Details

analyze972.0ms (7.5%)

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
7.8%	92%	0.2%	8
15.6%	84.2%	0.2%	9
23.4%	76.4%	0.2%	10
25%	74.9%	0.2%	11
37.9%	59.6%	2.5%	12
41.4%	55.7%	2.9%	13
46.3%	50.6%	3.1%	14

Compiler

Compiled 16 to 11 computations (31.3% saved)

sample1.4s (10.9%)

Results

1.0s	8256×	body	128	valid
236.0ms	1878×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify294.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

2150×	`fma-neg_binary64`
1161×	`div-sub_binary64`
897×	`fma-def_binary64`
414×	`associate-/l*_binary64`
410×	`distribute-rgt-in_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	33	16
3	65	16
4	113	16
5	197	16
6	397	16
7	814	16
8	1449	16
9	1832	16
10	1941	16
11	2036	16
12	2110	16
13	2224	16
14	2174	16
15	2652	16
16	2330	16
17	2358	16
18	2376	16
19	2392	16
20	2384	16
21	2468	16
22	2468	16
23	2388	16
24	2450	16
25	2428	16
26	2426	16
27	2428	16
28	2430	16
29	2440	16
30	2440	16
31	2255	16

prune2.0ms (0%)

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

5.9b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	5.9b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
✓	5.6b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series46.0ms (0.4%)

Counts

2 → 66

Calls

2 calls:

32.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
14.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

rewrite333.0ms (2.6%)

Algorithm

1×	rewrite-expression-head

Rules

1429×	`times-frac_binary64`
1339×	`add-sqr-sqrt_binary64`
1335×	`*-un-lft-identity_binary64`
936×	`prod-diff_binary64`
935×	`add-cube-cbrt_binary64`

Counts

2 → 1074

Calls

2 calls:

36.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
23.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

simplify1.3s (9.7%)

Algorithm

1×	egg-herbie

Rules

687×	`times-frac_binary64`
569×	`associate-l_binary64`
557×	`associate-r_binary64`
314×	`*-commutative_binary64`
243×	`distribute-rgt-in_binary64`

Counts

1140 → 1067

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	990	85623
1	1699	43502
2	3794	41798
3	4686	41798
4	5040	41798

prune1.6s (12.1%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	1059	8	1067
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1060	8	1068

Error

0.0b

Counts

1068 → 8

Alt Table

Status	Error	Program
	30.0b	(/.f64 (.f64 x (-.f64 (.f64 (/.f64 y z) (/.f64 y z)) (*.f64 (/.f64 t (-.f64 1 z)) (/.f64 t (-.f64 1 z))))) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
	8.5b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
	6.3b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 (/.f64 (*.f64 (cbrt.f64 t) (cbrt.f64 t)) 1)) (/.f64 (cbrt.f64 t) (-.f64 1 z)))))
	53.1b	(.f64 (.f64 x (+.f64 (/.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (/.f64 t (-.f64 1 z))))) (-.f64 (/.f64 (sqrt.f64 y) (sqrt.f64 z)) (sqrt.f64 (/.f64 t (-.f64 1 z)))))
	28.9b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 (sqrt.f64 (/.f64 t (-.f64 1 z)))) (sqrt.f64 (/.f64 t (-.f64 1 z))))))
	17.2b	(/.f64 x (/.f64 z (+.f64 y t)))
▶	5.9b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	30.9b	(.f64 x (+.f64 (fma.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) z) (neg.f64 (.f64 (/.f64 t (cbrt.f64 (-.f64 1 z))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))))))) (fma.f64 (neg.f64 (/.f64 t (cbrt.f64 (-.f64 1 z)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z)))) (.f64 (/.f64 t (cbrt.f64 (-.f64 1 z))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))))))))

Compiler

Compiled 57711 to 31339 computations (45.7% saved)

localize9.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z))))
✓	5.6b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))

series49.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

34.0ms	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
16.0ms	(fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z))))

rewrite5.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 32

Calls

2 calls:

3.0ms	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
0.0ms	(fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z))))

simplify96.0ms (0.7%)

Algorithm

1×	egg-herbie

Rules

797×	`fma-neg_binary64`
432×	`cancel-sign-sub-inv_binary64`
422×	`fma-def_binary64`
234×	`associate-/l/_binary64`
218×	`associate-l_binary64`

Counts

116 → 90

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	112	2138
1	274	1926
2	826	1862
3	2632	1827
4	4572	1827
5	4974	1827

prune72.0ms (0.6%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	89	1	90
Fresh	2	5	7
Picked	0	1	1
Done	0	0	0
Total	91	7	98

Error

Counts

98 → 7

Alt Table

Status	Error	Program
	16.0b	(*.f64 (/.f64 x z) (+.f64 y t))
	17.2b	(/.f64 x (/.f64 z (+.f64 y t)))
	30.0b	(/.f64 (.f64 x (-.f64 (.f64 (/.f64 y z) (/.f64 y z)) (*.f64 (/.f64 t (-.f64 1 z)) (/.f64 t (-.f64 1 z))))) (+.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
▶	8.5b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
	28.9b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 (sqrt.f64 (/.f64 t (-.f64 1 z)))) (sqrt.f64 (/.f64 t (-.f64 1 z))))))
✓	5.9b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	30.9b	(.f64 x (+.f64 (fma.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) z) (neg.f64 (.f64 (/.f64 t (cbrt.f64 (-.f64 1 z))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))))))) (fma.f64 (neg.f64 (/.f64 t (cbrt.f64 (-.f64 1 z)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z)))) (.f64 (/.f64 t (cbrt.f64 (-.f64 1 z))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))))))))

Compiler

Compiled 1967 to 1089 computations (44.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	3.1b	(/.f64 (*.f64 t x) (-.f64 1 z))
✓	6.4b	(/.f64 (*.f64 y x) z)

series56.0ms (0.4%)

Counts

3 → 42

Calls

3 calls:

27.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
17.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
13.0ms	(/.f64 (*.f64 y x) z)

rewrite39.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

96×	`times-frac_binary64`
84×	`prod-diff_binary64`
81×	`*-un-lft-identity_binary64`
81×	`add-sqr-sqrt_binary64`
49×	`add-cube-cbrt_binary64`

Counts

3 → 173

Calls

3 calls:

12.0ms	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
5.0ms	(/.f64 (*.f64 t x) (-.f64 1 z))
3.0ms	(/.f64 (*.f64 y x) z)

simplify177.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

543×	`fma-neg_binary64`
265×	`cancel-sign-sub-inv_binary64`
213×	`distribute-rgt-neg-in_binary64`
205×	`div-sub_binary64`
190×	`distribute-rgt-out_binary64`

Counts

215 → 256

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	316	7070
1	799	5494
2	2811	4354
3	4318	4354
4	4944	4354

prune231.0ms (1.8%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	255	1	256
Fresh	1	4	5
Picked	1	0	1
Done	0	1	1
Total	257	6	263

Error

Counts

263 → 6

Alt Table

Status	Error	Program
	16.0b	(*.f64 (/.f64 x z) (+.f64 y t))
	17.2b	(/.f64 x (/.f64 z (+.f64 y t)))
	28.9b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 (sqrt.f64 (/.f64 t (-.f64 1 z)))) (sqrt.f64 (/.f64 t (-.f64 1 z))))))
✓	5.9b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	30.9b	(.f64 x (+.f64 (fma.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) z) (neg.f64 (.f64 (/.f64 t (cbrt.f64 (-.f64 1 z))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))))))) (fma.f64 (neg.f64 (/.f64 t (cbrt.f64 (-.f64 1 z)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z)))) (.f64 (/.f64 t (cbrt.f64 (-.f64 1 z))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))))))))
▶	8.6b	(-.f64 (/.f64 1 (/.f64 z (.f64 y x))) (/.f64 (.f64 t x) (-.f64 1 z)))

Compiler

Compiled 8437 to 4151 computations (50.8% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 1 (/.f64 z (.f64 y x))) (/.f64 (.f64 t x) (-.f64 1 z)))
✓	0.6b	(/.f64 1 (/.f64 z (*.f64 y x)))
	3.1b	(/.f64 (*.f64 t x) (-.f64 1 z))
✓	6.5b	(/.f64 z (*.f64 y x))

series57.0ms (0.4%)

Counts

3 → 84

Calls

3 calls:

27.0ms	(-.f64 (/.f64 1 (/.f64 z (.f64 y x))) (/.f64 (.f64 t x) (-.f64 1 z)))
16.0ms	(/.f64 z (*.f64 y x))
14.0ms	(/.f64 1 (/.f64 z (*.f64 y x)))

rewrite111.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

590×	`times-frac_binary64`
345×	`add-sqr-sqrt_binary64`
342×	`*-un-lft-identity_binary64`
312×	`prod-diff_binary64`
257×	`add-cube-cbrt_binary64`

Counts

3 → 450

Calls

3 calls:

26.0ms	(-.f64 (/.f64 1 (/.f64 z (.f64 y x))) (/.f64 (.f64 t x) (-.f64 1 z)))
5.0ms	(/.f64 1 (/.f64 z (*.f64 y x)))
3.0ms	(/.f64 z (*.f64 y x))

simplify491.0ms (3.8%)

Algorithm

1×	egg-herbie

Rules

822×	`fma-neg_binary64`
250×	`unsub-neg_binary64`
237×	`cancel-sign-sub-inv_binary64`
200×	`neg-mul-1_binary64`
198×	`distribute-rgt-out_binary64`

Counts

534 → 523

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	345	23706
1	759	17611
2	2639	12935
3	4118	12935
4	4928	12935
5	4967	12935

prune609.0ms (4.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	577	0	577
Fresh	0	4	4
Picked	0	1	1
Done	0	1	1
Total	577	6	583

Error

Counts

583 → 6

Alt Table

Status	Error	Program
	16.0b	(*.f64 (/.f64 x z) (+.f64 y t))
	17.2b	(/.f64 x (/.f64 z (+.f64 y t)))
	28.9b	(.f64 x (+.f64 (/.f64 y z) (.f64 (neg.f64 (sqrt.f64 (/.f64 t (-.f64 1 z)))) (sqrt.f64 (/.f64 t (-.f64 1 z))))))
✓	5.9b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	30.9b	(.f64 x (+.f64 (fma.f64 (/.f64 (sqrt.f64 y) 1) (/.f64 (sqrt.f64 y) z) (neg.f64 (.f64 (/.f64 t (cbrt.f64 (-.f64 1 z))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))))))) (fma.f64 (neg.f64 (/.f64 t (cbrt.f64 (-.f64 1 z)))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z)))) (.f64 (/.f64 t (cbrt.f64 (-.f64 1 z))) (/.f64 1 (.f64 (cbrt.f64 (-.f64 1 z)) (cbrt.f64 (-.f64 1 z))))))))
✓	8.6b	(-.f64 (/.f64 1 (/.f64 z (.f64 y x))) (/.f64 (.f64 t x) (-.f64 1 z)))

Compiler

Compiled 24964 to 13663 computations (45.3% saved)

regimes4.9s (37.7%)

Accuracy

Total 1.4b remaining (97.6%)

Threshold costs 0b (0%)

Counts

261 → 3

Compiler

Compiled 54079 to 36340 computations (32.8% saved)

bsearch17.0ms (0.1%)

Compiler: Compiled 13 to 9 computations (30.8% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Rules

10×	`+-commutative_binary64`
9×	`*-commutative_binary64`
9×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	90
1	44	90
2	62	90
3	73	90
4	80	90
5	82	90
6	81	90

end129.0ms (1%)

Compiler: Compiled 284 to 185 computations (34.9% saved)

Details

analyze972.0ms (7.5%)

sample1.4s (10.9%)

simplify294.0ms (2.3%)

prune2.0ms (0%)

localize7.0ms (0.1%)

series46.0ms (0.4%)

rewrite333.0ms (2.6%)

simplify1.3s (9.7%)

prune1.6s (12.1%)

localize9.0ms (0.1%)

series49.0ms (0.4%)

rewrite5.0ms (0%)

simplify96.0ms (0.7%)

prune72.0ms (0.6%)

localize8.0ms (0.1%)

series56.0ms (0.4%)

rewrite39.0ms (0.3%)

simplify177.0ms (1.4%)

prune231.0ms (1.8%)

localize10.0ms (0.1%)

series57.0ms (0.4%)

rewrite111.0ms (0.9%)

simplify491.0ms (3.8%)

prune609.0ms (4.7%)

regimes4.9s (37.7%)

bsearch17.0ms (0.1%)

simplify5.0ms (0%)

end129.0ms (1%)

Profiling