Details

analyze1.7s (27.7%)

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
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
3.7%	96.1%	0.2%	13
4.2%	94.5%	1.3%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample92.0ms (1.5%)

Algorithm

1×

intervals

Results

14.0ms	256×	body	128	valid
3.0ms	63×	body	128	invalid

Compiler

Compiled 47 to 35 computations (25.5% saved)

simplify105.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

669×	`fma-neg_binary64`
614×	`times-frac_binary64`
480×	`neg-mul-1_binary64`
416×	`div-sub_binary64`
394×	`unsub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 7 (0.0ms)

Iter	Nodes	Cost
0	15	25
1	28	23
2	55	23
3	101	21
4	220	21
5	423	21
6	834	20
7	1845	19
8	3893	19
9	4281	19
10	4633	19
11	4956	19
12	4804	19

prune4.0ms (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
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	7.7b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))

Compiler

Compiled 110 to 79 computations (28.2% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 -2 (/.f64 -2 z))
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

series53.0ms (0.9%)

Counts

3 → 84

Calls

3 calls:

40.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
11.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
1.0ms	(+.f64 -2 (/.f64 -2 z))

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`*-un-lft-identity_binary64`
69×	`times-frac_binary64`
68×	`add-sqr-sqrt_binary64`
68×	`add-cube-cbrt_binary64`
65×	`associate-+r+_binary64`

Counts

3 → 149

Calls

3 calls:

20.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
6.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
4.0ms	(+.f64 -2 (/.f64 -2 z))

simplify151.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

574×	`fma-def_binary64`
515×	`distribute-rgt-in_binary64`
488×	`distribute-lft-in_binary64`
259×	`fma-neg_binary64`
191×	`cancel-sign-sub-inv_binary64`

Counts

233 → 201

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	244	4900
1	649	3766
2	1555	3545
3	4800	3545
4	4939	3545

prune261.0ms (4.3%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	195	6	201
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	196	7	203

Error

Counts

203 → 7

Alt Table

Status	Error	Program
	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	37.6b	(*.f64 (sqrt.f64 (+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))) (sqrt.f64 (+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
▶	0.2b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	7.7b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
	0.8b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) t))))
	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))))
	26.0b	(/.f64 (+.f64 (.f64 x (+.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (.f64 y (-.f64 (.f64 -2 -2) (.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t) (/.f64 (+.f64 -2 (/.f64 -2 z)) t))))) (*.f64 y (+.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))))

Compiler

Compiled 6947 to 4829 computations (30.5% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(+.f64 -2 (/.f64 -2 z))
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

series33.0ms (0.5%)

Counts

1 → 48

Calls

1 calls:

33.0ms

(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

rewrite4.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

1 → 10

Calls

1 calls:

4.0ms

(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

simplify102.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

934×	`fma-def_binary64`
492×	`associate-l_binary64`
423×	`associate-+l+_binary64`
379×	`associate-r_binary64`
267×	`associate-*l/_binary64`

Counts

58 → 29

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	43	1177
1	83	1126
2	164	1126
3	357	1126
4	1233	1009
5	4295	1009
6	5040	1009

prune101.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	94	1	95
Fresh	1	5	6
Picked	0	1	1
Done	0	0	0
Total	95	7	102

Error

Counts

102 → 7

Alt Table

Status	Error	Program
	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))))
▶	0.1b	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 1 (*.f64 t z))))) 2)
	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	37.6b	(*.f64 (sqrt.f64 (+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))) (sqrt.f64 (+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
✓	0.2b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	0.8b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) t))))
	26.0b	(/.f64 (+.f64 (.f64 x (+.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (.f64 y (-.f64 (.f64 -2 -2) (.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t) (/.f64 (+.f64 -2 (/.f64 -2 z)) t))))) (*.f64 y (+.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))))

Compiler

Compiled 2290 to 1687 computations (26.3% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 1 (*.f64 t z))))) 2)
✓	0.0b	(+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 1 (*.f64 t z)))))
✓	0.0b	(+.f64 (/.f64 x y) (.f64 2 (/.f64 1 (.f64 t z))))
✓	0.4b	(/.f64 1 (*.f64 t z))

series94.0ms (1.6%)

Counts

4 → 36

Calls

4 calls:

34.0ms	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 1 (*.f64 t z))))) 2)
30.0ms	(+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 1 (*.f64 t z)))))
22.0ms	(+.f64 (/.f64 x y) (.f64 2 (/.f64 1 (.f64 t z))))
8.0ms	(/.f64 1 (*.f64 t z))

rewrite40.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

23×	`*-un-lft-identity_binary64`
23×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`
20×	`add-log-exp_binary64`
15×	`add-exp-log_binary64`

Counts

4 → 115

Calls

4 calls:

14.0ms	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 1 (*.f64 t z))))) 2)
10.0ms	(+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 1 (*.f64 t z)))))
6.0ms	(+.f64 (/.f64 x y) (.f64 2 (/.f64 1 (.f64 t z))))
3.0ms	(/.f64 1 (*.f64 t z))

simplify124.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

632×	`fma-def_binary64`
411×	`associate-*l/_binary64`
376×	`distribute-rgt-in_binary64`
335×	`distribute-lft-in_binary64`
247×	`associate-/l*_binary64`

Counts

151 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	176	2953
1	461	2386
2	1437	2341
3	4777	2341
4	5000	2341
5	4953	2341

prune188.0ms (3.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	168	1	169
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	169	7	176

Error

Counts

176 → 7

Alt Table

Status	Error	Program
▶	0.1b	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 (/.f64 1 t) z)))) 2)
	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))))
✓	0.1b	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 1 (*.f64 t z))))) 2)
	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
	37.6b	(*.f64 (sqrt.f64 (+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))) (sqrt.f64 (+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
✓	0.2b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	26.0b	(/.f64 (+.f64 (.f64 x (+.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (.f64 y (-.f64 (.f64 -2 -2) (.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t) (/.f64 (+.f64 -2 (/.f64 -2 z)) t))))) (*.f64 y (+.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))))

Compiler

Compiled 5388 to 3383 computations (37.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 2 (/.f64 (/.f64 1 t) z))
✓	0.0b	(+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 (/.f64 1 t) z))))
✓	0.0b	(+.f64 (/.f64 x y) (*.f64 2 (/.f64 (/.f64 1 t) z)))
✓	0.3b	(/.f64 (/.f64 1 t) z)

series68.0ms (1.1%)

Counts

4 → 144

Calls

4 calls:

30.0ms	(+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 (/.f64 1 t) z))))
21.0ms	(+.f64 (/.f64 x y) (*.f64 2 (/.f64 (/.f64 1 t) z)))
9.0ms	(*.f64 2 (/.f64 (/.f64 1 t) z))
8.0ms	(/.f64 (/.f64 1 t) z)

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

155×	`times-frac_binary64`
101×	`add-sqr-sqrt_binary64`
90×	`*-un-lft-identity_binary64`
89×	`add-cube-cbrt_binary64`
43×	`associate-r_binary64`

Counts

4 → 193

Calls

4 calls:

11.0ms	(*.f64 2 (/.f64 (/.f64 1 t) z))
10.0ms	(+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 (/.f64 1 t) z))))
5.0ms	(+.f64 (/.f64 x y) (*.f64 2 (/.f64 (/.f64 1 t) z)))
5.0ms	(/.f64 (/.f64 1 t) z)

simplify148.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

524×	`fma-def_binary64`
500×	`associate-*l/_binary64`
367×	`associate-/l*_binary64`
331×	`times-frac_binary64`
282×	`distribute-rgt-in_binary64`

Counts

337 → 289

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	209	4738
1	552	4535
2	1612	4491
3	4927	4491
4	4990	4491

prune327.0ms (5.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	288	1	289
Fresh	1	3	4
Picked	0	1	1
Done	0	2	2
Total	289	7	296

Error

Counts

296 → 7

Alt Table

Status	Error	Program
✓	0.1b	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 (/.f64 1 t) z)))) 2)
	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (cbrt.f64 t))))
✓	0.1b	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 2 (/.f64 1 (*.f64 t z))))) 2)
	0.7b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))))
✓	0.2b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	26.2b	(-.f64 (+.f64 (.f64 2 (/.f64 1 t)) (+.f64 (/.f64 x y) (.f64 (sqrt.f64 (/.f64 2 (.f64 t z))) (sqrt.f64 (/.f64 2 (.f64 t z)))))) 2)
	26.0b	(/.f64 (+.f64 (.f64 x (+.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))) (.f64 y (-.f64 (.f64 -2 -2) (.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t) (/.f64 (+.f64 -2 (/.f64 -2 z)) t))))) (*.f64 y (+.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))))

Compiler

Compiled 8290 to 5281 computations (36.3% saved)

regimes1.2s (20.2%)

Accuracy

Total 0.1b remaining (90.5%)

Threshold costs 0.1b (90.5%)

Counts

140 → 1

Compiler

Compiled 23366 to 17763 computations (24% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`+-commutative_binary64`
1×	`*-commutative_binary64`
1×	`sub-neg_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	22
1	19	22
2	20	22
3	19	22

end1.0ms (0%)

Compiler: Compiled 19 to 14 computations (26.3% saved)

sample1.1s (18.2%)

Algorithm

1×

intervals

Results

454.0ms	8000×	body	128	valid
142.0ms	2347×	body	128	invalid

Compiler

Compiled 247 to 187 computations (24.3% saved)

Details

analyze1.7s (27.7%)

sample92.0ms (1.5%)

simplify105.0ms (1.8%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series53.0ms (0.9%)

rewrite46.0ms (0.8%)

simplify151.0ms (2.5%)

prune261.0ms (4.3%)

localize9.0ms (0.1%)

series33.0ms (0.5%)

rewrite4.0ms (0.1%)

simplify102.0ms (1.7%)

prune101.0ms (1.7%)

localize13.0ms (0.2%)

series94.0ms (1.6%)

rewrite40.0ms (0.7%)

simplify124.0ms (2.1%)

prune188.0ms (3.1%)

localize11.0ms (0.2%)

series68.0ms (1.1%)

rewrite46.0ms (0.8%)

simplify148.0ms (2.5%)

prune327.0ms (5.5%)

regimes1.2s (20.2%)

simplify2.0ms (0%)

end1.0ms (0%)

sample1.1s (18.2%)

Profiling