Details

analyze338.0ms (5.5%)

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)

sample133.0ms (2.2%)

Algorithm

1×

intervals

Results

15.0ms	123×	body	256	valid
10.0ms	276×	pre	128	true
9.0ms	91×	body	128	valid
8.0ms	42×	body	512	valid
1.0ms	20×	body	128	nan

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify316.0ms (5.2%)

Algorithm

1×	egg-herbie

Rules

1968×	`fma-neg_binary64`
1363×	`fma-def_binary64`
898×	`div-sub_binary64`
743×	`associate-/l*_binary64`
567×	`times-frac_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	13	26
1	30	22
2	64	22
3	135	22
4	201	22
5	335	22
6	554	22
7	929	22
8	1477	22
9	2115	22
10	2599	22
11	2554	22
12	2602	22
13	2671	22
14	3117	22
15	2327	22
16	2375	22
17	2383	22
18	2389	22
19	2395	22
20	2397	22
21	2397	22
22	2585	22
23	2685	22
24	2619	22
25	2631	22
26	2661	22
27	2677	22
28	2707	22
29	2707	22
30	2751	22
31	2851	22
32	2827	22
33	2827	22
34	2638	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

52.3b

Counts

3 → 2

Alt Table

Status	Error	Program
	52.3b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
▶	52.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 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	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
✓	0.2b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
✓	0.3b	(.f64 (.f64 3 a) c)
✓	27.8b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

series160.0ms (2.6%)

Counts

4 → 100

Calls

4 calls:

89.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
56.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
10.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
4.0ms	(.f64 (.f64 3 a) c)

rewrite29.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

22×	`*-un-lft-identity_binary64`
14×	`add-cbrt-cube_binary64`
14×	`add-exp-log_binary64`
10×	`add-log-exp_binary64`
10×	`add-sqr-sqrt_binary64`

Counts

4 → 93

Calls

4 calls:

9.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
7.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
4.0ms	(.f64 (.f64 3 a) c)
3.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))

simplify112.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

791×	`fma-def_binary64`
309×	`fma-neg_binary64`
282×	`cancel-sign-sub-inv_binary64`
189×	`associate-r_binary64`
182×	`associate-l_binary64`

Counts

193 → 187

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	247	3732
1	687	3410
2	2579	3302
3	4808	3302
4	4889	3302

prune214.0ms (3.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	176	11	187
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	178	11	189

Error

0.1b

Counts

189 → 11

Alt Table

Status	Error	Program
	52.3b	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 1/3 a))
	52.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (expm1.f64 (log1p.f64 (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	2.2b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (*.f64 3 a))
	52.3b	(cbrt.f64 (/.f64 (.f64 (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 (.f64 (.f64 3 a) (.f64 3 a)) (.f64 3 a))))
	52.3b	(/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	52.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	51.4b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	2.6b	(/.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (/.f64 -27/16 (/.f64 (pow.f64 b 5) (pow.f64 (.f64 c a) 3))))) (.f64 3 a))
	52.3b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
	52.2b	(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))) (.f64 3 a))
▶	1.7b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))

Compiler

Compiled 5598 to 3294 computations (41.2% saved)

localize38.0ms (0.6%)

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 (.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))

series201.0ms (3.3%)

Counts

4 → 120

Calls

4 calls:

91.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
75.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
19.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
16.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite66.0ms (1.1%)

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:

8.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
7.0ms	(.f64 (.f64 a a) (pow.f64 c 3))
6.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
6.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))

simplify144.0ms (2.3%)

Algorithm

1×	egg-herbie

Rules

394×	`times-frac_binary64`
380×	`associate-l_binary64`
327×	`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

prune375.0ms (6.1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	228	0	228
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	228	11	239

Error

0.1b

Counts

239 → 11

Alt Table

Status	Error	Program
	52.3b	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 1/3 a))
	52.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (expm1.f64 (log1p.f64 (.f64 (.f64 3 a) c)))))) (.f64 3 a))
▶	2.2b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (*.f64 3 a))
	52.3b	(cbrt.f64 (/.f64 (.f64 (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 (.f64 (.f64 3 a) (.f64 3 a)) (.f64 3 a))))
	52.3b	(/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	52.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	51.4b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	2.6b	(/.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (/.f64 -27/16 (/.f64 (pow.f64 b 5) (pow.f64 (.f64 c a) 3))))) (.f64 3 a))
	52.3b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
	52.2b	(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))) (.f64 3 a))
✓	1.7b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))

Compiler

Compiled 12136 to 7435 computations (38.7% saved)

localize25.0ms (0.4%)

Local error

Found 4 expressions with local error:

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

series125.0ms (2%)

Counts

4 → 84

Calls

4 calls:

79.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
21.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
13.0ms	(pow.f64 (*.f64 c a) 3)
11.0ms	(.f64 (.f64 c a) (*.f64 c a))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-exp-log_binary64`
46×	`pow1_binary64`
42×	`prod-exp_binary64`
39×	`add-cbrt-cube_binary64`
27×	`add-sqr-sqrt_binary64`

Counts

4 → 161

Calls

4 calls:

12.0ms	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
5.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
5.0ms	(.f64 (.f64 c a) (*.f64 c a))
2.0ms	(pow.f64 (*.f64 c a) 3)

simplify107.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

606×	`associate-/r/_binary64`
575×	`unswap-sqr_binary64`
271×	`times-frac_binary64`
225×	`associate-l_binary64`
209×	`associate-r_binary64`

Counts

245 → 184

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	197	3172
1	384	2525
2	2271	2487
3	4987	2487
4	5017	2487

prune342.0ms (5.6%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	183	1	184
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	183	12	195

Error

0.1b

Counts

195 → 12

Alt Table

Status	Error	Program
	52.3b	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 1/3 a))
	52.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (expm1.f64 (log1p.f64 (.f64 (.f64 3 a) c)))))) (.f64 3 a))
✓	2.2b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (*.f64 3 a))
	52.3b	(cbrt.f64 (/.f64 (.f64 (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 (.f64 (.f64 3 a) (.f64 3 a)) (.f64 3 a))))
	52.3b	(/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	52.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	51.4b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	5.8b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)))) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (*.f64 3 a))
▶	2.6b	(/.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (/.f64 -27/16 (/.f64 (pow.f64 b 5) (pow.f64 (.f64 c a) 3))))) (.f64 3 a))
	52.3b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
	52.2b	(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))) (.f64 3 a))
✓	1.7b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))

Compiler

Compiled 11039 to 6452 computations (41.6% saved)

localize19.0ms (0.3%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (pow.f64 b 5) (pow.f64 (*.f64 c a) 3))
	0.4b	(/.f64 (.f64 (.f64 c a) (*.f64 c a)) (pow.f64 b 3))
	0.5b	(.f64 (.f64 c a) (*.f64 c a))
	0.8b	(pow.f64 (*.f64 c a) 3)

series144.0ms (2.4%)

Counts

1 → 36

Calls

1 calls:

144.0ms

(/.f64 (pow.f64 b 5) (pow.f64 (*.f64 c a) 3))

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`times-frac_binary64`
35×	`unpow-prod-down_binary64`
27×	`*-un-lft-identity_binary64`
27×	`add-sqr-sqrt_binary64`
27×	`add-cube-cbrt_binary64`

Counts

1 → 96

Calls

1 calls:

5.0ms

(/.f64 (pow.f64 b 5) (pow.f64 (*.f64 c a) 3))

simplify97.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

737×	`associate-l_binary64`
590×	`associate-r_binary64`
361×	`associate-*l/_binary64`
327×	`log-prod_binary64`
312×	`associate-*r/_binary64`

Counts

132 → 102

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	149	2687
1	243	2633
2	1169	2505
3	4639	2505
4	5344	2505

prune340.0ms (5.5%)

Pruning

12 alts after pruning (9 fresh and 3 done)

	Pruned	Kept	Total
New	229	0	229
Fresh	0	9	9
Picked	0	1	1
Done	0	2	2
Total	229	12	241

Error

0.1b

Counts

241 → 12

Alt Table

Status	Error	Program
	52.3b	(.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (/.f64 1/3 a))
	52.3b	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (expm1.f64 (log1p.f64 (.f64 (.f64 3 a) c)))))) (.f64 3 a))
✓	2.2b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (*.f64 3 a))
	52.3b	(cbrt.f64 (/.f64 (.f64 (.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 (.f64 (.f64 3 a) (.f64 3 a)) (.f64 3 a))))
	52.3b	(/.f64 (.f64 (.f64 (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (cbrt.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))))) (.f64 3 a))
	52.3b	(.f64 (.f64 (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a)))) (cbrt.f64 (/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))))
	51.4b	(/.f64 (fma.f64 (sqrt.f64 b) (neg.f64 (sqrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
	5.8b	(/.f64 (-.f64 (.f64 -3/2 (/.f64 (.f64 c a) b)) (fma.f64 9/8 (log.f64 (exp.f64 (/.f64 (pow.f64 (.f64 c a) 2) (pow.f64 b 3)))) (fma.f64 27/16 (/.f64 (pow.f64 (.f64 c a) 3) (pow.f64 b 5)) (.f64 405/128 (/.f64 (.f64 (pow.f64 c 4) (pow.f64 a 4)) (pow.f64 b 7)))))) (*.f64 3 a))
✓	2.6b	(/.f64 (fma.f64 -3/2 (/.f64 (.f64 c a) b) (fma.f64 (/.f64 (.f64 (.f64 c a) (.f64 c a)) (pow.f64 b 3)) -9/8 (/.f64 -27/16 (/.f64 (pow.f64 b 5) (pow.f64 (.f64 c a) 3))))) (.f64 3 a))
	52.3b	(/.f64 (/.f64 (-.f64 (.f64 (neg.f64 b) (neg.f64 b)) (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (-.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))) (.f64 3 a))
	52.2b	(/.f64 (/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3)) (+.f64 (.f64 (neg.f64 b) (neg.f64 b)) (-.f64 (.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))) (.f64 3 a))
✓	1.7b	(neg.f64 (fma.f64 9/16 (/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5)) (fma.f64 135/128 (/.f64 (.f64 (pow.f64 a 3) (pow.f64 c 4)) (pow.f64 b 7)) (fma.f64 1/2 (/.f64 c b) (.f64 3/8 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))

Compiler

Compiled 10277 to 5294 computations (48.5% saved)

regimes707.0ms (11.5%)

Accuracy

Total 1.2b remaining (85.6%)

Threshold costs 0b (0%)

Counts

83 → 1

Compiler

Compiled 14357 to 9825 computations (31.6% saved)

simplify7.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	36	69
1	53	67
2	72	67
3	99	67
4	139	67
5	170	67
6	198	67
7	215	67
8	223	67
9	225	67
10	221	67

end1.0ms (0%)

Compiler: Compiled 48 to 37 computations (22.9% saved)

sample2.0s (33.1%)

Algorithm

1×

intervals

Results

488.0ms	3825×	body	256	valid
319.0ms	8817×	pre	128	true
272.0ms	1436×	body	512	valid
187.0ms	2739×	body	128	valid
52.0ms	817×	body	128	nan

Compiler

Compiled 628 to 413 computations (34.2% saved)

Iter	Nodes	Cost
0	36	69
1	53	67
2	72	67
3	99	67
4	139	67
5	170	67
6	198	67
7	215	67
8	223	67
9	225	67
10	221	67

Iter	Nodes	Cost
0	36	69
1	53	67
2	72	67
3	99	67
4	139	67
5	170	67
6	198	67
7	215	67
8	223	67
9	225	67
10	221	67

Details

analyze338.0ms (5.5%)

sample133.0ms (2.2%)

simplify316.0ms (5.2%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

series160.0ms (2.6%)

rewrite29.0ms (0.5%)

simplify112.0ms (1.8%)

prune214.0ms (3.5%)

localize38.0ms (0.6%)

series201.0ms (3.3%)

rewrite66.0ms (1.1%)

simplify144.0ms (2.3%)

prune375.0ms (6.1%)

localize25.0ms (0.4%)

series125.0ms (2%)

rewrite34.0ms (0.6%)

simplify107.0ms (1.7%)

prune342.0ms (5.6%)

localize19.0ms (0.3%)

series144.0ms (2.4%)

rewrite11.0ms (0.2%)

simplify97.0ms (1.6%)

prune340.0ms (5.5%)

regimes707.0ms (11.5%)

simplify7.0ms (0.1%)

end1.0ms (0%)

sample2.0s (33.1%)

Profiling

Iter	Nodes	Cost
0	36	69
1	53	67
2	72	67
3	99	67
4	139	67
5	170	67
6	198	67
7	215	67
8	223	67
9	225	67
10	221	67