Details

analyze406.0ms (6.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	0%	100%	0
0%	0%	100%	1
0%	0%	100%	2
0%	0%	100%	3
0%	0%	100%	4
0%	0%	100%	5
0%	0%	100%	6
0%	0%	100%	7
0%	0%	100%	8
0%	0%	100%	9
0%	0%	100%	10
0%	0%	100%	11
0%	0%	100%	12
0%	0%	100%	13
0%	0%	100%	14

Compiler

Compiled 33 to 24 computations (27.3% saved)

sample55.0ms (0.8%)

Algorithm

1×

intervals

Results

15.0ms	127×	body	256	valid
10.0ms	46×	body	512	valid
8.0ms	286×	pre	128	true
5.0ms	83×	body	128	valid
2.0ms	30×	body	128	nan

Compiler

Compiled 56 to 41 computations (26.8% saved)

simplify277.0ms (4.2%)

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 → 1

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 (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

53.1b

Counts

2 → 2

Alt Table

Status	Error	Program
▶	53.1b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	53.1b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))

Compiler

Compiled 94 to 64 computations (31.9% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
0.2b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
27.6b	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)

rewrite97.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

49.7b

Rules

42×	`add-sqr-sqrt_binary64`
32×	`*-un-lft-identity_binary64`
28×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
17×	`sqrt-prod_binary64`

Counts

4 → 109

Calls

4 calls:

9.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
4.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
0.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

Compiler

Compiled 2813 to 1478 computations (47.5% saved)

series156.0ms (2.4%)

Error

0.2b

Counts

4 → 72

Calls

4 calls:

45.0ms	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
37.0ms	(-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
27.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
26.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))

Compiler

Compiled 2658 to 1932 computations (27.3% saved)

simplify150.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

672×	`fma-neg_binary64`
472×	`distribute-rgt-in_binary64`
259×	`cancel-sign-sub-inv_binary64`
169×	`*-commutative_binary64`
167×	`associate-l_binary64`

Counts

181 → 136

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	268	5303
1	671	4311
2	2494	4003
3	4700	4003
4	4889	4003

prune55.0ms (0.8%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	130	6	136
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	132	6	138

Error

0.0b

Counts

138 → 6

Alt Table

Status	Error	Program
	53.4b	(.f64 (.f64 (+.f64 (sqrt.f64 b) (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))) (-.f64 (sqrt.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (sqrt.f64 b))) (/.f64 1/2 a))
	1.5b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))
	1.8b	(.f64 (fma.f64 2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3))) (fma.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (/.f64 -1/2 a))
▶	0.3b	(/.f64 (.f64 (/.f64 1/2 a) (+.f64 (.f64 c (.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
	0.4b	(/.f64 (.f64 1/2 (+.f64 (.f64 c (.f64 a -4)) 0)) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
	0.4b	(.f64 (/.f64 (+.f64 (.f64 c (.f64 a -4)) 0) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))))) (/.f64 1/2 a))

Compiler

Compiled 1661 to 976 computations (41.2% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
0.1b	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
0.1b	(/.f64 (.f64 (/.f64 1/2 a) (+.f64 (.f64 c (.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
0.3b	(.f64 (/.f64 1/2 a) (+.f64 (.f64 c (*.f64 a -4)) 0))

rewrite146.0ms (2.2%)

Algorithm

1×	rewrite-expression-head

Error

Rules

22×	`*-un-lft-identity_binary64`
21×	`add-sqr-sqrt_binary64`
18×	`add-cbrt-cube_binary64`
18×	`add-exp-log_binary64`
16×	`add-cube-cbrt_binary64`

Counts

4 → 104

Calls

4 calls:

13.0ms	(/.f64 (.f64 (/.f64 1/2 a) (+.f64 (.f64 c (.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
8.0ms	(.f64 (/.f64 1/2 a) (+.f64 (.f64 c (*.f64 a -4)) 0))
3.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
0.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

Compiler

Compiled 3457 to 2184 computations (36.8% saved)

series132.0ms (2%)

Error

0.0b

Counts

4 → 60

Calls

4 calls:

47.0ms	(/.f64 (.f64 (/.f64 1/2 a) (+.f64 (.f64 c (.f64 a -4)) 0)) (+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b))
33.0ms	(+.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))) b)
30.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))
9.0ms	(.f64 (/.f64 1/2 a) (+.f64 (.f64 c (*.f64 a -4)) 0))

Compiler

Compiled 2609 to 1875 computations (28.1% saved)

simplify115.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

350×	`associate-r_binary64`
285×	`associate-l_binary64`
277×	`associate-/l*_binary64`
254×	`div-sub_binary64`
252×	`fma-neg_binary64`

Counts

164 → 141

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	254	4398
1	713	3693
2	4049	3676
3	4989	3676

prune91.0ms (1.4%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	137	4	141
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	141	6	147

Error

Counts

147 → 6

Alt Table

Status	Error	Program
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (cbrt.f64 (/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) (cbrt.f64 (/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))))
▶	0.1b	(/.f64 (.f64 -2 c) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))
	0.4b	(/.f64 (/.f64 1/2 a) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.f64 a (.f64 c -4))))
	2.6b	(/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (.f64 2 (-.f64 b (.f64 (/.f64 c b) a))))
	0.4b	(/.f64 (.f64 1/2 (+.f64 (.f64 c (.f64 a -4)) 0)) (.f64 a (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))
	1.5b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (+.f64 (/.f64 c b) (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))

Compiler

Compiled 2677 to 1546 computations (42.2% saved)

localize11.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
0.0b	(fma.f64 a (.f64 c -4) (.f64 b b))
0.1b	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
0.1b	(/.f64 (.f64 -2 c) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))

rewrite101.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Error

Rules

14×	`*-un-lft-identity_binary64`
9×	`add-sqr-sqrt_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
8×	`add-cube-cbrt_binary64`

Counts

4 → 69

Calls

4 calls:

5.0ms	(/.f64 (.f64 -2 c) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
1.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
0.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

Compiler

Compiled 1622 to 909 computations (44% saved)

series148.0ms (2.2%)

Error

Counts

4 → 73

Calls

4 calls:

45.0ms	(/.f64 (.f64 -2 c) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b)))))
30.0ms	(+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))
27.0ms	(sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))
26.0ms	(fma.f64 a (.f64 c -4) (.f64 b b))

Compiler

Compiled 2623 to 1867 computations (28.8% saved)

simplify83.0ms (1.3%)

Algorithm

1×	egg-herbie

Rules

731×	`times-frac_binary64`
707×	`associate-/l*_binary64`
311×	`fma-def_binary64`
248×	`associate-/l/_binary64`
195×	`associate-/r/_binary64`

Counts

142 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	200	3242
1	493	2973
2	1576	2892
3	5066	2892

prune73.0ms (1.1%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	125	3	128
Fresh	3	2	5
Picked	1	0	1
Done	0	0	0
Total	129	5	134

Error

Counts

134 → 5

Alt Table

Status	Error	Program
	1.4b	(/.f64 (.f64 c -2) (fma.f64 2 (-.f64 b (fma.f64 (/.f64 c b) a (.f64 (/.f64 (.f64 (.f64 c c) a) (pow.f64 b 3)) a))) (.f64 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -4)))
	0.4b	(/.f64 (/.f64 1/2 a) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.f64 a (.f64 c -4))))
	1.5b	(-.f64 (.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
▶	0.4b	(/.f64 -2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) c))
	1.5b	(.f64 (.f64 (cbrt.f64 (/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))) (cbrt.f64 (/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b))))))) (cbrt.f64 (/.f64 (/.f64 (.f64 -2 (.f64 c a)) a) (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))))))

Compiler

Compiled 1683 to 975 computations (42.1% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(fma.f64 c (.f64 a -4) (.f64 b b))
0.1b	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
0.1b	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) c)
0.3b	(/.f64 -2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) c))

rewrite139.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Error

Rules

108×	`times-frac_binary64`
97×	`*-un-lft-identity_binary64`
63×	`add-sqr-sqrt_binary64`
63×	`add-cube-cbrt_binary64`
19×	`associate-/r*_binary64`

Counts

4 → 146

Calls

4 calls:

7.0ms	(/.f64 -2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) c))
5.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) c)
3.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
0.0ms	(fma.f64 c (.f64 a -4) (.f64 b b))

Compiler

Compiled 3772 to 2131 computations (43.5% saved)

series154.0ms (2.3%)

Error

Counts

4 → 72

Calls

4 calls:

46.0ms	(/.f64 -2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) c))
34.0ms	(/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) c)
29.0ms	(+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b))))
27.0ms	(fma.f64 c (.f64 a -4) (.f64 b b))

Compiler

Compiled 2517 to 1816 computations (27.9% saved)

simplify187.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

762×	`times-frac_binary64`
367×	`fma-def_binary64`
314×	`associate-/l/_binary64`
242×	`fma-neg_binary64`
161×	`associate-/r/_binary64`

Counts

218 → 145

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	304	6554
1	727	6177
2	2155	6084
3	4870	6084
4	4954	6084

prune63.0ms (1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	144	1	145
Fresh	1	3	4
Picked	0	1	1
Done	0	0	0
Total	145	5	150

Error

Counts

150 → 5

Alt Table

Status	Error	Program
	1.4b	(/.f64 (.f64 c -2) (fma.f64 2 (-.f64 b (fma.f64 (/.f64 c b) a (.f64 (/.f64 (.f64 (.f64 c c) a) (pow.f64 b 3)) a))) (.f64 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5)) -4)))
	0.4b	(/.f64 (/.f64 1/2 a) (/.f64 (+.f64 b (sqrt.f64 (fma.f64 a (.f64 c -4) (.f64 b b)))) (.f64 a (.f64 c -4))))
	1.5b	(.f64 (.f64 (cbrt.f64 c) (cbrt.f64 c)) (/.f64 -2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) (cbrt.f64 c))))
	1.5b	(-.f64 (.f64 (/.f64 (.f64 (pow.f64 c 3) (.f64 a a)) (pow.f64 b 5)) -2) (fma.f64 5 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 3)) (pow.f64 b 7)) (fma.f64 (/.f64 (*.f64 c c) (pow.f64 b 3)) a (/.f64 c b))))
✓	0.4b	(/.f64 -2 (/.f64 (+.f64 b (sqrt.f64 (fma.f64 c (.f64 a -4) (.f64 b b)))) c))

Compiler

Compiled 1679 to 958 computations (42.9% saved)

regimes2.2s (33.2%)

Accuracy

Total 0.1b remaining (78.4%)

Threshold costs 0.1b (78.4%)

Compiler

Compiled 41116 to 26882 computations (34.6% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

3×	`*-commutative_binary64`
1×	`+-commutative_binary64`
1×	`*-lft-identity_binary64`
1×	`1-exp_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	15	22
1	21	22
2	20	22

end2.0ms (0%)

Compiler: Compiled 18 to 12 computations (33.3% saved)

sample1.7s (26.2%)

Algorithm

1×

intervals

Results

482.0ms	3772×	body	256	valid
281.0ms	1511×	body	512	valid
267.0ms	8773×	pre	128	true
181.0ms	2717×	body	128	valid
48.0ms	773×	body	128	nan

Compiler

Compiled 203 to 138 computations (32% saved)

Details

analyze406.0ms (6.1%)

sample55.0ms (0.8%)

simplify277.0ms (4.2%)

prune4.0ms (0.1%)

localize12.0ms (0.2%)

rewrite97.0ms (1.5%)

series156.0ms (2.4%)

simplify150.0ms (2.3%)

prune55.0ms (0.8%)

localize14.0ms (0.2%)

rewrite146.0ms (2.2%)

series132.0ms (2%)

simplify115.0ms (1.7%)

prune91.0ms (1.4%)

localize11.0ms (0.2%)

rewrite101.0ms (1.5%)

series148.0ms (2.2%)

simplify83.0ms (1.3%)

prune73.0ms (1.1%)

localize10.0ms (0.2%)

rewrite139.0ms (2.1%)

series154.0ms (2.3%)

simplify187.0ms (2.8%)

prune63.0ms (1%)

regimes2.2s (33.2%)

simplify3.0ms (0%)

end2.0ms (0%)

sample1.7s (26.2%)

Profiling