Details

analyze1.9s (26.3%)

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)

sample1.5s (20.4%)

Results

1.1s	8256×	body	128	valid
311.0ms	2402×	body	128	invalid

Compiler

Compiled 65 to 47 computations (27.7% saved)

simplify104.0ms (1.4%)

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

0.0b

Counts

3 → 2

Alt Table

Status	Error	Program
	7.4b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 110 to 79 computations (28.2% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series47.0ms (0.6%)

Counts

3 → 84

Calls

3 calls:

32.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
13.0ms	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
1.0ms	(+.f64 -2 (/.f64 -2 z))

rewrite49.0ms (0.7%)

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:

21.0ms	(+.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))

simplify122.0ms (1.7%)

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

prune200.0ms (2.8%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	198	3	201
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	198	5	203

Error

0.0b

Counts

203 → 5

Alt Table

Status	Error	Program
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	7.4b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
	50.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (sqrt.f64 (+.f64 -2 (/.f64 -2 z))) (/.f64 (sqrt.f64 (+.f64 -2 (/.f64 -2 z))) t))))
	0.5b	(+.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)))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 6740 to 4676 computations (30.6% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

series44.0ms (0.6%)

Counts

2 → 72

Calls

2 calls:

29.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
14.0ms	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))

rewrite21.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`add-sqr-sqrt_binary64`
23×	`*-un-lft-identity_binary64`
20×	`times-frac_binary64`
18×	`add-cube-cbrt_binary64`
13×	`fma-def_binary64`

Counts

2 → 79

Calls

2 calls:

10.0ms	(*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))
7.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))

simplify139.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

583×	`distribute-rgt-in_binary64`
562×	`distribute-lft-in_binary64`
452×	`fma-def_binary64`
260×	`times-frac_binary64`
226×	`associate-*l/_binary64`

Counts

151 → 131

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	159	2527
1	439	2344
2	1293	2210
3	4077	2210
4	4984	2210
5	4987	2210
6	4941	2210

prune136.0ms (1.9%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	155	5	160

Error

0.0b

Counts

160 → 5

Alt Table

Status	Error	Program
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	7.4b	(+.f64 (/.f64 x y) (/.f64 (+.f64 2 (.f64 (.f64 z 2) (-.f64 1 t))) (*.f64 t z)))
	50.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (sqrt.f64 (+.f64 -2 (/.f64 -2 z))) (/.f64 (sqrt.f64 (+.f64 -2 (/.f64 -2 z))) t))))
▶	0.5b	(+.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)))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 3713 to 2584 computations (30.4% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.1b	(/.f64 (+.f64 -2 (/.f64 -2 z)) t)
✓	0.4b	(.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)))
✓	0.5b	(*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))
✓	0.6b	(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

series909.0ms (12.6%)

Counts

3 → 72

Calls

3 calls:

481.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

368.0ms

(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

60.0ms

(*.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)))

rewrite71.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

122×	`cbrt-prod_binary64`
114×	`*-un-lft-identity_binary64`
91×	`times-frac_binary64`
88×	`add-sqr-sqrt_binary64`
60×	`add-cube-cbrt_binary64`

Counts

3 → 181

Calls

3 calls:

22.0ms

(*.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)))

19.0ms

(*.f64 (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)) (cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

8.0ms

(cbrt.f64 (/.f64 (+.f64 -2 (/.f64 -2 z)) t))

simplify224.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

793×	`fma-def_binary64`
506×	`times-frac_binary64`
279×	`associate-r_binary64`
275×	`cancel-sign-sub-inv_binary64`
272×	`associate-l_binary64`

Counts

253 → 276

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	323	7739
1	734	7358
2	2319	6759
3	4761	6652
4	4989	6652
5	4963	6652

prune626.0ms (8.7%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	516	2	518
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	517	6	523

Error

Counts

523 → 6

Alt Table

Status	Error	Program
	0.6b	(+.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))) (/.f64 (cbrt.f64 (+.f64 -2 (/.f64 -2 z))) (cbrt.f64 t)))))
▶	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (+.f64 -2 (/.f64 -2 z)) (/.f64 1 t))))
	50.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (sqrt.f64 (+.f64 -2 (/.f64 -2 z))) (/.f64 (sqrt.f64 (+.f64 -2 (/.f64 -2 z))) t))))
✓	0.5b	(+.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)))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 22181 to 16344 computations (26.3% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (/.f64 x y) (-.f64 -2 (+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))))
✓	0.0b	(+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))
✓	0.7b	(/.f64 -2 (*.f64 t z))

series50.0ms (0.7%)

Counts

3 → 72

Calls

3 calls:

31.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))))
10.0ms	(+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))
9.0ms	(/.f64 -2 (*.f64 t z))

rewrite36.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

47×	`*-un-lft-identity_binary64`
28×	`add-sqr-sqrt_binary64`
28×	`add-cube-cbrt_binary64`
26×	`fma-def_binary64`
21×	`associate-+r+_binary64`

Counts

3 → 107

Calls

3 calls:

18.0ms	(+.f64 (/.f64 x y) (-.f64 -2 (+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))))
7.0ms	(+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))
3.0ms	(/.f64 -2 (*.f64 t z))

simplify96.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

613×	`distribute-rgt-in_binary64`
594×	`fma-def_binary64`
577×	`distribute-lft-in_binary64`
288×	`fma-neg_binary64`
178×	`cancel-sign-sub-inv_binary64`

Counts

179 → 164

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	179	2846
1	457	2755
2	1384	2740
3	4853	2740
4	4976	2740

prune153.0ms (2.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	163	1	164
Fresh	1	1	2
Picked	0	1	1
Done	1	2	3
Total	165	5	170

Error

Counts

170 → 5

Alt Table

Status	Error	Program
	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (+.f64 (/.f64 -2 t) (/.f64 (/.f64 -2 t) z))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (+.f64 (/.f64 -2 t) (/.f64 -2 (*.f64 t z)))))
	50.1b	(+.f64 (/.f64 x y) (-.f64 -2 (*.f64 (sqrt.f64 (+.f64 -2 (/.f64 -2 z))) (/.f64 (sqrt.f64 (+.f64 -2 (/.f64 -2 z))) t))))
✓	0.5b	(+.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)))))
✓	0.1b	(+.f64 (/.f64 x y) (-.f64 -2 (/.f64 (+.f64 -2 (/.f64 -2 z)) t)))

Compiler

Compiled 4467 to 2695 computations (39.7% saved)

regimes701.0ms (9.7%)

Accuracy

Total 0.1b remaining (83%)

Threshold costs 0.1b (83%)

Counts

69 → 1

Compiler

Compiled 11536 to 8929 computations (22.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

6×	`+-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	12	19
1	16	19
2	23	19
3	32	19
4	39	19
5	42	19
6	43	19
7	42	19

end86.0ms (1.2%)

Compiler: Compiled 150 to 115 computations (23.3% saved)

Details

analyze1.9s (26.3%)

sample1.5s (20.4%)

simplify104.0ms (1.4%)

prune4.0ms (0.1%)

localize8.0ms (0.1%)

series47.0ms (0.6%)

rewrite49.0ms (0.7%)

simplify122.0ms (1.7%)

prune200.0ms (2.8%)

localize9.0ms (0.1%)

series44.0ms (0.6%)

rewrite21.0ms (0.3%)

simplify139.0ms (1.9%)

prune136.0ms (1.9%)

localize11.0ms (0.2%)

series909.0ms (12.6%)

rewrite71.0ms (1%)

simplify224.0ms (3.1%)

prune626.0ms (8.7%)

localize9.0ms (0.1%)

series50.0ms (0.7%)

rewrite36.0ms (0.5%)

simplify96.0ms (1.3%)

prune153.0ms (2.1%)

regimes701.0ms (9.7%)

simplify3.0ms (0%)

end86.0ms (1.2%)

Profiling