z))

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-log-exp_binary64`
10×	`sum-log_binary64`
9×	`fma-def_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`

Counts

4 → 73

Calls

4 calls:

7.0ms	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
4.0ms	(+.f64 (+.f64 x (.f64 y z)) (.f64 t a))
4.0ms	(.f64 (.f64 a z) b)
2.0ms	(+.f64 x (*.f64 y z))

simplify82.0ms (1%)

Algorithm

1×	egg-herbie

Rules

846×	`fma-def_binary64`
720×	`distribute-rgt-in_binary64`
683×	`distribute-lft-in_binary64`
194×	`cancel-sign-sub-inv_binary64`
192×	`fma-neg_binary64`

Counts

277 → 134

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	135	2855
1	406	2550
2	1474	2538
3	5045	2538

prune87.0ms (1.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	132	2	134
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	132	4	136

Error

0.0b

Counts

136 → 4

Alt Table

Status	Error	Program
▶	2.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	3.6b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
	2.7b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 (.f64 a z) b))))

Compiler

Compiled 2775 to 527 computations (81% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	2.1b	(fma.f64 z (fma.f64 a b y) x)

series42.0ms (0.5%)

Counts

2 → 132

Calls

2 calls:

23.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
19.0ms	(fma.f64 z (fma.f64 a b y) x)

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 20

Calls

2 calls:

0.0ms	(fma.f64 z (fma.f64 a b y) x)
0.0ms	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))

simplify122.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

576×	`fma-def_binary64`
520×	`associate-+r+_binary64`
505×	`associate-l_binary64`
470×	`associate-+l+_binary64`
444×	`associate-r_binary64`

Counts

152 → 52

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	56	1796
1	103	1579
2	236	1579
3	906	1579
4	3548	1579
5	3771	1579
6	4661	1579
7	4888	1579
8	4888	1579

prune35.0ms (0.4%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	52	0	52
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	52	4	56

Error

0.0b

Counts

56 → 4

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
	3.6b	(fma.f64 y z (fma.f64 a (fma.f64 z b t) x))
✓	2.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
▶	2.7b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 (.f64 a z) b))))

Compiler

Compiled 769 to 188 computations (75.6% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 (.f64 a z) b)))
✓	0.5b	(.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (*.f64 a z) b)))
	6.0b	(.f64 (.f64 a z) b)
✓	16.1b	(cbrt.f64 (.f64 (.f64 a z) b))

series2.3s (29.3%)

Counts

3 → 108

Calls

3 calls:

1.5s

(*.f64 (cbrt.f64 (*.f64 (*.f64 a z) b)) (cbrt.f64 (*.f64 (*.f64 a z) b)))

718.0ms

(cbrt.f64 (*.f64 (*.f64 a z) b))

49.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 a z) b)) (cbrt.f64 (*.f64 (*.f64 a z) b))) (cbrt.f64 (*.f64 (*.f64 a z) b)))

rewrite18.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`pow1_binary64`
16×	`pow1/3_binary64`
11×	`pow-prod-up_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`

Counts

3 → 79

Calls

3 calls:

7.0ms

(*.f64 (*.f64 (cbrt.f64 (*.f64 (*.f64 a z) b)) (cbrt.f64 (*.f64 (*.f64 a z) b))) (cbrt.f64 (*.f64 (*.f64 a z) b)))

4.0ms

(*.f64 (cbrt.f64 (*.f64 (*.f64 a z) b)) (cbrt.f64 (*.f64 (*.f64 a z) b)))

2.0ms

(cbrt.f64 (*.f64 (*.f64 a z) b))

simplify93.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

759×	`unswap-sqr_binary64`
382×	`fma-neg_binary64`
331×	`exp-sum_binary64`
303×	`exp-prod_binary64`
266×	`*-commutative_binary64`

Counts

187 → 135

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	176	3166
1	391	2882
2	923	2340
3	2431	2074
4	5682	2074

prune253.0ms (3.2%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	277	2	279
Fresh	1	0	1
Picked	0	1	1
Done	0	2	2
Total	278	5	283

Error

Counts

283 → 5

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
▶	2.7b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 a z))) (cbrt.f64 b)))
✓	2.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	2.7b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 (.f64 a z) b))))
	2.7b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 a z) b)))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 a z) b))))))

Compiler

Compiled 9720 to 1580 computations (83.7% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.9b	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 a z))) (cbrt.f64 b))
	6.0b	(.f64 (.f64 a z) b)
✓	13.6b	(cbrt.f64 (*.f64 a z))
	16.1b	(cbrt.f64 (.f64 (.f64 a z) b))

series452.0ms (5.8%)

Counts

2 → 60

Calls

2 calls:

400.0ms	(cbrt.f64 (*.f64 a z))
52.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 a z))) (cbrt.f64 b))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-exp-log_binary64`
11×	`pow1_binary64`
9×	`pow-prod-down_binary64`
6×	`associate-r_binary64`
6×	`cbrt-unprod_binary64`

Counts

2 → 38

Calls

2 calls:

9.0ms	(.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 a z))) (cbrt.f64 b))
2.0ms	(cbrt.f64 (*.f64 a z))

simplify108.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

626×	`fma-def_binary64`
438×	`unswap-sqr_binary64`
368×	`*-commutative_binary64`
364×	`fma-neg_binary64`
206×	`exp-sum_binary64`

Counts

98 → 60

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	104	1507
1	223	1499
2	738	1360
3	1234	1248
4	1883	886
5	3933	886
6	4885	886
7	5039	886

prune236.0ms (3%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	176	0	176
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	176	5	181

Error

Counts

181 → 5

Alt Table

Status	Error	Program
✓	2.3b	(fma.f64 a t (fma.f64 z (fma.f64 a b y) x))
✓	2.7b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 a z))) (cbrt.f64 b)))
✓	2.5b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 a z) b))
✓	2.7b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (.f64 (.f64 a z) b))))
	2.7b	(+.f64 (+.f64 (+.f64 x (.f64 y z)) (.f64 t a)) (.f64 (.f64 (cbrt.f64 (.f64 (.f64 a z) b)) (cbrt.f64 (.f64 (.f64 a z) b))) (.f64 (.f64 (cbrt.f64 (cbrt.f64 (.f64 (.f64 a z) b))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 a z) b)))) (cbrt.f64 (cbrt.f64 (.f64 (.f64 a z) b))))))

Compiler

Compiled 6387 to 1130 computations (82.3% saved)

regimes768.0ms (9.8%)

Accuracy

Total 1.0b remaining (98.4%)

Threshold costs 0b (0%)

Counts

73 → 2

Compiler

Compiled 12733 to 7441 computations (41.6% saved)

bsearch5.0ms (0.1%)

Steps

Iters	Range		Point
1	-9.294820110798861e+52	-2.801854185560118e+52	-5.054739958356597e+52

Compiler

Compiled 7 to 6 computations (14.3% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`
3×	`+-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	21	41
1	28	41
2	28	41

end1.0ms (0%)

Compiler: Compiled 35 to 19 computations (45.7% saved)

sample1.4s (17.4%)

Algorithm

1×

intervals

Results

468.0ms	8000×	body	128	valid
226.0ms	3882×	body	128	invalid

Compiler

Compiled 226 to 115 computations (49.1% saved)

Details

analyze1.7s (21.5%)

sample38.0ms (0.5%)

simplify9.0ms (0.1%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series54.0ms (0.7%)

rewrite20.0ms (0.3%)

simplify82.0ms (1%)

prune87.0ms (1.1%)

localize8.0ms (0.1%)

series42.0ms (0.5%)

rewrite1.0ms (0%)

simplify122.0ms (1.6%)

prune35.0ms (0.4%)

localize16.0ms (0.2%)

series2.3s (29.3%)

rewrite18.0ms (0.2%)

simplify93.0ms (1.2%)

prune253.0ms (3.2%)

localize17.0ms (0.2%)

series452.0ms (5.8%)

rewrite13.0ms (0.2%)

simplify108.0ms (1.4%)

prune236.0ms (3%)

regimes768.0ms (9.8%)

bsearch5.0ms (0.1%)

simplify3.0ms (0%)

end1.0ms (0%)

sample1.4s (17.4%)

Profiling