Details

analyze950.0ms (9.1%)

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 (13.6%)

Results

1.0s	8256×	body	128	valid
250.0ms	1864×	body	128	invalid

Compiler

Compiled 47 to 32 computations (31.9% saved)

simplify284.0ms (2.7%)

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

3.5b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	3.5b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

Compiler

Compiled 45 to 30 computations (33.3% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))
✓	3.4b	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))

series47.0ms (0.5%)

Counts

2 → 66

Calls

2 calls:

29.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
17.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

rewrite346.0ms (3.3%)

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:

38.0ms	(*.f64 x (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))
22.0ms	(-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))

simplify1.2s (12%)

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

prune1.2s (11.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	1060	7	1067
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	1061	7	1068

Error

0.0b

Counts

1068 → 7

Alt Table

Status	Error	Program
	31.2b	(.f64 (.f64 x (sqrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))) (sqrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
	7.8b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
	4.1b	(.f64 x (+.f64 (fma.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (.f64 (/.f64 1 (-.f64 1 z)) t))))
▶	3.5b	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	3.5b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	20.4b	(/.f64 (.f64 x (-.f64 (.f64 y (-.f64 1 z)) (.f64 z t))) (.f64 z (-.f64 1 z)))
	18.7b	(/.f64 x (/.f64 z (+.f64 y t)))

Compiler

Compiled 57549 to 31227 computations (45.7% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 y z) (neg.f64 (/.f64 t (-.f64 1 z))))
✓	3.4b	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (-.f64 1 z)))))

series45.0ms (0.4%)

Counts

2 → 84

Calls

2 calls:

31.0ms	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (-.f64 1 z)))))
13.0ms	(+.f64 (/.f64 y z) (neg.f64 (/.f64 t (-.f64 1 z))))

rewrite56.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
17×	`times-frac_binary64`
13×	`fma-def_binary64`
13×	`add-sqr-sqrt_binary64`
11×	`add-cube-cbrt_binary64`

Counts

2 → 63

Calls

2 calls:

27.0ms	(+.f64 (/.f64 y z) (neg.f64 (/.f64 t (-.f64 1 z))))
25.0ms	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (-.f64 1 z)))))

simplify126.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

640×	`fma-def_binary64`
420×	`distribute-rgt-in_binary64`
361×	`fma-neg_binary64`
356×	`distribute-lft-in_binary64`
214×	`associate-*l/_binary64`

Counts

147 → 121

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	137	2310
1	385	2182
2	1431	2130
3	4544	2130
4	4999	2130
5	5000	2130
6	5011	2130

prune86.0ms (0.8%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	120	1	121
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	121	7	128

Error

0.0b

Counts

128 → 7

Alt Table

Status	Error	Program
	31.2b	(.f64 (.f64 x (sqrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))) (sqrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
	7.8b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
	18.3b	(*.f64 (/.f64 x z) (+.f64 y t))
	4.1b	(.f64 x (+.f64 (fma.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (.f64 (/.f64 1 (-.f64 1 z)) t))))
✓	3.5b	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (-.f64 1 z)))))
▶	3.5b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	18.7b	(/.f64 x (/.f64 z (+.f64 y t)))

Compiler

Compiled 2556 to 1293 computations (49.4% saved)

localize13.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.2b	(fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z))))
✓	3.4b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))

series47.0ms (0.5%)

Counts

2 → 84

Calls

2 calls:

33.0ms	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
14.0ms	(fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z))))

rewrite6.0ms (0.1%)

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:

5.0ms	(*.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))))

simplify90.0ms (0.9%)

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

prune61.0ms (0.6%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	90	0	90
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	90	7	97

Error

0.0b

Counts

97 → 7

Alt Table

Status	Error	Program
	31.2b	(.f64 (.f64 x (sqrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))) (sqrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
	7.8b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
	18.3b	(*.f64 (/.f64 x z) (+.f64 y t))
▶	4.1b	(.f64 x (+.f64 (fma.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (.f64 (/.f64 1 (-.f64 1 z)) t))))
✓	3.5b	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (-.f64 1 z)))))
✓	3.5b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	18.7b	(/.f64 x (/.f64 z (+.f64 y t)))

Compiler

Compiled 1859 to 1008 computations (45.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
✓	0.6b	(cbrt.f64 z)
✓	3.4b	(.f64 x (+.f64 (fma.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (.f64 (/.f64 1 (-.f64 1 z)) t))))
✓	26.0b	(fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))

series1.1s (10.1%)

Counts

4 → 96

Calls

4 calls:

959.0ms	(.f64 x (+.f64 (fma.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (.f64 (/.f64 1 (-.f64 1 z)) t))))
36.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
29.0ms	(cbrt.f64 z)
27.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))

rewrite14.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
19×	`cbrt-prod_binary64`
17×	`*-un-lft-identity_binary64`
15×	`add-cube-cbrt_binary64`
13×	`pow1_binary64`

Counts

4 → 90

Calls

4 calls:

4.0ms	(*.f64 (cbrt.f64 z) (cbrt.f64 z))
4.0ms	(.f64 x (+.f64 (fma.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (cbrt.f64 z)) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (.f64 (/.f64 1 (-.f64 1 z)) t))))
1.0ms	(cbrt.f64 z)
0.0ms	(fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (*.f64 (/.f64 1 (-.f64 1 z)) t))

simplify142.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

676×	`fma-def_binary64`
525×	`distribute-rgt-in_binary64`
494×	`unswap-sqr_binary64`
448×	`distribute-lft-in_binary64`
395×	`fma-neg_binary64`

Counts

186 → 157

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	158	3326
1	369	2556
2	1413	1834
3	3795	1816
4	4293	1804
5	4871	1804
6	4786	1804

prune211.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	194	1	195
Fresh	0	4	4
Picked	1	0	1
Done	0	2	2
Total	195	7	202

Error

Counts

202 → 7

Alt Table

Status	Error	Program
	31.2b	(.f64 (.f64 x (sqrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z))))) (sqrt.f64 (-.f64 (/.f64 y z) (/.f64 t (-.f64 1 z)))))
	7.8b	(-.f64 (/.f64 (.f64 y x) z) (/.f64 (.f64 t x) (-.f64 1 z)))
	18.3b	(*.f64 (/.f64 x z) (+.f64 y t))
✓	3.5b	(*.f64 x (+.f64 (/.f64 y z) (neg.f64 (/.f64 t (-.f64 1 z)))))
✓	3.5b	(*.f64 x (fma.f64 y (/.f64 1 z) (neg.f64 (/.f64 t (-.f64 1 z)))))
	4.2b	(.f64 x (+.f64 (fma.f64 (/.f64 1 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 y (.f64 (cbrt.f64 (.f64 (cbrt.f64 z) (cbrt.f64 z))) (cbrt.f64 (cbrt.f64 z)))) (neg.f64 (.f64 (/.f64 1 (-.f64 1 z)) t))) (fma.f64 (neg.f64 (/.f64 1 (-.f64 1 z))) t (.f64 (/.f64 1 (-.f64 1 z)) t))))
	18.7b	(/.f64 x (/.f64 z (+.f64 y t)))

Compiler

Compiled 8133 to 4730 computations (41.8% saved)

regimes2.7s (26.3%)

Accuracy

Total 2.1b remaining (98.8%)

Threshold costs 0b (0%)

Counts

221 → 4

Compiler

Compiled 46672 to 31240 computations (33.1% saved)

bsearch14.0ms (0.1%)

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

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

13×	`*-commutative_binary64`
12×	`+-commutative_binary64`
10×	`sub-neg_binary64`
7×	`neg-sub0_binary64`
7×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	135
1	65	135
2	86	135
3	98	135
4	104	135
5	105	135
6	103	135

end154.0ms (1.5%)

Compiler: Compiled 341 to 213 computations (37.5% saved)

Details

analyze950.0ms (9.1%)

sample1.4s (13.6%)

simplify284.0ms (2.7%)

prune2.0ms (0%)

localize8.0ms (0.1%)

series47.0ms (0.5%)

rewrite346.0ms (3.3%)

simplify1.2s (12%)

prune1.2s (11.8%)

localize8.0ms (0.1%)

series45.0ms (0.4%)

rewrite56.0ms (0.5%)

simplify126.0ms (1.2%)

prune86.0ms (0.8%)

localize13.0ms (0.1%)

series47.0ms (0.5%)

rewrite6.0ms (0.1%)

simplify90.0ms (0.9%)

prune61.0ms (0.6%)

localize17.0ms (0.2%)

series1.1s (10.1%)

rewrite14.0ms (0.1%)

simplify142.0ms (1.4%)

prune211.0ms (2%)

regimes2.7s (26.3%)

bsearch14.0ms (0.1%)

simplify8.0ms (0.1%)

end154.0ms (1.5%)

Profiling