Details

analyze959.0ms (5.4%)

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
13.3%	86.5%	0.2%	9
19.9%	79.9%	0.2%	10
22.8%	77%	0.2%	11
25.4%	72.7%	1.9%	12
35.8%	59.6%	4.6%	13
42%	52.3%	5.8%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.3s (7.4%)

Results

943.0ms	8256×	body	128	valid
257.0ms	2157×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify70.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

973×	`fma-def_binary64`
752×	`fma-neg_binary64`
239×	`cancel-sign-sub-inv_binary64`
193×	`distribute-rgt-in_binary64`
133×	`distribute-lft-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	33	11
3	64	11
4	125	11
5	238	11
6	414	11
7	791	11
8	1182	11
9	1373	11
10	1483	11
11	1532	11
12	1538	11
13	1543	11
14	1543	11
15	1458	11

prune3.0ms (0%)

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
▶	2.1b	(fma.f64 (-.f64 y x) (/.f64 z t) x)
	7.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))

Compiler

Compiled 71 to 40 computations (43.7% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	2.0b	(fma.f64 (-.f64 y x) (/.f64 z t) x)

series25.0ms (0.1%)

Counts

1 → 48

Calls

1 calls:

25.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

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:

0.0ms

(fma.f64 (-.f64 y x) (/.f64 z t) x)

simplify67.0ms (0.4%)

Algorithm

1×	egg-herbie

Rules

539×	`distribute-rgt-neg-out_binary64`
515×	`distribute-lft-neg-out_binary64`
375×	`distribute-rgt-in_binary64`
373×	`distribute-lft-in_binary64`
270×	`times-frac_binary64`

Counts

58 → 31

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	41	946
1	88	635
2	194	623
3	469	623
4	2305	623
5	4632	623
6	5238	623

prune21.0ms (0.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	27	4	31
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	28	5	33

Error

0.0b

Counts

33 → 5

Alt Table

Status	Error	Program
	7.1b	(+.f64 x (/.f64 (*.f64 (-.f64 y x) z) t))
	31.1b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	43.1b	(cbrt.f64 (.f64 (.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x) (fma.f64 (-.f64 y x) (/.f64 z t) x)) (fma.f64 (-.f64 y x) (/.f64 z t) x)))
▶	2.1b	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)
	36.9b	(*.f64 z (/.f64 (-.f64 y x) t))

Compiler

Compiled 536 to 163 computations (69.6% saved)

localize7.0ms (0%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)
✓	5.3b	(*.f64 (-.f64 y x) (/.f64 z t))

series46.0ms (0.3%)

Counts

2 → 96

Calls

2 calls:

26.0ms	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)
20.0ms	(*.f64 (-.f64 y x) (/.f64 z t))

rewrite19.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
10×	`times-frac_binary64`
10×	`add-cube-cbrt_binary64`

Counts

2 → 54

Calls

2 calls:

8.0ms	(*.f64 (-.f64 y x) (/.f64 z t))
7.0ms	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)

simplify103.0ms (0.6%)

Algorithm

1×	egg-herbie

Rules

417×	`associate-l_binary64`
395×	`distribute-rgt-in_binary64`
376×	`distribute-lft-in_binary64`
352×	`associate-r_binary64`
351×	`fma-neg_binary64`

Counts

150 → 98

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	141	2201
1	369	1746
2	1183	1737
3	4199	1737
4	4679	1737
5	5004	1737

prune58.0ms (0.3%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	93	5	98
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	95	8	103

Error

0.0b

Counts

103 → 8

Alt Table

Status	Error	Program
✓	2.1b	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)
▶	2.6b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))) x)
	36.9b	(*.f64 z (/.f64 (-.f64 y x) t))
	31.2b	(+.f64 (.f64 (sqrt.f64 (.f64 z (/.f64 (-.f64 y x) t))) (sqrt.f64 (*.f64 z (/.f64 (-.f64 y x) t)))) x)
	7.1b	(+.f64 (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)) x)
	36.6b	(+.f64 (*.f64 (/.f64 (-.f64 y x) (sqrt.f64 t)) (/.f64 z (sqrt.f64 t))) x)
	31.1b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	6.2b	(+.f64 (.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) t)) x)

Compiler

Compiled 1803 to 530 computations (70.6% saved)

localize10.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))
✓	0.6b	(cbrt.f64 (-.f64 y x))
✓	2.2b	(*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))
✓	3.3b	(.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))

series653.0ms (3.7%)

Counts

4 → 144

Calls

4 calls:

556.0ms	(*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))
38.0ms	(*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))
30.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))
29.0ms	(cbrt.f64 (-.f64 y x))

rewrite66.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

126×	`cbrt-div_binary64`
88×	`frac-times_binary64`
63×	`flip--_binary64`
63×	`flip3--_binary64`
52×	`add-sqr-sqrt_binary64`

Counts

4 → 201

Calls

4 calls:

17.0ms	(.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))
10.0ms	(*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))
8.0ms	(*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x)))
2.0ms	(cbrt.f64 (-.f64 y x))

simplify200.0ms (1.1%)

Algorithm

1×	egg-herbie

Rules

714×	`associate-r_binary64`
681×	`associate-l_binary64`
584×	`fma-def_binary64`
245×	`fma-neg_binary64`
229×	`*-commutative_binary64`

Counts

345 → 368

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	499	9455
1	1417	8611
2	4662	8609
3	5187	8609

prune358.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	471	1	472
Fresh	0	6	6
Picked	1	0	1
Done	0	1	1
Total	472	8	480

Error

0.0b

Counts

480 → 8

Alt Table

Status	Error	Program
▶	2.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))))) x)
	36.6b	(+.f64 (*.f64 (/.f64 (-.f64 y x) (sqrt.f64 t)) (/.f64 z (sqrt.f64 t))) x)
	36.9b	(*.f64 z (/.f64 (-.f64 y x) t))
	31.2b	(+.f64 (.f64 (sqrt.f64 (.f64 z (/.f64 (-.f64 y x) t))) (sqrt.f64 (*.f64 z (/.f64 (-.f64 y x) t)))) x)
	7.1b	(+.f64 (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)) x)
	31.1b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	6.2b	(+.f64 (.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) t)) x)
✓	2.1b	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)

Compiler

Compiled 16800 to 5715 computations (66% saved)

localize13.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.6b	(cbrt.f64 (-.f64 y x))
	2.2b	(*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))
✓	3.3b	(.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))))
✓	8.1b	(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))

series1.1s (5.9%)

Counts

2 → 96

Calls

2 calls:

991.0ms

(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))

61.0ms

(*.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))))

rewrite2.4s (13.3%)

Algorithm

1×	rewrite-expression-head

Rules

11349×	`cbrt-div_binary64`
7455×	`frac-times_binary64`
3242×	`flip--_binary64`
3242×	`flip3--_binary64`
2971×	`associate-*l/_binary64`

Counts

2 → 1990

Calls

2 calls:

73.0ms

(*.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (*.f64 (*.f64 (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))))

5.0ms

(cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))

simplify5.2s (29.1%)

Algorithm

1×	egg-herbie

Rules

2925×	`associate-l_binary64`
25×	`sqr-pow_binary64`
22×	`sub-neg_binary64`
15×	`fma-neg_binary64`
13×	`unswap-sqr_binary64`

Counts

2086 → 3842

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	3544	233920
1	7319	233920

prune4.4s (25%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	4529	0	4529
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	4529	8	4537

Error

0.0b

Counts

4537 → 8

Alt Table

Status	Error	Program
✓	2.8b	(+.f64 (.f64 (.f64 (cbrt.f64 (-.f64 y x)) (cbrt.f64 (-.f64 y x))) (.f64 (.f64 (cbrt.f64 (.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))) (cbrt.f64 (.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t)))) (cbrt.f64 (*.f64 (cbrt.f64 (-.f64 y x)) (/.f64 z t))))) x)
	36.6b	(+.f64 (*.f64 (/.f64 (-.f64 y x) (sqrt.f64 t)) (/.f64 z (sqrt.f64 t))) x)
	36.9b	(*.f64 z (/.f64 (-.f64 y x) t))
	31.2b	(+.f64 (.f64 (sqrt.f64 (.f64 z (/.f64 (-.f64 y x) t))) (sqrt.f64 (*.f64 z (/.f64 (-.f64 y x) t)))) x)
	7.1b	(+.f64 (.f64 (.f64 (-.f64 y x) z) (/.f64 1 t)) x)
	31.1b	(*.f64 (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)) (sqrt.f64 (fma.f64 (-.f64 y x) (/.f64 z t) x)))
	6.2b	(+.f64 (.f64 (.f64 (-.f64 y x) (*.f64 (cbrt.f64 z) (cbrt.f64 z))) (/.f64 (cbrt.f64 z) t)) x)
✓	2.1b	(+.f64 (*.f64 (-.f64 y x) (/.f64 z t)) x)

Compiler

Compiled 361262 to 78494 computations (78.3% saved)

regimes645.0ms (3.6%)

Accuracy

Total 1.8b remaining (99%)

Threshold costs 0b (0%)

Counts

93 → 1

Compiler

Compiled 11246 to 5578 computations (50.4% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	13	13
2	18	13
3	20	13
4	21	13
5	21	13

end104.0ms (0.6%)

Compiler: Compiled 193 to 95 computations (50.8% saved)

Details

analyze959.0ms (5.4%)

sample1.3s (7.4%)

simplify70.0ms (0.4%)

prune3.0ms (0%)

localize5.0ms (0%)

series25.0ms (0.1%)

rewrite1.0ms (0%)

simplify67.0ms (0.4%)

prune21.0ms (0.1%)

localize7.0ms (0%)

series46.0ms (0.3%)

rewrite19.0ms (0.1%)

simplify103.0ms (0.6%)

prune58.0ms (0.3%)

localize10.0ms (0.1%)

series653.0ms (3.7%)

rewrite66.0ms (0.4%)

simplify200.0ms (1.1%)

prune358.0ms (2%)

localize13.0ms (0.1%)

series1.1s (5.9%)

rewrite2.4s (13.3%)

simplify5.2s (29.1%)

prune4.4s (25%)

regimes645.0ms (3.6%)

simplify2.0ms (0%)

end104.0ms (0.6%)

Profiling