Details

analyze366.0ms (5.9%)

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 43 to 31 computations (27.9% saved)

sample1.5s (24.6%)

Results

1.2s	7958×	body	128	valid
124.0ms	829×	body	128	invalid
82.0ms	298×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify267.0ms (4.3%)

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 (0.1%)

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

28.7b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	28.8b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	28.8b	(.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 (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
✓	0.3b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	28.6b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

series192.0ms (3.1%)

Counts

4 → 96

Calls

4 calls:

84.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
54.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
42.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
12.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 90

Calls

4 calls:

9.0ms	(/.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	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
4.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))

simplify121.0ms (1.9%)

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 → 206

Iterations

Useful iterations: 3 (0.0ms)

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

prune153.0ms (2.5%)

Pruning

15 alts after pruning (15 fresh and 0 done)

	Pruned	Kept	Total
New	192	14	206
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	193	15	208

Error

0.7b

Counts

208 → 15

Alt Table

Status	Error	Program
	28.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	46.7b	(/.f64 (log.f64 (.f64 (/.f64 1 (exp.f64 b)) (exp.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (*.f64 2 a))
	32.0b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	30.5b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a))
	28.8b	(/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 2 a) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	28.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	28.7b	(/.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))))))))
	30.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (exp.f64 (log.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))))) (*.f64 2 a))
	5.4b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	29.0b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	31.6b	(/.f64 (log1p.f64 (expm1.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
▶	5.3b	(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))))))
	28.8b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.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))))) (.f64 2 a))
	28.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (neg.f64 b) (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))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
	5.4b	(/.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (*.f64 2 a))

Compiler

Compiled 6428 to 3802 computations (40.9% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(.f64 (.f64 a a) (pow.f64 c 3))
✓	0.3b	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
✓	0.3b	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
✓	0.4b	(*.f64 (pow.f64 a 3) (pow.f64 c 4))

series492.0ms (7.9%)

Counts

4 → 120

Calls

4 calls:

340.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
115.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
21.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
16.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite41.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

112×	`add-exp-log_binary64`
54×	`prod-exp_binary64`
42×	`add-sqr-sqrt_binary64`
39×	`div-exp_binary64`
39×	`pow-exp_binary64`

Counts

4 → 194

Calls

4 calls:

7.0ms	(/.f64 (*.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7))
7.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
7.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
6.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

simplify143.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

381×	`associate-l_binary64`
354×	`times-frac_binary64`
322×	`associate-r_binary64`
274×	`log-div_binary64`
272×	`associate-/l*_binary64`

Counts

314 → 226

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	272	4804
1	586	4461
2	3216	4382
3	4601	4382
4	5008	4382

prune417.0ms (6.7%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	224	2	226
Fresh	0	14	14
Picked	0	1	1
Done	0	0	0
Total	224	17	241

Error

0.7b

Counts

241 → 17

Alt Table

Status	Error	Program
	28.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	46.7b	(/.f64 (log.f64 (.f64 (/.f64 1 (exp.f64 b)) (exp.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (*.f64 2 a))
	32.0b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	30.5b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a))
	28.8b	(/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 2 a) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	28.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	11.7b	(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) (log.f64 (exp.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))))
	28.7b	(/.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))))))))
	30.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (exp.f64 (log.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))))) (*.f64 2 a))
	6.1b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (log.f64 (exp.f64 (/.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))))))
	28.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (neg.f64 b) (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))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
▶	5.4b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	29.0b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	31.6b	(/.f64 (log1p.f64 (expm1.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
✓	5.3b	(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))))))
	28.8b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.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))))) (.f64 2 a))
	5.4b	(/.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (*.f64 2 a))

Compiler

Compiled 11722 to 6999 computations (40.3% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
✓	0.4b	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
✓	0.4b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))

series233.0ms (3.7%)

Counts

4 → 0

Calls

4 calls:

113.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
79.0ms	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
21.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
20.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))

rewrite67.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

146×	`add-exp-log_binary64`
72×	`prod-exp_binary64`
68×	`pow-exp_binary64`
68×	`pow-to-exp_binary64`
60×	`div-exp_binary64`

Counts

4 → 233

Calls

4 calls:

8.0ms	(/.f64 (*.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))
7.0ms	(*.f64 (pow.f64 c 3) (pow.f64 a 3))
7.0ms	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
6.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))

simplify103.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

706×	`associate-/r/_binary64`
326×	`associate-l_binary64`
303×	`associate-r_binary64`
229×	`associate-/l*_binary64`
228×	`times-frac_binary64`

Counts

233 → 227

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	284	4102
1	563	3766
2	2829	3612
3	4989	3612

prune467.0ms (7.5%)

Pruning

18 alts after pruning (16 fresh and 2 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	226	18	244

Error

0.7b

Counts

244 → 18

Alt Table

Status	Error	Program
	28.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	46.7b	(/.f64 (log.f64 (.f64 (/.f64 1 (exp.f64 b)) (exp.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (*.f64 2 a))
	12.0b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	29.0b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	32.0b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	30.5b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a))
	28.8b	(/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 2 a) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	28.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	11.7b	(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) (log.f64 (exp.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))))
	28.7b	(/.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))))))))
	30.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (exp.f64 (log.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))))) (*.f64 2 a))
	6.1b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (log.f64 (exp.f64 (/.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))))))
	28.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (neg.f64 b) (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))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
✓	5.4b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	31.6b	(/.f64 (log1p.f64 (expm1.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
✓	5.3b	(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))))))
	28.8b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.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))))) (.f64 2 a))
▶	5.4b	(/.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (*.f64 2 a))

Compiler

Compiled 15066 to 10626 computations (29.5% saved)

localize26.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.4b	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
	0.4b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
✓	0.5b	(.f64 (.f64 c a) (*.f64 c a))
✓	0.8b	(pow.f64 (*.f64 c a) 3)

series103.0ms (1.7%)

Counts

3 → 84

Calls

3 calls:

78.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
14.0ms	(pow.f64 (*.f64 c a) 3)
11.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite25.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

67×	`add-exp-log_binary64`
45×	`pow1_binary64`
36×	`add-cbrt-cube_binary64`
33×	`prod-exp_binary64`
18×	`pow-prod-down_binary64`

Counts

3 → 117

Calls

3 calls:

8.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
6.0ms	(.f64 (.f64 c a) (*.f64 c a))
3.0ms	(pow.f64 (*.f64 c a) 3)

simplify91.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

606×	`associate-/r/_binary64`
449×	`unswap-sqr_binary64`
271×	`times-frac_binary64`
213×	`log-div_binary64`
178×	`associate-/l*_binary64`

Counts

201 → 127

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	136	2595
1	268	2056
2	1885	2030
3	4538	2030
4	4963	2030

prune335.0ms (5.4%)

Pruning

18 alts after pruning (15 fresh and 3 done)

	Pruned	Kept	Total
New	176	1	177
Fresh	1	14	15
Picked	0	1	1
Done	0	2	2
Total	177	18	195

Error

0.7b

Counts

195 → 18

Alt Table

Status	Error	Program
	12.0b	(/.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)))))) (fma.f64 4 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (*.f64 2 a))
	28.8b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	46.7b	(/.f64 (log.f64 (.f64 (/.f64 1 (exp.f64 b)) (exp.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (*.f64 2 a))
	32.0b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	30.5b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (*.f64 2 a))
	28.8b	(/.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (/.f64 (.f64 2 a) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))))))
	28.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	11.7b	(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) (log.f64 (exp.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))))
	28.7b	(/.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))))))))
	30.5b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (exp.f64 (log.f64 (fma.f64 (.f64 c a) -4 (.f64 b b)))))) (*.f64 2 a))
	6.1b	(neg.f64 (fma.f64 2 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 5 (log.f64 (exp.f64 (/.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))))))
	28.8b	(/.f64 (cbrt.f64 (.f64 (.f64 (+.f64 (neg.f64 b) (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))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
✓	5.4b	(/.f64 (neg.f64 (+.f64 (.f64 2 (/.f64 (.f64 c a) b)) (+.f64 (.f64 2 (/.f64 (.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))) (+.f64 (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))) (.f64 4 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))) (*.f64 2 a))
	29.0b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	31.6b	(/.f64 (log1p.f64 (expm1.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.f64 2 a))
✓	5.3b	(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))))))
	28.8b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.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))))) (.f64 2 a))
✓	5.4b	(/.f64 (-.f64 (.f64 -2 (+.f64 (/.f64 (.f64 c a) b) (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)))) (fma.f64 4 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 10 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7))))) (*.f64 2 a))

Compiler

Compiled 10254 to 5931 computations (42.2% saved)

regimes492.0ms (7.9%)

Accuracy

Total 4.5b remaining (85%)

Threshold costs 0b (0%)

Counts

86 → 2

Compiler

Compiled 11314 to 7764 computations (31.4% saved)

bsearch22.0ms (0.4%)

Steps

Iters	Range		Point
2	0.11833565236834932	0.13252788870896753	0.12224626186314973

Compiler

Compiled 4 to 3 computations (25% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

14×	`*-commutative_binary64`
9×	`+-commutative_binary64`
7×	`sub-neg_binary64`
6×	`neg-sub0_binary64`
6×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	44	149
1	65	143
2	85	143
3	95	143
4	101	143
5	103	143
6	102	143

end431.0ms (6.9%)

Compiler: Compiled 917 to 607 computations (33.8% saved)

Details

analyze366.0ms (5.9%)

sample1.5s (24.6%)

simplify267.0ms (4.3%)

prune4.0ms (0.1%)

localize11.0ms (0.2%)

series192.0ms (3.1%)

rewrite29.0ms (0.5%)

simplify121.0ms (1.9%)

prune153.0ms (2.5%)

localize24.0ms (0.4%)

series492.0ms (7.9%)

rewrite41.0ms (0.7%)

simplify143.0ms (2.3%)

prune417.0ms (6.7%)

localize33.0ms (0.5%)

series233.0ms (3.7%)

rewrite67.0ms (1.1%)

simplify103.0ms (1.6%)

prune467.0ms (7.5%)

localize26.0ms (0.4%)

series103.0ms (1.7%)

rewrite25.0ms (0.4%)

simplify91.0ms (1.5%)

prune335.0ms (5.4%)

regimes492.0ms (7.9%)

bsearch22.0ms (0.4%)

simplify7.0ms (0.1%)

end431.0ms (6.9%)

Profiling