Details

analyze356.0ms (4.8%)

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)

sample129.0ms (1.8%)

Algorithm

1×

intervals

Results

12.0ms	106×	body	256	valid
9.0ms	150×	body	128	valid
9.0ms	275×	pre	128	true
1.0ms	19×	body	128	nan

Compiler

Compiled 66 to 48 computations (27.3% saved)

simplify364.0ms (5%)

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

45.8b

Counts

3 → 2

Alt Table

Status	Error	Program
	45.8b	(.f64 (-.f64 (sqrt.f64 (fma.f64 a (.f64 c -3) (*.f64 b b))) b) (/.f64 1/3 a))
▶	45.8b	(/.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)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.1b	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
✓	0.3b	(/.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)
✓	39.5b	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))

series161.0ms (2.2%)

Counts

4 → 100

Calls

4 calls:

92.0ms	(/.f64 (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (.f64 3 a))
52.0ms	(+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))))
12.0ms	(-.f64 (.f64 b b) (.f64 (*.f64 3 a) c))
5.0ms	(.f64 (.f64 3 a) c)

rewrite30.0ms (0.4%)

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))
8.0ms	(+.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))

simplify123.0ms (1.7%)

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

prune167.0ms (2.3%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	177	10	187
Fresh	1	0	1
Picked	1	0	1
Done	0	0	0
Total	179	10	189

Error

0.3b

Counts

189 → 10

Alt Table

Status	Error	Program
	45.8b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3)) (.f64 (.f64 3 a) (+.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))))))))
	45.8b	(/.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))
	3.0b	(/.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))
	45.8b	(/.f64 1 (/.f64 (.f64 3 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))
	45.8b	(/.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))
	4.0b	(/.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))
	44.8b	(/.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))
	45.7b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
	45.8b	(.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))))
▶	2.6b	(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 5496 to 3228 computations (41.3% saved)

localize31.0ms (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))
✓	0.3b	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
✓	0.4b	(.f64 (.f64 a a) (pow.f64 c 3))
✓	0.4b	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))

series207.0ms (2.8%)

Counts

4 → 120

Calls

4 calls:

96.0ms	(/.f64 (.f64 (.f64 a a) (pow.f64 c 3)) (pow.f64 b 5))
76.0ms	(/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3))
20.0ms	(*.f64 (pow.f64 a 3) (pow.f64 c 4))
14.0ms	(.f64 (.f64 a a) (pow.f64 c 3))

rewrite39.0ms (0.5%)

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

simplify146.0ms (2%)

Algorithm

1×	egg-herbie

Rules

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

Counts

306 → 227

Iterations

Useful iterations: 2 (0.0ms)

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

prune424.0ms (5.8%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	226	1	227
Fresh	0	9	9
Picked	0	1	1
Done	0	0	0
Total	226	11	237

Error

0.3b

Counts

237 → 11

Alt Table

Status	Error	Program
	45.8b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3)) (.f64 (.f64 3 a) (+.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))))))))
	45.8b	(/.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))
▶	3.0b	(/.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))
	45.8b	(/.f64 1 (/.f64 (.f64 3 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))
	45.8b	(/.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))
	4.0b	(/.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))
	6.0b	(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 (log.f64 (exp.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))))
	44.8b	(/.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))
	45.7b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
	45.8b	(.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))))
✓	2.6b	(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 12085 to 7415 computations (38.6% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5))
✓	0.4b	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
✓	0.5b	(.f64 (.f64 c a) (*.f64 c a))
✓	0.7b	(pow.f64 (*.f64 c a) 3)

series153.0ms (2.1%)

Counts

4 → 84

Calls

4 calls:

109.0ms	(/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5))
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))

rewrite31.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`times-frac_binary64`
51×	`add-exp-log_binary64`
48×	`unpow-prod-down_binary64`
47×	`add-sqr-sqrt_binary64`
46×	`pow1_binary64`

Counts

4 → 200

Calls

4 calls:

6.0ms	(/.f64 (pow.f64 (*.f64 c a) 3) (pow.f64 b 5))
5.0ms	(*.f64 (pow.f64 c 4) (pow.f64 a 4))
5.0ms	(.f64 (.f64 c a) (*.f64 c a))
4.0ms	(pow.f64 (*.f64 c a) 3)

simplify133.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

766×	`associate-/r/_binary64`
507×	`log-prod_binary64`
477×	`unswap-sqr_binary64`
271×	`associate-/l*_binary64`
209×	`associate-l_binary64`

Counts

284 → 225

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	251	4074
1	439	3729
2	2309	3581
3	4654	3581
4	5471	3581

prune391.0ms (5.3%)

Pruning

11 alts after pruning (9 fresh and 2 done)

	Pruned	Kept	Total
New	225	0	225
Fresh	0	9	9
Picked	0	1	1
Done	0	1	1
Total	225	11	236

Error

0.3b

Counts

236 → 11

Alt Table

Status	Error	Program
	45.8b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3)) (.f64 (.f64 3 a) (+.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))))))))
	45.8b	(/.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))
✓	3.0b	(/.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))
	45.8b	(/.f64 1 (/.f64 (.f64 3 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))
	45.8b	(/.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))
▶	4.0b	(/.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))
	6.0b	(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 (log.f64 (exp.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))))
	44.8b	(/.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))
	45.7b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
	45.8b	(.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))))
✓	2.6b	(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 13624 to 7933 computations (41.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

series202.0ms (2.7%)

Counts

2 → 72

Calls

2 calls:

119.0ms

(/.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))

82.0ms

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

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

56×	`add-exp-log_binary64`
25×	`add-cbrt-cube_binary64`
25×	`prod-exp_binary64`
17×	`div-exp_binary64`
15×	`times-frac_binary64`

Counts

2 → 80

Calls

2 calls:

8.0ms

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

3.0ms

(/.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))

simplify118.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

664×	`associate-/r/_binary64`
414×	`fma-def_binary64`
317×	`times-frac_binary64`
214×	`associate-/l*_binary64`
211×	`unswap-sqr_binary64`

Counts

152 → 117

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	180	4624
1	425	4067
2	2212	3988
3	4742	3988
4	5202	3988

prune260.0ms (3.5%)

Pruning

13 alts after pruning (11 fresh and 2 done)

	Pruned	Kept	Total
New	174	3	177
Fresh	0	8	8
Picked	1	0	1
Done	0	2	2
Total	175	13	188

Error

0.3b

Counts

188 → 13

Alt Table

Status	Error	Program
	45.8b	(/.f64 (+.f64 (pow.f64 (neg.f64 b) 3) (pow.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))) 3)) (.f64 (.f64 3 a) (+.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))))))))
	45.8b	(/.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))
✓	3.0b	(/.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))
	45.8b	(/.f64 1 (/.f64 (.f64 3 a) (+.f64 (neg.f64 b) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c))))))
	45.8b	(/.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))
	4.0b	(/.f64 1 (/.f64 3 (/.f64 (fma.f64 -3/2 (.f64 (/.f64 c b) a) (fma.f64 (.f64 (/.f64 (.f64 (.f64 c c) a) (pow.f64 b 3)) a) -9/8 (/.f64 -27/16 (/.f64 (pow.f64 b 5) (pow.f64 (*.f64 c a) 3))))) a)))
	6.0b	(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 (log.f64 (exp.f64 (/.f64 (.f64 c (.f64 c a)) (pow.f64 b 3)))))))))
	44.8b	(/.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))
	45.7b	(/.f64 (fma.f64 (.f64 (cbrt.f64 b) (cbrt.f64 b)) (neg.f64 (cbrt.f64 b)) (sqrt.f64 (-.f64 (.f64 b b) (.f64 (.f64 3 a) c)))) (*.f64 3 a))
	4.2b	(cbrt.f64 (/.f64 (.f64 (.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))))) (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)))))) (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 (.f64 (.f64 3 3) 3) (.f64 (.f64 a a) a))))
	45.8b	(.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))))
✓	2.6b	(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)))))))
	3.9b	(/.f64 (/.f64 (fma.f64 -3/2 (.f64 (/.f64 c b) a) (fma.f64 (.f64 (/.f64 (.f64 (.f64 c c) a) (pow.f64 b 3)) a) -9/8 (/.f64 -27/16 (/.f64 (pow.f64 b 5) (pow.f64 (*.f64 c a) 3))))) 3) a)

Compiler

Compiled 8291 to 4253 computations (48.7% saved)

regimes1.7s (22.5%)

Accuracy

Total 2.6b remaining (86.1%)

Threshold costs 0b (0%)

Counts

203 → 1

Compiler

Compiled 40129 to 25830 computations (35.6% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	32	63
1	41	63
2	43	63
3	44	63
4	44	63

end1.0ms (0%)

Compiler: Compiled 46 to 33 computations (28.3% saved)

sample2.2s (29.2%)

Algorithm

1×

intervals

Results

362.0ms	2968×	body	256	valid
320.0ms	5028×	body	128	valid
294.0ms	8843×	pre	128	true
51.0ms	843×	body	128	nan
1.0ms	4×	body	512	valid

Compiler

Compiled 722 to 465 computations (35.6% saved)

Details

analyze356.0ms (4.8%)

sample129.0ms (1.8%)

simplify364.0ms (5%)

prune4.0ms (0.1%)

localize9.0ms (0.1%)

series161.0ms (2.2%)

rewrite30.0ms (0.4%)

simplify123.0ms (1.7%)

prune167.0ms (2.3%)

localize31.0ms (0.4%)

series207.0ms (2.8%)

rewrite39.0ms (0.5%)

simplify146.0ms (2%)

prune424.0ms (5.8%)

localize27.0ms (0.4%)

series153.0ms (2.1%)

rewrite31.0ms (0.4%)

simplify133.0ms (1.8%)

prune391.0ms (5.3%)

localize17.0ms (0.2%)

series202.0ms (2.7%)

rewrite20.0ms (0.3%)

simplify118.0ms (1.6%)

prune260.0ms (3.5%)

regimes1.7s (22.5%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample2.2s (29.2%)

Profiling