Details

analyze964.0ms (6.9%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
25%	74.9%	0.1%	4
37.4%	62.4%	0.1%	5
37.4%	62.4%	0.1%	6
37.4%	56.2%	6.4%	7
45.2%	48.4%	6.4%	8
49.1%	42.1%	8.7%	9
51.5%	35.1%	13.4%	10
58.1%	27.7%	14.2%	11
60.8%	22.6%	16.5%	12
62.3%	18.7%	19%	13
66.2%	14.4%	19.4%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample3.2s (22.6%)

Results

1.0s	5500×	body	128	valid
773.0ms	1124×	body	2048	valid
412.0ms	699×	body	1024	valid
332.0ms	386×	body	4096	valid
159.0ms	384×	body	512	valid
121.0ms	669×	body	128	invalid
46.0ms	163×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify217.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

2079×	`fma-neg_binary64`
1006×	`fma-def_binary64`
919×	`div-sub_binary64`
626×	`distribute-rgt-in_binary64`
435×	`cancel-sign-sub-inv_binary64`

Counts

1 → 2

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	38	24
2	95	24
3	227	22
4	357	22
5	614	22
6	1103	22
7	1373	22
8	1636	22
9	2330	22
10	3187	22
11	2880	22
12	2827	22
13	2896	22
14	2922	22
15	3797	22
16	4824	22
17	5240	22

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

31.9b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	31.9b	(.f64 -1/2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) a))

Compiler

Compiled 71 to 46 computations (35.2% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
✓	0.6b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
✓	25.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series403.0ms (2.9%)

Counts

3 → 60

Calls

3 calls:

219.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
106.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
77.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

rewrite21.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
14×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
5×	`distribute-lft-out_binary64`

Counts

3 → 67

Calls

3 calls:

8.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) a)
4.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
2.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

simplify406.0ms (2.9%)

Algorithm

1×	egg-herbie

Rules

820×	`times-frac_binary64`
539×	`associate-/l*_binary64`
458×	`fma-def_binary64`
246×	`fma-neg_binary64`
189×	`cancel-sign-sub-inv_binary64`

Counts

127 → 169

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	188	3311
1	510	3170
2	1534	3008
3	4840	3008
4	4954	3008

prune209.0ms (1.5%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	159	10	169
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	160	10	170

Error

3.6b

Counts

170 → 10

Alt Table

Status	Error	Program
	40.1b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	41.3b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	32.2b	(.f64 -1/2 (.f64 (/.f64 1 (.f64 (cbrt.f64 a) (cbrt.f64 a))) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (cbrt.f64 a))))
	32.0b	(.f64 -1/2 (.f64 (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) 1) (/.f64 (sqrt.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) a)))
	46.9b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
	49.7b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
▶	31.9b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	32.9b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	37.3b	(.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))
	48.7b	(.f64 -1/2 (.f64 (/.f64 1 (sqrt.f64 a)) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 a))))

Compiler

Compiled 4798 to 2900 computations (39.6% saved)

localize22.0ms (0.2%)

Local error

Found 3 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))) (/.f64 1 a))
	0.6b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
	25.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

series139.0ms (1%)

Counts

1 → 20

Calls

1 calls:

139.0ms

(*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))

rewrite23.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

16×	`add-sqr-sqrt_binary64`
13×	`associate-r_binary64`
12×	`*-un-lft-identity_binary64`
11×	`times-frac_binary64`
10×	`add-exp-log_binary64`

Counts

1 → 43

Calls

1 calls:

14.0ms

(*.f64 (+.f64 b (sqrt.f64 (fma.f64 a (*.f64 c -4) (*.f64 b b)))) (/.f64 1 a))

simplify130.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

460×	`times-frac_binary64`
408×	`associate-l_binary64`
317×	`unswap-sqr_binary64`
311×	`associate-/l*_binary64`
305×	`fma-def_binary64`

Counts

63 → 91

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	131	1718
1	370	1571
2	1178	1497
3	4445	1497
4	5276	1497

prune301.0ms (2.2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	182	1	183
Fresh	3	6	9
Picked	0	1	1
Done	0	0	0
Total	185	8	193

Error

3.6b

Counts

193 → 8

Alt Table

Status	Error	Program
	40.1b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	41.3b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	46.9b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
	49.7b	(.f64 -1/2 (/.f64 (.f64 2 (fma.f64 (/.f64 c b) a (/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3)))) a))
	49.4b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 a (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 -4 a))) b)))))
✓	31.9b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
▶	32.9b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	37.3b	(.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))

Compiler

Compiled 5212 to 3267 computations (37.3% saved)

localize22.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
✓	0.1b	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
✓	0.6b	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
✓	9.7b	(sqrt.f64 (.f64 a (.f64 c -4)))

series1.2s (8.3%)

Counts

4 → 42

Calls

4 calls:

663.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
283.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
174.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
32.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

rewrite48.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

114×	`times-frac_binary64`
99×	`*-un-lft-identity_binary64`
65×	`add-sqr-sqrt_binary64`
65×	`add-cube-cbrt_binary64`
22×	`associate-/r*_binary64`

Counts

4 → 164

Calls

4 calls:

13.0ms	(/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
8.0ms	(/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
5.0ms	(+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))
4.0ms	(sqrt.f64 (.f64 a (.f64 c -4)))

simplify267.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

502×	`associate-*l/_binary64`
496×	`fma-def_binary64`
478×	`fma-neg_binary64`
422×	`associate-/r/_binary64`
308×	`cancel-sign-sub-inv_binary64`

Counts

206 → 291

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	261	6252
1	644	5816
2	2163	5690
3	4938	5684
4	5187	5684

prune841.0ms (6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	288	3	291
Fresh	1	5	6
Picked	0	1	1
Done	0	1	1
Total	289	10	299

Error

1.2b

Counts

299 → 10

Alt Table

Status	Error	Program
	49.4b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 a (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 -4 a))) b)))))
	40.1b	(.f64 -1/2 (/.f64 1 (.f64 (/.f64 b (*.f64 -4 c)) -2)))
	47.4b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))
▶	37.3b	(.f64 -1/2 (/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))) a))
	40.1b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	41.3b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	46.9b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
	57.3b	(.f64 -1/2 (/.f64 1 (/.f64 a (fma.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3)) (fma.f64 (/.f64 (pow.f64 (.f64 -4 (.f64 c a)) 3) (pow.f64 b 5)) -1/16 (/.f64 2 (/.f64 b (.f64 c a))))))))
✓	31.9b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
✓	32.9b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))

Compiler

Compiled 9104 to 6016 computations (33.9% saved)

localize33.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))) a)
✓	3.4b	(exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4))))))
	9.7b	(sqrt.f64 (.f64 a (.f64 c -4)))
✓	11.0b	(+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))

series869.0ms (6.2%)

Counts

3 → 42

Calls

3 calls:

425.0ms

(/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))) a)

245.0ms

(+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))

199.0ms

(exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))

rewrite15.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`*-un-lft-identity_binary64`
15×	`add-sqr-sqrt_binary64`
15×	`add-cube-cbrt_binary64`
12×	`times-frac_binary64`
5×	`distribute-lft-out_binary64`

Counts

3 → 69

Calls

3 calls:

6.0ms

(/.f64 (+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))) a)

4.0ms

(+.f64 b (exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4)))))))

2.0ms

(exp.f64 (log.f64 (hypot.f64 b (sqrt.f64 (*.f64 a (*.f64 c -4))))))

simplify145.0ms (1%)

Algorithm

1×	egg-herbie

Rules

837×	`times-frac_binary64`
498×	`associate-/l*_binary64`
439×	`associate-/r*_binary64`
424×	`fma-def_binary64`
352×	`fma-neg_binary64`

Counts

111 → 173

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	209	3059
1	521	2817
2	1393	2779
3	4754	2775
4	4985	2767
5	4958	2767

prune218.0ms (1.6%)

Pruning

10 alts after pruning (8 fresh and 2 done)

	Pruned	Kept	Total
New	192	1	193
Fresh	0	7	7
Picked	1	0	1
Done	0	2	2
Total	193	10	203

Error

1.2b

Counts

203 → 10

Alt Table

Status	Error	Program
	49.4b	(.f64 -1/2 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (.f64 a (-.f64 b (hypot.f64 (sqrt.f64 (.f64 c (*.f64 -4 a))) b)))))
	40.1b	(.f64 -1/2 (/.f64 1 (.f64 (/.f64 b (*.f64 -4 c)) -2)))
	38.3b	(.f64 -1/2 (/.f64 (+.f64 b (pow.f64 (exp.f64 (.f64 (cbrt.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) (cbrt.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) (cbrt.f64 (log.f64 (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))) a))
✓	31.9b	(.f64 -1/2 (.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (/.f64 1 a)))
	40.1b	(.f64 -1/2 (.f64 2 (/.f64 c b)))
	41.3b	(*.f64 -1/2 (/.f64 (+.f64 b b) a))
	46.9b	(.f64 -1/2 (/.f64 (/.f64 (-.f64 (.f64 b b) (fma.f64 a (.f64 c -4) (.f64 b b))) (-.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))) a))
	57.3b	(.f64 -1/2 (/.f64 1 (/.f64 a (fma.f64 1/8 (/.f64 (pow.f64 (sqrt.f64 (.f64 -4 (.f64 c a))) 4) (pow.f64 b 3)) (fma.f64 (/.f64 (pow.f64 (.f64 -4 (.f64 c a)) 3) (pow.f64 b 5)) -1/16 (/.f64 2 (/.f64 b (.f64 c a))))))))
✓	32.9b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (sqrt.f64 (.f64 a (*.f64 c -4))))))))
	47.4b	(.f64 -1/2 (/.f64 1 (/.f64 a (+.f64 b (hypot.f64 b (.f64 (sqrt.f64 a) (sqrt.f64 (*.f64 c -4))))))))

Compiler

Compiled 5551 to 3663 computations (34% saved)

regimes3.9s (28.1%)

Accuracy

Total 6.9b remaining (73.1%)

Threshold costs 0b (0%)

Counts

203 → 3

Compiler

Compiled 18864 to 13326 computations (29.4% saved)

bsearch92.0ms (0.7%)

Steps

Iters	Range		Point
4	4.199021549675812e+120	7.979983627339533e+128	2.4796580311829948e+128
10	-0.6073820109206627	-6.806189290200473e-18	-6.901485601872386e-18

Compiler

Compiled 4 to 3 computations (25% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`/-rgt-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	29	54
1	37	54
2	36	54

end321.0ms (2.3%)

Compiler: Compiled 318 to 222 computations (30.2% saved)

Details

analyze964.0ms (6.9%)

sample3.2s (22.6%)

simplify217.0ms (1.6%)

prune4.0ms (0%)

localize10.0ms (0.1%)

series403.0ms (2.9%)

rewrite21.0ms (0.1%)

simplify406.0ms (2.9%)

prune209.0ms (1.5%)

localize22.0ms (0.2%)

series139.0ms (1%)

rewrite23.0ms (0.2%)

simplify130.0ms (0.9%)

prune301.0ms (2.2%)

localize22.0ms (0.2%)

series1.2s (8.3%)

rewrite48.0ms (0.3%)

simplify267.0ms (1.9%)

prune841.0ms (6%)

localize33.0ms (0.2%)

series869.0ms (6.2%)

rewrite15.0ms (0.1%)

simplify145.0ms (1%)

prune218.0ms (1.6%)

regimes3.9s (28.1%)

bsearch92.0ms (0.7%)

simplify3.0ms (0%)

end321.0ms (2.3%)

Profiling