Details

analyze1.1s (13.6%)

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
12.5%	87.3%	0.2%	5
12.5%	87.3%	0.2%	6
18.7%	81.1%	0.2%	7
28.1%	71.7%	0.2%	8
42.1%	57.7%	0.2%	9
42.1%	57.7%	0.2%	10
49.1%	50.7%	0.2%	11
57.3%	42.5%	0.2%	12
66.9%	32.9%	0.2%	13
66.9%	32.9%	0.2%	14

Compiler

Compiled 22 to 16 computations (27.3% saved)

sample1.7s (21.7%)

Results

1.6s

8256×

body

128

valid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify177.0ms (2.2%)

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

prune8.0ms (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

0.5b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
	9.4b	(+.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)

localize20.0ms (0.3%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
✓	0.5b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

series79.0ms (1%)

Counts

2 → 72

Calls

2 calls:

57.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
22.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

rewrite124.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

2 → 132

Calls

2 calls:

43.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
19.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)

simplify223.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

563×	`fma-def_binary64`
447×	`distribute-rgt-in_binary64`
425×	`distribute-lft-in_binary64`
234×	`fma-neg_binary64`
189×	`exp-prod_binary64`

Counts

204 → 178

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	235	4642
1	625	3549
2	1504	3327
3	4434	3327
4	4943	3327

prune478.0ms (6%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	172	6	178
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	174	6	180

Error

0.0b

Counts

180 → 6

Alt Table

Status	Error	Program
	1.1b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 t)))))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 1 (/.f64 t (+.f64 -2 (/.f64 -2 z))))))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
	1.0b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))))
▶	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 6439 to 4467 computations (30.6% saved)

localize18.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	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)

series83.0ms (1%)

Counts

1 → 48

Calls

1 calls:

83.0ms

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

rewrite1.0ms (0%)

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:

1.0ms

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

simplify146.0ms (1.8%)

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

prune172.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	73	0	73
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	73	6	79

Error

0.0b

Counts

79 → 6

Alt Table

Status	Error	Program
	1.1b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 t)))))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 1 (/.f64 t (+.f64 -2 (/.f64 -2 z))))))
▶	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
	1.0b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))))
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 1761 to 1279 computations (27.4% saved)

localize27.0ms (0.3%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 2 t) (/.f64 2 (*.f64 t z)))
✓	0.5b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
✓	0.6b	(/.f64 2 (*.f64 t z))

series97.0ms (1.2%)

Counts

3 → 72

Calls

3 calls:

58.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
19.0ms	(+.f64 (/.f64 2 t) (/.f64 2 (*.f64 t z)))
19.0ms	(/.f64 2 (*.f64 t z))

rewrite56.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`fma-def_binary64`
26×	`*-un-lft-identity_binary64`
21×	`times-frac_binary64`
20×	`add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`

Counts

3 → 89

Calls

3 calls:

16.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
15.0ms	(+.f64 (/.f64 2 t) (/.f64 2 (*.f64 t z)))
5.0ms	(/.f64 2 (*.f64 t z))

simplify189.0ms (2.4%)

Algorithm

1×	egg-herbie

Rules

546×	`distribute-rgt-in_binary64`
506×	`distribute-lft-in_binary64`
488×	`fma-def_binary64`
221×	`fma-neg_binary64`
210×	`associate-/l*_binary64`

Counts

161 → 125

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	160	2549
1	425	2403
2	1288	2398
3	4826	2398
4	4950	2398

prune258.0ms (3.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	124	1	125
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	125	6	131

Error

0.0b

Counts

131 → 6

Alt Table

Status	Error	Program
	1.1b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 t)))))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 1 (/.f64 t (+.f64 -2 (/.f64 -2 z))))))
✓	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
	1.0b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))))
▶	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 3557 to 2272 computations (36.1% saved)

localize16.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))
✓	0.2b	(/.f64 (/.f64 2 t) z)
✓	0.5b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))

series109.0ms (1.4%)

Counts

3 → 96

Calls

3 calls:

70.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
20.0ms	(+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))
19.0ms	(/.f64 (/.f64 2 t) z)

rewrite101.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

95×	`times-frac_binary64`
70×	`*-un-lft-identity_binary64`
60×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`
26×	`fma-def_binary64`

Counts

3 → 138

Calls

3 calls:

46.0ms	(+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))
18.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
15.0ms	(/.f64 (/.f64 2 t) z)

simplify144.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

552×	`distribute-rgt-in_binary64`
513×	`distribute-lft-in_binary64`
485×	`fma-def_binary64`
458×	`times-frac_binary64`
147×	`associate-/l/_binary64`

Counts

234 → 202

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	258	3705
1	632	3560
2	1751	3552
3	5063	3552

prune491.0ms (6.1%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	201	1	202
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	201	7	208

Error

Counts

208 → 7

Alt Table

Status	Error	Program
	1.1b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (/.f64 (.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 (+.f64 -2 (/.f64 -2 z)))) (*.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 t)))))
	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 1 (/.f64 t (+.f64 -2 (/.f64 -2 z))))))
✓	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 2 (.f64 t z)))))))
	1.0b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 (/.f64 1 (.f64 (cbrt.f64 t) (cbrt.f64 t))) (/.f64 (+.f64 -2 (/.f64 -2 z)) (cbrt.f64 t)))))
	0.8b	(+.f64 (/.f64 x y) (-.f64 -2 (.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (.f64 (cbrt.f64 (/.f64 2 t)) (cbrt.f64 (/.f64 2 t))) (/.f64 z (cbrt.f64 (/.f64 2 t)))))))))
✓	0.6b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 1 (neg.f64 (+.f64 (/.f64 2 t) (/.f64 (/.f64 2 t) z))))))
✓	0.1b	(fma.f64 x (/.f64 1 y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 5621 to 3698 computations (34.2% saved)

regimes1.9s (23.5%)

Accuracy

Total 0.1b remaining (35.5%)

Threshold costs 0.1b (35.5%)

Counts

101 → 1

Compiler

Compiled 27266 to 20827 computations (23.6% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
4×	`sub-neg_binary64`
3×	`*-commutative_binary64`
3×	`neg-sub0_binary64`
3×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	13	20
1	18	20
2	24	20
3	33	20
4	40	20
5	43	20
6	44	20
7	42	20

end275.0ms (3.4%)

Compiler: Compiled 215 to 164 computations (23.7% saved)

Details

analyze1.1s (13.6%)

sample1.7s (21.7%)

simplify177.0ms (2.2%)

prune8.0ms (0.1%)

localize20.0ms (0.3%)

series79.0ms (1%)

rewrite124.0ms (1.6%)

simplify223.0ms (2.8%)

prune478.0ms (6%)

localize18.0ms (0.2%)

series83.0ms (1%)

rewrite1.0ms (0%)

simplify146.0ms (1.8%)

prune172.0ms (2.1%)

localize27.0ms (0.3%)

series97.0ms (1.2%)

rewrite56.0ms (0.7%)

simplify189.0ms (2.4%)

prune258.0ms (3.2%)

localize16.0ms (0.2%)

series109.0ms (1.4%)

rewrite101.0ms (1.3%)

simplify144.0ms (1.8%)

prune491.0ms (6.1%)

regimes1.9s (23.5%)

simplify6.0ms (0.1%)

end275.0ms (3.4%)

Profiling