Details

analyze2.4s (16.4%)

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
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.4%	0.2%	12
12.2%	87.6%	0.2%	13
21.8%	77.8%	0.4%	14

Compiler

Compiled 19 to 12 computations (36.8% saved)

sample63.0ms (0.4%)

Algorithm

1×

intervals

Results

24.0ms	221×	body	128	valid
6.0ms	19×	body	512	valid
4.0ms	41×	body	128	invalid
3.0ms	7×	body	1024	valid
1.0ms	2×	body	2048	valid
1.0ms	7×	body	256	valid

Compiler

Compiled 42 to 28 computations (33.3% saved)

simplify116.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

836×	`unsub-neg_binary64`
769×	`fma-def_binary64`
696×	`div-sub_binary64`
646×	`sub-neg_binary64`
478×	`neg-mul-1_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	21	19
2	52	17
3	144	17
4	421	17
5	1092	17
6	2657	17
7	3901	17
8	4408	17
9	4807	17
10	4881	17

prune6.0ms (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

9.3b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	12.2b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	25.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))

Compiler

Compiled 100 to 55 computations (45% saved)

localize16.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
✓	12.1b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

rewrite33.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

13.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
1.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

series267.0ms (1.8%)

Counts

2 → 108

Calls

2 calls:

193.0ms	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
72.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

simplify246.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

523×	`cancel-sign-sub-inv_binary64`
479×	`sub-neg_binary64`
353×	`associate-+r+_binary64`
286×	`+-commutative_binary64`
272×	`associate-+l+_binary64`

Counts

172 → 294

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	356	6269
1	1045	6192
2	3851	6156
3	5233	6156

prune173.0ms (1.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	289	5	294
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	289	7	296

Error

0.5b

Counts

296 → 7

Alt Table

Status	Error	Program
▶	13.0b	(fma.f64 (-.f64 y z) (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	28.6b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	25.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	13.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	34.2b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	39.4b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
✓	12.2b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

Compiler

Compiled 4761 to 1446 computations (69.6% saved)

localize22.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	5.7b	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
	5.7b	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
✓	5.7b	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
✓	12.1b	(fma.f64 (-.f64 y z) (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) x)

rewrite18.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`*-un-lft-identity_binary64`
33×	`add-sqr-sqrt_binary64`
31×	`cbrt-prod_binary64`
25×	`times-frac_binary64`
13×	`add-cube-cbrt_binary64`

Counts

2 → 52

Calls

2 calls:

10.0ms

(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))

1.0ms

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

series850.0ms (5.7%)

Counts

2 → 108

Calls

2 calls:

517.0ms

(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))

332.0ms

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

simplify483.0ms (3.2%)

Algorithm

1×	egg-herbie

Rules

698×	`fma-def_binary64`
411×	`*-commutative_binary64`
271×	`+-commutative_binary64`
221×	`sub-neg_binary64`
208×	`associate-r_binary64`

Counts

160 → 284

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1125	13127
1	3879	12878
2	4997	12868
3	4991	12868

prune1.3s (8.7%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	736	1	737
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	736	8	744

Error

0.5b

Counts

744 → 8

Alt Table

Status	Error	Program
✓	13.0b	(fma.f64 (-.f64 y z) (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	28.6b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	25.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
	13.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	34.2b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
▶	12.8b	(fma.f64 (-.f64 y z) (.f64 (.f64 (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	39.4b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
✓	12.2b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

Compiler

Compiled 47950 to 21863 computations (54.4% saved)

localize32.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.6b	(cbrt.f64 (-.f64 t x))
	5.7b	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
	5.7b	(cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))
✓	12.1b	(fma.f64 (-.f64 y z) (.f64 (.f64 (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) x)

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`cbrt-prod_binary64`
5×	`*-un-lft-identity_binary64`
5×	`add-sqr-sqrt_binary64`
3×	`add-cube-cbrt_binary64`
2×	`cbrt-div_binary64`

Counts

2 → 27

Calls

2 calls:

4.0ms

(cbrt.f64 (-.f64 t x))

1.0ms

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

series311.0ms (2.1%)

Counts

2 → 84

Calls

2 calls:

265.0ms

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

46.0ms

(cbrt.f64 (-.f64 t x))

simplify288.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

398×	`associate-+r+_binary64`
327×	`+-commutative_binary64`
298×	`associate-+l+_binary64`
275×	`times-frac_binary64`
252×	`fma-neg_binary64`

Counts

111 → 203

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	435	5438
1	1298	5306
2	4806	5306
3	4985	5306

prune895.0ms (6%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	2015	0	2015
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	2015	8	2023

Error

0.5b

Counts

2023 → 8

Alt Table

Status	Error	Program
✓	13.0b	(fma.f64 (-.f64 y z) (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	28.6b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	25.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
▶	13.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	34.2b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
✓	12.8b	(fma.f64 (-.f64 y z) (.f64 (.f64 (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	39.4b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
✓	12.2b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

Compiler

Compiled 36187 to 15985 computations (55.8% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x))
	12.1b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	12.1b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)
	12.1b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

rewrite3.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`cbrt-prod_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-sqr-sqrt_binary64`
2×	`add-cube-cbrt_binary64`
1×	`add-cbrt-cube_binary64`

Counts

1 → 13

Calls

1 calls:

1.0ms

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

series2.6s (17.3%)

Counts

1 → 60

Calls

1 calls:

2.6s	(cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x))

simplify557.0ms (3.7%)

Algorithm

1×	egg-herbie

Rules

437×	`associate-r_binary64`
430×	`fma-def_binary64`
263×	`associate-/l*_binary64`
153×	`associate-*r/_binary64`
146×	`associate-*l/_binary64`

Counts

73 → 131

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	1832	27769
1	5012	27769

prune985.0ms (6.6%)

Pruning

9 alts after pruning (6 fresh and 3 done)

	Pruned	Kept	Total
New	1060	2	1062
Fresh	0	4	4
Picked	0	1	1
Done	1	2	3
Total	1061	9	1070

Error

0.5b

Counts

1070 → 9

Alt Table

Status	Error	Program
✓	13.0b	(fma.f64 (-.f64 y z) (.f64 (.f64 (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) (cbrt.f64 (/.f64 (-.f64 t x) (-.f64 a z)))) x)
	28.6b	(*.f64 t (-.f64 (/.f64 y (-.f64 a z)) (/.f64 z (-.f64 a z))))
	25.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) (-.f64 t x)) (-.f64 a z)))
✓	13.3b	(.f64 (.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	34.2b	(-.f64 (+.f64 (/.f64 (.f64 y x) z) (+.f64 t (/.f64 (.f64 a t) z))) (+.f64 (/.f64 (.f64 y t) z) (/.f64 (.f64 a x) z)))
	13.5b	(.f64 (.f64 (.f64 (.f64 (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))) (cbrt.f64 (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	59.2b	(.f64 (.f64 (exp.f64 (*.f64 1/3 (-.f64 (log.f64 (-.f64 (/.f64 x (-.f64 a z)) (/.f64 t (-.f64 a z)))) (log.f64 (/.f64 -1 y))))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x))) (cbrt.f64 (fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)))
	39.4b	(*.f64 (-.f64 (+.f64 (/.f64 z (-.f64 a z)) 1) (/.f64 y (-.f64 a z))) x)
✓	12.2b	(fma.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)) x)

Compiler

Compiled 54493 to 18595 computations (65.9% saved)

regimes1.3s (8.7%)

Accuracy

Total 7.3b remaining (89.6%)

Threshold costs 0b (0%)

Compiler

Compiled 10278 to 5052 computations (50.8% saved)

bsearch5.0ms (0%)

Compiler: Compiled 18 to 11 computations (38.9% saved)

simplify22.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`+-commutative_binary64`
23×	`*-commutative_binary64`
20×	`sub-neg_binary64`
15×	`neg-sub0_binary64`
15×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	51	197
1	77	197
2	99	197
3	127	197
4	166	197
5	184	197
6	194	197
7	197	197
8	196	197

end2.0ms (0%)

Compiler: Compiled 138 to 49 computations (64.5% saved)

sample1.9s (12.6%)

Algorithm

1×

intervals

Results

585.0ms	6721×	body	128	valid
128.0ms	392×	body	1024	valid
116.0ms	451×	body	512	valid
102.0ms	1222×	body	128	invalid
60.0ms	372×	body	256	valid
25.0ms	64×	body	2048	valid

Compiler

Compiled 477 to 192 computations (59.7% saved)

Iter	Nodes	Cost
0	51	197
1	77	197
2	99	197
3	127	197
4	166	197
5	184	197
6	194	197
7	197	197
8	196	197

Iter	Nodes	Cost
0	51	197
1	77	197
2	99	197
3	127	197
4	166	197
5	184	197
6	194	197
7	197	197
8	196	197

Details

analyze2.4s (16.4%)

sample63.0ms (0.4%)

simplify116.0ms (0.8%)

prune6.0ms (0%)

localize16.0ms (0.1%)

rewrite33.0ms (0.2%)

series267.0ms (1.8%)

simplify246.0ms (1.6%)

prune173.0ms (1.2%)

localize22.0ms (0.1%)

rewrite18.0ms (0.1%)

series850.0ms (5.7%)

simplify483.0ms (3.2%)

prune1.3s (8.7%)

localize32.0ms (0.2%)

rewrite7.0ms (0%)

series311.0ms (2.1%)

simplify288.0ms (1.9%)

prune895.0ms (6%)

localize26.0ms (0.2%)

rewrite3.0ms (0%)

series2.6s (17.3%)

simplify557.0ms (3.7%)

prune985.0ms (6.6%)

regimes1.3s (8.7%)

bsearch5.0ms (0%)

simplify22.0ms (0.1%)

end2.0ms (0%)

sample1.9s (12.6%)

Profiling

Iter	Nodes	Cost
0	51	197
1	77	197
2	99	197
3	127	197
4	166	197
5	184	197
6	194	197
7	197	197
8	196	197