Details

analyze1.7s (16.3%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.8%	0.2%	0
0%	99.8%	0.2%	1
0%	99.8%	0.2%	2
0%	99.8%	0.2%	3
0%	99.8%	0.2%	4
0%	99.8%	0.2%	5
0%	99.8%	0.2%	6
0%	99.8%	0.2%	7
0%	99.8%	0.2%	8
3.1%	71.7%	25.1%	9
4.7%	69.8%	25.5%	10
7%	66.9%	26.1%	11
10.9%	61.5%	27.6%	12
11.1%	47%	41.9%	13
12.8%	44.4%	42.8%	14

Compiler

Compiled 24 to 20 computations (16.7% saved)

sample99.0ms (0.9%)

Algorithm

1×

intervals

Results

29.0ms	363×	body	128	nan
22.0ms	256×	body	128	valid

Compiler

Compiled 51 to 43 computations (15.7% saved)

simplify95.0ms (0.9%)

Algorithm

1×	egg-herbie

Rules

2067×	`associate-/l*_binary64`
1151×	`associate-/l/_binary64`
961×	`associate-/r/_binary64`
904×	`*-commutative_binary64`
879×	`associate-l_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	20	26
1	40	23
2	121	20
3	446	20
4	1750	20
5	3005	20
6	3002	20
7	3002	20
8	3753	20
9	4074	20
10	4215	20
11	4225	20
12	4229	20
13	4230	20
14	5398	20

prune4.0ms (0%)

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

1.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	1.6b	(.f64 (/.f64 1 3) (acos.f64 (.f64 (/.f64 (.f64 3 (/.f64 x (.f64 y 27))) (*.f64 z 2)) (sqrt.f64 t))))
▶	1.2b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

Compiler

Compiled 116 to 91 computations (21.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(/.f64 (sqrt.f64 t) z)
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
✓	2.9b	(/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18))
✓	4.2b	(.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))

series106.0ms (1%)

Counts

4 → 120

Calls

4 calls:

48.0ms	(.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))
28.0ms	(/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18))
19.0ms	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
11.0ms	(/.f64 (sqrt.f64 t) z)

rewrite37.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

116×	`times-frac_binary64`
66×	`add-sqr-sqrt_binary64`
62×	`*-un-lft-identity_binary64`
62×	`add-cube-cbrt_binary64`
39×	`sqrt-prod_binary64`

Counts

4 → 179

Calls

4 calls:

11.0ms	(.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))
6.0ms	(/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18))
3.0ms	(/.f64 (sqrt.f64 t) z)
3.0ms	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

simplify188.0ms (1.8%)

Algorithm

1×	egg-herbie

Rules

740×	`associate-/r*_binary64`
664×	`associate-/l/_binary64`
458×	`*-commutative_binary64`
395×	`associate-/r/_binary64`
173×	`log-div_binary64`

Counts

299 → 245

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	241	5359
1	541	4814
2	1719	4813
3	4107	4813
4	4737	4813
5	4988	4813

prune217.0ms (2.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	243	2	245
Fresh	1	0	1
Picked	0	1	1
Done	0	0	0
Total	244	3	247

Error

1.0b

Counts

247 → 3

Alt Table

Status	Error	Program
▶	1.2b	(.f64 (.f64 1/3 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))) (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18))))))
	1.3b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
✓	1.2b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

Compiler

Compiled 5277 to 2536 computations (51.9% saved)

localize11.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.2b	(/.f64 (sqrt.f64 t) z)
✓	1.0b	(sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))
	2.9b	(/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18))
	4.2b	(.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))

series22.0ms (0.2%)

Counts

1 → 48

Calls

1 calls:

22.0ms

(sqrt.f64 (acos.f64 (*.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

rewrite1.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

3×	`sqrt-prod_binary64`
3×	`add-sqr-sqrt_binary64`
2×	`*-un-lft-identity_binary64`
2×	`add-cube-cbrt_binary64`
2×	`pow1_binary64`

Counts

1 → 15

Calls

1 calls:

1.0ms

(sqrt.f64 (acos.f64 (*.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

simplify265.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

1032×	`sqr-pow_binary64`
529×	`cube-prod_binary64`
522×	`pow-sqr_binary64`
430×	`fabs-mul_binary64`
362×	`unswap-sqr_binary64`

Counts

63 → 17

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	38	1246
1	59	1230
2	115	1230
3	258	1230
4	467	1230
5	562	1230
6	560	1230
7	613	1230
8	788	1230
9	1093	1230
10	1095	1230
11	1225	1230
12	1379	1230
13	1546	1230
14	1775	1230
15	2076	1230
16	2424	1230
17	2899	1230
18	3517	1230
19	3713	1230
20	3887	1230
21	4001	1230
22	4048	1230
23	4100	1230
24	4978	1230
25	4780	1230

prune331.0ms (3.2%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	455	1	456
Fresh	0	1	1
Picked	0	1	1
Done	1	0	1
Total	456	3	459

Error

Counts

459 → 3

Alt Table

Status	Error	Program
▶	0.3b	(.f64 (.f64 1/3 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18))))))) (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18))))))))
✓	1.2b	(.f64 (.f64 1/3 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))) (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18))))))
	1.3b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

Compiler

Compiled 16079 to 8133 computations (49.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	1.0b	(sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))
✓	1.0b	(.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))))
	2.9b	(/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18))
	4.2b	(.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))

series2.1s (19.6%)

Counts

1 → 48

Calls

1 calls:

2.1s	(.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))))

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

40×	`cbrt-prod_binary64`
35×	`add-sqr-sqrt_binary64`
20×	`sqrt-prod_binary64`
13×	`*-un-lft-identity_binary64`
13×	`add-cube-cbrt_binary64`

Counts

1 → 58

Calls

1 calls:

6.0ms

(*.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (*.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (*.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))))

simplify181.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

490×	`log-div_binary64`
443×	`unswap-sqr_binary64`
430×	`associate-/l*_binary64`
338×	`fma-def_binary64`
333×	`sqr-pow_binary64`

Counts

106 → 66

Iterations

Useful iterations: 6 (0.0ms)

Iter	Nodes	Cost
0	73	3559
1	121	3493
2	295	2723
3	640	2648
4	1150	2372
5	1794	2372
6	3008	2352
7	4640	2352
8	5107	2352

prune1.1s (10.5%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	802	0	802
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	802	3	805

Error

Counts

805 → 3

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (.f64 1/3 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18))))))) (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18))))))))
✓	1.2b	(.f64 (.f64 1/3 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))) (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18))))))
▶	1.3b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

Compiler

Compiled 51604 to 28092 computations (45.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.2b	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
✓	3.0b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
✓	5.6b	(/.f64 x (*.f64 y z))

series119.0ms (1.1%)

Counts

4 → 0

Calls

4 calls:

44.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
36.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
21.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))
16.0ms	(/.f64 x (*.f64 y z))

rewrite24.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

34×	`add-cbrt-cube_binary64`
34×	`add-exp-log_binary64`
19×	`add-sqr-sqrt_binary64`
14×	`cbrt-unprod_binary64`
14×	`prod-exp_binary64`

Counts

4 → 101

Calls

4 calls:

6.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
6.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
3.0ms	(/.f64 x (*.f64 y z))
3.0ms	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

simplify86.0ms (0.8%)

Algorithm

1×	egg-herbie

Rules

950×	`times-frac_binary64`
716×	`associate-*l/_binary64`
462×	`associate-/l*_binary64`
425×	`associate-/r*_binary64`
142×	`log-div_binary64`

Counts

101 → 128

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	153	1867
1	327	1566
2	1062	1565
3	4748	1565
4	4996	1565
5	5009	1565

prune56.0ms (0.5%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	128	0	128
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	128	3	131

Error

Counts

131 → 3

Alt Table

Status	Error	Program
✓	0.3b	(.f64 (.f64 1/3 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))) (.f64 (.f64 (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))) (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18))))))) (cbrt.f64 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18))))))))
✓	1.2b	(.f64 (.f64 1/3 (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))))) (sqrt.f64 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18))))))
✓	1.3b	(.f64 1/3 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))

Compiler

Compiled 2704 to 1206 computations (55.4% saved)

regimes637.0ms (6.1%)

Accuracy

Total 0.6b remaining (97.6%)

Threshold costs 0.6b (97.6%)

Counts

43 → 1

Compiler

Compiled 18938 to 12932 computations (31.7% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Rules

5×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	91
1	24	91
2	24	91

end7.0ms (0.1%)

Compiler: Compiled 180 to 114 computations (36.7% saved)

sample3.1s (29.2%)

Algorithm

1×

intervals

Results

915.0ms	10133×	body	128	nan
767.0ms	8000×	body	128	valid

Compiler

Compiled 196 to 134 computations (31.6% saved)

Details

analyze1.7s (16.3%)

sample99.0ms (0.9%)

simplify95.0ms (0.9%)

prune4.0ms (0%)

localize9.0ms (0.1%)

series106.0ms (1%)

rewrite37.0ms (0.4%)

simplify188.0ms (1.8%)

prune217.0ms (2.1%)

localize11.0ms (0.1%)

series22.0ms (0.2%)

rewrite1.0ms (0%)

simplify265.0ms (2.5%)

prune331.0ms (3.2%)

localize17.0ms (0.2%)

series2.1s (19.6%)

rewrite16.0ms (0.2%)

simplify181.0ms (1.7%)

prune1.1s (10.5%)

localize9.0ms (0.1%)

series119.0ms (1.1%)

rewrite24.0ms (0.2%)

simplify86.0ms (0.8%)

prune56.0ms (0.5%)

regimes637.0ms (6.1%)

simplify3.0ms (0%)

end7.0ms (0.1%)

sample3.1s (29.2%)

Profiling