Details

analyze1.0s (16.5%)

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
3.1%	96.7%	0.2%	7
6.2%	93.6%	0.2%	8
8.6%	91.2%	0.2%	9
28.1%	71.7%	0.2%	10
31%	68.8%	0.2%	11
40.5%	59.3%	0.2%	12
49.6%	50.2%	0.2%	13
59%	40.8%	0.2%	14

Compiler

Compiled 22 to 14 computations (36.4% saved)

sample1.3s (20.7%)

Results

1.2s	8256×	body	128	valid
48.0ms	346×	body	128	invalid

Compiler

Compiled 65 to 41 computations (36.9% saved)

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

573×	`neg-mul-1_binary64`
569×	`unsub-neg_binary64`
509×	`times-frac_binary64`
460×	`neg-sub0_binary64`
418×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	14	25
1	28	25
2	45	25
3	84	25
4	185	25
5	383	25
6	1133	25
7	3784	25
8	4245	25
9	4554	25
10	4899	25
11	4864	25

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	1	1	2
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	2	3

Error

7.3b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.3b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))

Compiler

Compiled 80 to 46 computations (42.5% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (*.f64 t z) x)
✓	0.0b	(-.f64 (*.f64 y z) x)
✓	0.5b	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
✓	9.7b	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))

series144.0ms (2.3%)

Counts

4 → 114

Calls

4 calls:

86.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
47.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
5.0ms	(-.f64 (*.f64 y z) x)
5.0ms	(-.f64 (*.f64 t z) x)

rewrite34.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

46×	`*-un-lft-identity_binary64`
26×	`add-sqr-sqrt_binary64`
26×	`add-cube-cbrt_binary64`
25×	`times-frac_binary64`
10×	`distribute-lft-out_binary64`

Counts

4 → 117

Calls

4 calls:

12.0ms	(/.f64 (+.f64 x (/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))) (+.f64 x 1))
7.0ms	(/.f64 (-.f64 (.f64 y z) x) (-.f64 (.f64 t z) x))
6.0ms	(-.f64 (*.f64 y z) x)
3.0ms	(-.f64 (*.f64 t z) x)

simplify183.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

550×	`times-frac_binary64`
544×	`fma-neg_binary64`
420×	`associate-/l*_binary64`
300×	`associate-/r*_binary64`
201×	`associate--l+_binary64`

Counts

231 → 263

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	412	8297
1	1260	7857
2	4933	7855
3	5379	7855

prune287.0ms (4.6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	257	6	263
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	258	6	264

Error

0.0b

Counts

264 → 6

Alt Table

Status	Error	Program
	7.6b	(/.f64 (+.f64 x (.f64 (/.f64 (.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (.f64 y z) x))) (.f64 (cbrt.f64 (-.f64 (.f64 t z) x)) (cbrt.f64 (-.f64 (.f64 t z) x)))) (/.f64 (cbrt.f64 (-.f64 (.f64 y z) x)) (cbrt.f64 (-.f64 (*.f64 t z) x))))) (+.f64 x 1))
▶	2.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	26.1b	(-.f64 (+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (.f64 (+.f64 1 x) t))) (/.f64 x (.f64 (+.f64 1 x) (*.f64 t z))))
	19.6b	(/.f64 (+.f64 x (/.f64 y t)) (+.f64 x 1))
	7.3b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
	7.3b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))

Compiler

Compiled 9453 to 3538 computations (62.6% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.1b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	2.2b	(/.f64 x (-.f64 (*.f64 t z) x))
✓	8.1b	(/.f64 z (-.f64 (*.f64 t z) x))

series141.0ms (2.2%)

Counts

3 → 120

Calls

3 calls:

88.0ms	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
26.0ms	(/.f64 z (-.f64 (*.f64 t z) x))
26.0ms	(/.f64 x (-.f64 (*.f64 t z) x))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64`
19×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
18×	`times-frac_binary64`
7×	`add-cbrt-cube_binary64`

Counts

3 → 72

Calls

3 calls:

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

simplify175.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

400×	`times-frac_binary64`
326×	`fma-neg_binary64`
313×	`associate-/l*_binary64`
305×	`sub-neg_binary64`
241×	`associate-+r+_binary64`

Counts

192 → 210

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	331	6888
1	973	6477
2	4210	6352
3	4995	6350
4	5047	6350

prune275.0ms (4.4%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	257	3	260
Fresh	3	2	5
Picked	0	1	1
Done	0	0	0
Total	260	6	266

Error

Counts

266 → 6

Alt Table

Status	Error	Program
✓	2.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	19.3b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
	15.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (cbrt.f64 (pow.f64 (-.f64 (.f64 t z) x) 3))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	32.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 (/.f64 z (sqrt.f64 (-.f64 (.f64 t z) x))) (sqrt.f64 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))
▶	7.3b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
	7.3b	(/.f64 (+.f64 x (/.f64 1 (/.f64 (-.f64 (.f64 t z) x) (-.f64 (.f64 y z) x)))) (+.f64 x 1))

Compiler

Compiled 10265 to 3909 computations (61.9% saved)

localize13.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.5b	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
✓	9.7b	(/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))

series127.0ms (2%)

Counts

2 → 96

Calls

2 calls:

74.0ms	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
52.0ms	(/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))

rewrite22.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`*-un-lft-identity_binary64`
25×	`times-frac_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
10×	`distribute-lft-out_binary64`

Counts

2 → 73

Calls

2 calls:

12.0ms	(/.f64 (+.f64 x (/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))) (+.f64 x 1))
4.0ms	(/.f64 (fma.f64 y z (neg.f64 x)) (-.f64 (*.f64 t z) x))

simplify153.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

417×	`times-frac_binary64`
356×	`fma-neg_binary64`
316×	`associate-/l*_binary64`
280×	`+-commutative_binary64`
256×	`associate-+r+_binary64`

Counts

169 → 197

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	360	7835
1	1126	7288
2	4815	7286
3	5126	7286

prune204.0ms (3.2%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	221	1	222
Fresh	1	3	4
Picked	1	0	1
Done	0	1	1
Total	223	5	228

Error

Counts

228 → 5

Alt Table

Status	Error	Program
✓	2.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
▶	7.3b	(/.f64 (+.f64 x (.f64 (fma.f64 y z (neg.f64 x)) (/.f64 1 (-.f64 (.f64 t z) x)))) (+.f64 x 1))
	19.3b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
	15.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (cbrt.f64 (pow.f64 (-.f64 (.f64 t z) x) 3))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	32.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 (/.f64 z (sqrt.f64 (-.f64 (.f64 t z) x))) (sqrt.f64 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))

Compiler

Compiled 8377 to 3207 computations (61.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.0b	(-.f64 (*.f64 t z) x)
✓	0.5b	(/.f64 (+.f64 x (.f64 (fma.f64 y z (neg.f64 x)) (/.f64 1 (-.f64 (.f64 t z) x)))) (+.f64 x 1))
✓	0.6b	(/.f64 1 (-.f64 (*.f64 t z) x))
✓	9.4b	(.f64 (fma.f64 y z (neg.f64 x)) (/.f64 1 (-.f64 (.f64 t z) x)))

series145.0ms (2.3%)

Counts

3 → 132

Calls

3 calls:

73.0ms	(/.f64 (+.f64 x (.f64 (fma.f64 y z (neg.f64 x)) (/.f64 1 (-.f64 (.f64 t z) x)))) (+.f64 x 1))
51.0ms	(.f64 (fma.f64 y z (neg.f64 x)) (/.f64 1 (-.f64 (.f64 t z) x)))
20.0ms	(/.f64 1 (-.f64 (*.f64 t z) x))

rewrite27.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

37×	`*-un-lft-identity_binary64`
35×	`add-sqr-sqrt_binary64`
32×	`times-frac_binary64`
28×	`add-cube-cbrt_binary64`
18×	`add-exp-log_binary64`

Counts

3 → 112

Calls

3 calls:

8.0ms	(.f64 (fma.f64 y z (neg.f64 x)) (/.f64 1 (-.f64 (.f64 t z) x)))
7.0ms	(/.f64 (+.f64 x (.f64 (fma.f64 y z (neg.f64 x)) (/.f64 1 (-.f64 (.f64 t z) x)))) (+.f64 x 1))
4.0ms	(/.f64 1 (-.f64 (*.f64 t z) x))

simplify177.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

436×	`times-frac_binary64`
396×	`fma-neg_binary64`
323×	`associate-/l*_binary64`
270×	`associate-/r*_binary64`
240×	`associate-+l+_binary64`

Counts

244 → 259

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	391	9318
1	1220	8643
2	4801	8641
3	5148	8641

prune311.0ms (4.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	284	0	284
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	284	5	289

Error

Counts

289 → 5

Alt Table

Status	Error	Program
✓	2.5b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (-.f64 (.f64 t z) x)) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
✓	7.3b	(/.f64 (+.f64 x (.f64 (fma.f64 y z (neg.f64 x)) (/.f64 1 (-.f64 (.f64 t z) x)))) (+.f64 x 1))
	19.3b	(+.f64 (/.f64 x (+.f64 1 x)) (/.f64 y (*.f64 (+.f64 1 x) t)))
	15.0b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 z (cbrt.f64 (pow.f64 (-.f64 (.f64 t z) x) 3))) (/.f64 (-.f64 x (/.f64 x (-.f64 (.f64 t z) x))) (+.f64 x 1)))
	32.8b	(fma.f64 (/.f64 y (+.f64 x 1)) (/.f64 (/.f64 z (sqrt.f64 (-.f64 (.f64 t z) x))) (sqrt.f64 (-.f64 (.f64 t z) x))) (/.f64 (-.f64 x (/.f64 x (-.f64 (*.f64 t z) x))) (+.f64 x 1)))

Compiler

Compiled 10236 to 4319 computations (57.8% saved)

regimes1.3s (20.2%)

Accuracy

Total 0.7b remaining (96.4%)

Threshold costs 0.7b (96.4%)

Counts

155 → 2

Compiler

Compiled 19370 to 11837 computations (38.9% saved)

bsearch6.0ms (0.1%)

Compiler: Compiled 21 to 13 computations (38.1% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	31	102
1	47	102
2	60	102
3	66	102
4	69	102
5	68	102

end107.0ms (1.7%)

Compiler: Compiled 287 to 160 computations (44.3% saved)

Details

analyze1.0s (16.5%)

sample1.3s (20.7%)

simplify94.0ms (1.5%)

prune2.0ms (0%)

localize11.0ms (0.2%)

series144.0ms (2.3%)

rewrite34.0ms (0.5%)

simplify183.0ms (2.9%)

prune287.0ms (4.6%)

localize12.0ms (0.2%)

series141.0ms (2.2%)

rewrite13.0ms (0.2%)

simplify175.0ms (2.8%)

prune275.0ms (4.4%)

localize13.0ms (0.2%)

series127.0ms (2%)

rewrite22.0ms (0.3%)

simplify153.0ms (2.4%)

prune204.0ms (3.2%)

localize12.0ms (0.2%)

series145.0ms (2.3%)

rewrite27.0ms (0.4%)

simplify177.0ms (2.8%)

prune311.0ms (4.9%)

regimes1.3s (20.2%)

bsearch6.0ms (0.1%)

simplify6.0ms (0.1%)

end107.0ms (1.7%)

Profiling