Details

analyze350.0ms (5.7%)

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%)

Results

1.2s	7941×	body	128	valid
128.0ms	866×	body	128	invalid
82.0ms	315×	body	256	valid

Compiler

Compiled 106 to 76 computations (28.3% saved)

simplify258.0ms (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 → 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

29.2b

Counts

3 → 2

Alt Table

Status	Error	Program
▶	29.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
	29.3b	(.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)

localize10.0ms (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))
✓	0.2b	(-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))
✓	29.3b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))

series177.0ms (2.9%)

Counts

4 → 96

Calls

4 calls:

77.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))
50.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))
39.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c)))
10.0ms	(-.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:

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))

simplify118.0ms (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

prune141.0ms (2.3%)

Pruning

17 alts after pruning (17 fresh and 0 done)

	Pruned	Kept	Total
New	190	16	206
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	191	17	208

Error

0.7b

Counts

208 → 17

Alt Table

Status	Error	Program
	33.5b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	6.3b	(/.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))
	29.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
	6.3b	(/.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))
	29.3b	(/.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))
	29.2b	(/.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))))))))
	29.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	29.3b	(cbrt.f64 (/.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 (.f64 (.f64 2 a) (.f64 2 a)) (.f64 2 a))))
	22.2b	(neg.f64 (/.f64 c b))
	29.3b	(.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))))
	32.2b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	47.3b	(/.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))
	29.4b	(/.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))
	34.8b	(/.f64 (expm1.f64 (log1p.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.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 (/.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))))))
	29.3b	(/.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 (.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	29.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))

Compiler

Compiled 6554 to 3884 computations (40.7% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
✓	0.4b	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
✓	0.4b	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
✓	0.4b	(.f64 (.f64 a a) (pow.f64 c 3))

series193.0ms (3.1%)

Counts

4 → 120

Calls

4 calls:

90.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
67.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
20.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
16.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

109×	`add-exp-log_binary64`
54×	`prod-exp_binary64`
42×	`add-sqr-sqrt_binary64`
30×	`div-exp_binary64`
29×	`unpow-prod-down_binary64`

Counts

4 → 186

Calls

4 calls:

7.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
6.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
6.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
6.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

simplify414.0ms (6.8%)

Algorithm

1×	egg-herbie

Rules

394×	`times-frac_binary64`
381×	`associate-l_binary64`
328×	`associate-r_binary64`
312×	`log-div_binary64`
300×	`associate-/l*_binary64`

Counts

306 → 228

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	273	4694
1	600	4318
2	3453	4239
3	4707	4239
4	5155	4239

prune436.0ms (7.1%)

Pruning

19 alts after pruning (18 fresh and 1 done)

	Pruned	Kept	Total
New	225	3	228
Fresh	1	15	16
Picked	0	1	1
Done	0	0	0
Total	226	19	245

Error

0.7b

Counts

245 → 19

Alt Table

Status	Error	Program
	33.5b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	6.3b	(/.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))
	29.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
▶	6.3b	(/.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))
	47.3b	(/.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))
	12.5b	(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) (log.f64 (exp.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))))
	29.3b	(/.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))
	29.2b	(/.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))))))))
	29.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	29.3b	(cbrt.f64 (/.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 (.f64 (.f64 2 a) (.f64 2 a)) (.f64 2 a))))
	32.2b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	8.3b	(neg.f64 (fma.f64 2 (log.f64 (exp.f64 (/.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))))))
	29.4b	(/.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))
	34.8b	(/.f64 (expm1.f64 (log1p.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.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 (/.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))))))
	21.7b	(neg.f64 (fma.f64 2 (/.f64 (log.f64 (exp.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))))))
	29.3b	(/.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 (.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	29.3b	(.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))))
	29.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))

Compiler

Compiled 12031 to 7169 computations (40.4% saved)

localize33.0ms (0.5%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
✓	0.3b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
✓	0.3b	(*.f64 (pow.f64 c 2) (pow.f64 a 2))
✓	0.3b	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))

series209.0ms (3.4%)

Counts

4 → 0

Calls

4 calls:

97.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
80.0ms	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
20.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
12.0ms	(*.f64 (pow.f64 c 2) (pow.f64 a 2))

rewrite39.0ms (0.6%)

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 → 225

Calls

4 calls:

7.0ms	(*.f64 (pow.f64 c 2) (pow.f64 a 2))
6.0ms	(/.f64 (*.f64 (pow.f64 c 2) (pow.f64 a 2)) (pow.f64 b 3))
6.0ms	(/.f64 (*.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))
5.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))

simplify95.0ms (1.5%)

Algorithm

1×	egg-herbie

Rules

699×	`associate-/r/_binary64`
477×	`unswap-sqr_binary64`
255×	`associate-l_binary64`
250×	`times-frac_binary64`
236×	`associate-/l*_binary64`

Counts

225 → 235

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	288	3670
1	547	3316
2	2613	3269
3	5276	3269

prune520.0ms (8.5%)

Pruning

21 alts after pruning (19 fresh and 2 done)

	Pruned	Kept	Total
New	233	2	235
Fresh	0	17	17
Picked	0	1	1
Done	0	1	1
Total	233	21	254

Error

0.7b

Counts

254 → 21

Alt Table

Status	Error	Program
	33.5b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
▶	6.3b	(/.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))
	29.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
✓	6.3b	(/.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))
	7.8b	(/.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 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))))) (*.f64 2 a))
	47.3b	(/.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))
	12.5b	(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) (log.f64 (exp.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))))
	21.7b	(neg.f64 (fma.f64 2 (/.f64 (log.f64 (exp.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))))))
	12.4b	(/.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))
	29.3b	(/.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))
	29.2b	(/.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))))))))
	29.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	29.3b	(cbrt.f64 (/.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 (.f64 (.f64 2 a) (.f64 2 a)) (.f64 2 a))))
	32.2b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	8.3b	(neg.f64 (fma.f64 2 (log.f64 (exp.f64 (/.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))))))
	29.4b	(/.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))
	34.8b	(/.f64 (expm1.f64 (log1p.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.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 (/.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))))))
	29.3b	(/.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 (.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	29.3b	(.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))))
	29.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))

Compiler

Compiled 15838 to 11128 computations (29.7% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
✓	0.3b	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
✓	0.5b	(.f64 (.f64 c a) (*.f64 c a))
✓	0.7b	(pow.f64 (*.f64 c a) 3)

series102.0ms (1.7%)

Counts

3 → 84

Calls

3 calls:

77.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
13.0ms	(pow.f64 (*.f64 c a) 3)
11.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite24.0ms (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))
5.0ms	(.f64 (.f64 c a) (*.f64 c a))
2.0ms	(pow.f64 (*.f64 c a) 3)

simplify118.0ms (1.9%)

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

prune337.0ms (5.5%)

Pruning

21 alts after pruning (18 fresh and 3 done)

	Pruned	Kept	Total
New	178	0	178
Fresh	0	18	18
Picked	0	1	1
Done	0	2	2
Total	178	21	199

Error

0.7b

Counts

199 → 21

Alt Table

Status	Error	Program
	33.5b	(log1p.f64 (expm1.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
✓	6.3b	(/.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))
	29.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (fma.f64 b b (.f64 c (.f64 a -4))))) (*.f64 2 a))
✓	6.3b	(/.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))
	7.8b	(/.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 (log.f64 (exp.f64 (/.f64 (.f64 (pow.f64 c 3) (pow.f64 a 3)) (pow.f64 b 5))))))))) (*.f64 2 a))
	47.3b	(/.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))
	12.5b	(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) (log.f64 (exp.f64 (/.f64 (.f64 c (*.f64 c a)) (pow.f64 b 3))))))))
	21.7b	(neg.f64 (fma.f64 2 (/.f64 (log.f64 (exp.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))))))
	12.4b	(/.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))
	29.3b	(/.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))
	29.2b	(/.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))))))))
	29.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -4) (*.f64 b b))) b) (/.f64 1/2 a))
	29.3b	(cbrt.f64 (/.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 (.f64 (.f64 2 a) (.f64 2 a)) (.f64 2 a))))
	32.2b	(log.f64 (exp.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))
	8.3b	(neg.f64 (fma.f64 2 (log.f64 (exp.f64 (/.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))))))
	29.4b	(/.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))
	34.8b	(/.f64 (expm1.f64 (log1p.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))))) (.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 (/.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))))))
	29.3b	(/.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 (.f64 2 a) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 4 a) c))))))
	29.3b	(.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))))
	29.3b	(cbrt.f64 (.f64 (.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a)) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))) (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 4 a) c)))) (.f64 2 a))))

Compiler

Compiled 10472 to 6085 computations (41.9% saved)

regimes430.0ms (7%)

Accuracy

Total 5.1b remaining (86.6%)

Threshold costs 0b (0%)

Counts

59 → 2

Compiler

Compiled 8628 to 5880 computations (31.8% saved)

bsearch22.0ms (0.4%)

Steps

Iters	Range		Point
4	18.245874148098437	29.85484737511736	18.608654561442776

Compiler

Compiled 4 to 3 computations (25% saved)

simplify6.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

28×	`*-commutative_binary64`
24×	`+-commutative_binary64`
20×	`sub-neg_binary64`
20×	`neg-sub0_binary64`
20×	`neg-mul-1_binary64`

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	43	93
1	64	89
2	86	89
3	114	89
4	144	89
5	177	89
6	199	89
7	212	89
8	216	89
9	214	89

end503.0ms (8.2%)

Compiler: Compiled 1015 to 693 computations (31.7% saved)

Details

analyze350.0ms (5.7%)

sample1.5s (24%)

simplify258.0ms (4.2%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series177.0ms (2.9%)

rewrite29.0ms (0.5%)

simplify118.0ms (1.9%)

prune141.0ms (2.3%)

localize24.0ms (0.4%)

series193.0ms (3.1%)

rewrite36.0ms (0.6%)

simplify414.0ms (6.8%)

prune436.0ms (7.1%)

localize33.0ms (0.5%)

series209.0ms (3.4%)

rewrite39.0ms (0.6%)

simplify95.0ms (1.5%)

prune520.0ms (8.5%)

localize25.0ms (0.4%)

series102.0ms (1.7%)

rewrite24.0ms (0.4%)

simplify118.0ms (1.9%)

prune337.0ms (5.5%)

regimes430.0ms (7%)

bsearch22.0ms (0.4%)

simplify6.0ms (0.1%)

end503.0ms (8.2%)

Profiling