Details

analyze1.3s (11.1%)

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
0%	99.9%	0.1%	4
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 21 to 15 computations (28.6% saved)

sample3.2s (27.6%)

Results

958.0ms	5336×	body	128	valid
811.0ms	1137×	body	2048	valid
492.0ms	788×	body	1024	valid
355.0ms	418×	body	4096	valid
178.0ms	1026×	body	128	invalid
176.0ms	401×	body	512	valid
60.0ms	176×	body	256	valid

Compiler

Compiled 62 to 44 computations (29% saved)

simplify296.0ms (2.6%)

Algorithm

1×	egg-herbie

Rules

1743×	`fma-neg_binary64`
1393×	`fma-def_binary64`
800×	`div-sub_binary64`
619×	`times-frac_binary64`
473×	`associate-/r/_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	15	26
1	33	22
2	67	22
3	138	22
4	204	22
5	338	22
6	558	22
7	924	22
8	1388	22
9	1604	22
10	2375	22
11	2742	22
12	2533	22
13	2621	22
14	3171	22
15	3313	22
16	3873	22
17	3679	22
18	4029	22
19	4317	22
20	4485	22
21	4561	22
22	4805	22
23	4793	22
24	4797	22
25	4797	22
26	4948	22

prune4.0ms (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

35.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	35.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	35.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))

Compiler

Compiled 111 to 74 computations (33.3% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
✓	1.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
✓	1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series206.0ms (1.8%)

Counts

4 → 96

Calls

4 calls:

89.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
63.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
43.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
11.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite28.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
11×	`add-sqr-sqrt_binary64`
10×	`fma-def_binary64`
10×	`add-cube-cbrt_binary64`
10×	`add-log-exp_binary64`

Counts

4 → 90

Calls

4 calls:

10.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

simplify153.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

701×	`fma-neg_binary64`
334×	`cancel-sign-sub-inv_binary64`
215×	`distribute-rgt-neg-in_binary64`
159×	`associate-r_binary64`
150×	`distribute-rgt-neg-out_binary64`

Counts

186 → 207

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	243	4208
1	695	3858
2	2512	3724
3	4694	3704
4	5031	3704

prune224.0ms (2%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	197	10	207
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	199	10	209

Error

4.5b

Counts

209 → 10

Alt Table

Status	Error	Program
	35.8b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	47.6b	(/.f64 (neg.f64 b) a)
▶	35.2b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (neg.f64 b)) (.f64 2 a))
	55.6b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	36.6b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	40.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	41.6b	(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))
	35.7b	(neg.f64 (/.f64 c b))
	47.1b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (.f64 (.f64 2 a) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))))
	35.3b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))

Compiler

Compiled 5745 to 3357 computations (41.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (neg.f64 b)) (.f64 2 a))
✓	1.7b	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) (neg.f64 b))
	1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series179.0ms (1.6%)

Counts

2 → 40

Calls

2 calls:

118.0ms	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (neg.f64 b)) (.f64 2 a))
61.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) (neg.f64 b))

rewrite40.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`*-un-lft-identity_binary64`
7×	`add-cbrt-cube_binary64`
7×	`add-exp-log_binary64`
6×	`distribute-lft-out_binary64`
6×	`add-log-exp_binary64`

Counts

2 → 55

Calls

2 calls:

19.0ms	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (neg.f64 b)) (.f64 2 a))
15.0ms	(+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))) (neg.f64 b))

simplify216.0ms (1.9%)

Algorithm

1×	egg-herbie

Rules

593×	`fma-def_binary64`
440×	`fma-neg_binary64`
283×	`distribute-rgt-in_binary64`
218×	`distribute-lft-in_binary64`
160×	`cancel-sign-sub-inv_binary64`

Counts

95 → 123

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	183	2627
1	548	2426
2	1899	2313
3	4699	2313
4	5000	2313
5	4993	2313
6	4919	2313

prune301.0ms (2.6%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	206	0	206
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	206	10	216

Error

4.5b

Counts

216 → 10

Alt Table

Status	Error	Program
	35.8b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	47.6b	(/.f64 (neg.f64 b) a)
✓	35.2b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (neg.f64 b)) (.f64 2 a))
	55.6b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	36.6b	(/.f64 (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b))) (*.f64 2 a))
	40.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	41.6b	(-.f64 (neg.f64 (/.f64 c b)) (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))
	35.7b	(neg.f64 (/.f64 c b))
	47.1b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) 3)) (.f64 (.f64 2 a) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))))
▶	35.3b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))

Compiler

Compiled 5731 to 3373 computations (41.1% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(/.f64 1 (/.f64 (.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))))
	1.7b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series153.0ms (1.3%)

Counts

1 → 20

Calls

1 calls:

153.0ms

(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

rewrite43.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`times-frac_binary64`
37×	`*-un-lft-identity_binary64`
22×	`add-exp-log_binary64`
21×	`add-sqr-sqrt_binary64`
21×	`add-cube-cbrt_binary64`

Counts

1 → 74

Calls

1 calls:

20.0ms

(/.f64 1 (/.f64 (*.f64 2 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (*.f64 b b) (*.f64 (*.f64 4 a) c))))))

simplify152.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

665×	`associate-/l*_binary64`
599×	`div-sub_binary64`
349×	`fma-def_binary64`
295×	`fma-neg_binary64`
265×	`associate-/r/_binary64`

Counts

94 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	164	3247
1	439	2847
2	1517	2670
3	4595	2670
4	6178	2670

prune337.0ms (3%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	254	3	257
Fresh	3	5	8
Picked	1	0	1
Done	0	1	1
Total	258	9	267

Error

4.4b

Counts

267 → 9

Alt Table

Status	Error	Program
	35.8b	(/.f64 (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (/.f64 (.f64 2 a) (sqrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	47.6b	(/.f64 (neg.f64 b) a)
	36.6b	(/.f64 1 (/.f64 (.f64 2 a) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))))
	35.7b	(neg.f64 (/.f64 c b))
✓	35.2b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (neg.f64 b)) (.f64 2 a))
	55.6b	(/.f64 (+.f64 (neg.f64 b) b) (*.f64 2 a))
	40.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	35.7b	(.f64 (.f64 (.f64 4 (.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
▶	29.5b	(/.f64 (.f64 (.f64 4 (.f64 c a)) (/.f64 1/2 a)) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))

Compiler

Compiled 7792 to 4778 computations (38.7% saved)

localize26.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.8b	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
	1.8b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	13.0b	(.f64 (.f64 4 (*.f64 c a)) (/.f64 1/2 a))
	22.3b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

series97.0ms (0.9%)

Counts

2 → 44

Calls

2 calls:

90.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
7.0ms	(.f64 (.f64 4 (*.f64 c a)) (/.f64 1/2 a))

rewrite32.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

60×	`prod-diff_binary64`
56×	`*-un-lft-identity_binary64`
56×	`add-sqr-sqrt_binary64`
52×	`add-cube-cbrt_binary64`
34×	`sqrt-prod_binary64`

Counts

2 → 135

Calls

2 calls:

10.0ms	(-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
7.0ms	(.f64 (.f64 4 (*.f64 c a)) (/.f64 1/2 a))

simplify156.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

581×	`fma-neg_binary64`
544×	`fma-def_binary64`
343×	`associate-l_binary64`
287×	`associate-r_binary64`
167×	`exp-prod_binary64`

Counts

179 → 176

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	262	6296
1	644	4141
2	2598	3117
3	4447	3115
4	4896	3115

prune231.0ms (2%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	257	2	259
Fresh	2	5	7
Picked	1	0	1
Done	0	1	1
Total	260	8	268

Error

4.4b

Counts

268 → 8

Alt Table

Status	Error	Program
	36.6b	(/.f64 1 (/.f64 (.f64 2 a) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (neg.f64 b) (hypot.f64 (sqrt.f64 (.f64 c (*.f64 a -4))) b)))))
	35.7b	(neg.f64 (/.f64 c b))
✓	35.2b	(/.f64 (+.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))) (neg.f64 b)) (.f64 2 a))
	40.6b	(/.f64 (+.f64 (neg.f64 b) (exp.f64 (log.f64 (hypot.f64 (sqrt.f64 (.f64 c (.f64 a -4))) b)))) (*.f64 2 a))
	47.6b	(/.f64 (neg.f64 b) a)
	40.2b	(/.f64 (.f64 (.f64 4 (.f64 c a)) (/.f64 1/2 a)) (/.f64 (.f64 4 (.f64 c a)) (-.f64 (hypot.f64 (sqrt.f64 (.f64 a (*.f64 c -4))) b) b)))
	35.7b	(.f64 (.f64 (.f64 4 (.f64 c a)) (/.f64 1/2 a)) (/.f64 1 (-.f64 (neg.f64 b) (hypot.f64 b (sqrt.f64 (.f64 a (.f64 c -4)))))))
	27.1b	(/.f64 (.f64 2 c) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))

Compiler

Compiled 10778 to 6056 computations (43.8% saved)

regimes3.6s (31.5%)

Accuracy

Total 1.6b remaining (23.6%)

Threshold costs 0b (0%)

Counts

235 → 4

Compiler

Compiled 21988 to 15526 computations (29.4% saved)

bsearch191.0ms (1.7%)

Steps

Iters	Range	Point
6	4.245300539973689e+84	2.9179576036075558e+85	2.3431308109665615e+85
11	-1.7242544591762952e-294	9.40127380898348e-302	-1.9357207753357807e-308
5	-3.8345071439982345e+37	-1.0151334156400121e+37	-3.7715774085615172e+37

Iters

Range

Point

4.245300539973689e+84

2.9179576036075558e+85

2.3431308109665615e+85

-1.7242544591762952e-294

9.40127380898348e-302

-1.9357207753357807e-308

-3.8345071439982345e+37

-1.0151334156400121e+37

-3.7715774085615172e+37

Compiler

Compiled 4 to 3 computations (25% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

16×	`+-commutative_binary64`
15×	`*-commutative_binary64`
13×	`sub-neg_binary64`
11×	`neg-sub0_binary64`
11×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	37	94
1	57	92
2	91	92
3	112	92
4	124	92
5	129	92
6	130	92
7	128	92

end267.0ms (2.3%)

Compiler: Compiled 283 to 192 computations (32.2% saved)

Details

analyze1.3s (11.1%)

sample3.2s (27.6%)

simplify296.0ms (2.6%)

prune4.0ms (0%)

localize11.0ms (0.1%)

series206.0ms (1.8%)

rewrite28.0ms (0.2%)

simplify153.0ms (1.3%)

prune224.0ms (2%)

localize21.0ms (0.2%)

series179.0ms (1.6%)

rewrite40.0ms (0.4%)

simplify216.0ms (1.9%)

prune301.0ms (2.6%)

localize26.0ms (0.2%)

series153.0ms (1.3%)

rewrite43.0ms (0.4%)

simplify152.0ms (1.3%)

prune337.0ms (3%)

localize26.0ms (0.2%)

series97.0ms (0.9%)

rewrite32.0ms (0.3%)

simplify156.0ms (1.4%)

prune231.0ms (2%)

regimes3.6s (31.5%)

bsearch191.0ms (1.7%)

simplify9.0ms (0.1%)

end267.0ms (2.3%)

Profiling