Details

analyze1.9s (11.2%)

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)

sample5.7s (34.2%)

Symmetry

(sort y z)

Results

3.7s	10481×	body	128	invalid
1.8s	8256×	body	128	valid

Compiler

Compiled 71 to 59 computations (16.9% saved)

simplify114.0ms (0.7%)

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

prune3.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Error

1.0b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.0b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))

Compiler

Compiled 70 to 53 computations (24.3% saved)

localize13.0ms (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)))))
✓	3.6b	(/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18))
✓	3.8b	(.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))

series213.0ms (1.3%)

Counts

4 → 120

Calls

4 calls:

122.0ms	(.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))
47.0ms	(/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18))
26.0ms	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
16.0ms	(/.f64 (sqrt.f64 t) z)

rewrite52.0ms (0.3%)

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:

20.0ms	(.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (.f64 y 18)))
8.0ms	(/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18))
5.0ms	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
3.0ms	(/.f64 (sqrt.f64 t) z)

simplify469.0ms (2.8%)

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

prune151.0ms (0.9%)

Pruning

2 alts after pruning (1 fresh and 1 done)

	Pruned	Kept	Total
New	244	1	245
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	244	2	246

Error

1.0b

Counts

246 → 2

Alt Table

Status	Error	Program
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
▶	1.0b	(log.f64 (cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))))

Compiler

Compiled 5217 to 2496 computations (52.2% saved)

localize20.0ms (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	(cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))))
✓	3.4b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
✓	5.2b	(/.f64 x (*.f64 y z))

series3.6s (21.8%)

Counts

4 → 48

Calls

4 calls:

3.4s	(cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))))
78.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
71.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
34.0ms	(/.f64 x (*.f64 y z))

rewrite42.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

32×	`add-cbrt-cube_binary64`
32×	`add-exp-log_binary64`
16×	`add-sqr-sqrt_binary64`
13×	`cbrt-unprod_binary64`
13×	`prod-exp_binary64`

Counts

4 → 95

Calls

4 calls:

17.0ms	(.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))
9.0ms	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
4.0ms	(/.f64 x (*.f64 y z))
3.0ms	(cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))))

simplify81.0ms (0.5%)

Algorithm

1×	egg-herbie

Rules

950×	`times-frac_binary64`
716×	`associate-*l/_binary64`
600×	`associate-*r/_binary64`
462×	`associate-/l*_binary64`
425×	`associate-/r*_binary64`

Counts

143 → 109

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	147	2776
1	304	2551
2	1002	2502
3	5304	2502

prune131.0ms (0.8%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	108	1	109
Fresh	0	0	0
Picked	0	1	1
Done	0	1	1
Total	108	3	111

Error

1.0b

Counts

111 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
▶	1.0b	(log.f64 (pow.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))) 1/3))
✓	1.0b	(log.f64 (cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))))

Compiler

Compiled 2349 to 1100 computations (53.2% saved)

localize19.0ms (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	(pow.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))) 1/3)
	3.4b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
	5.2b	(/.f64 x (*.f64 y z))

series3.0s (17.8%)

Counts

1 → 48

Calls

1 calls:

3.0s	(pow.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))) 1/3)

rewrite7.0ms (0%)

Algorithm

1×	rewrite-expression-head

Rules

4×	`pow-pow_binary64`
4×	`*-un-lft-identity_binary64`
4×	`add-sqr-sqrt_binary64`
4×	`add-cube-cbrt_binary64`
3×	`exp-prod_binary64`

Counts

1 → 23

Calls

1 calls:

5.0ms

(pow.f64 (exp.f64 (acos.f64 (*.f64 1/18 (*.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))) 1/3)

simplify170.0ms (1%)

Algorithm

1×	egg-herbie

Rules

572×	`log-prod_binary64`
539×	`distribute-rgt-in_binary64`
517×	`distribute-lft-in_binary64`
310×	`fma-def_binary64`
297×	`associate-l_binary64`

Counts

71 → 35

Iterations

Useful iterations: 4 (0.0ms)

Iter	Nodes	Cost
0	52	1620
1	95	1547
2	191	1547
3	504	1547
4	1378	1541
5	4806	1541
6	5002	1541

prune146.0ms (0.9%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	125	1	126
Fresh	0	0	0
Picked	0	1	1
Done	1	1	2
Total	126	3	129

Error

Counts

129 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
✓	1.0b	(log.f64 (pow.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))) 1/3))
▶	0.0b	(log.f64 (.f64 (pow.f64 (cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))) 2/3) (cbrt.f64 (cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))))))

Compiler

Compiled 2910 to 1430 computations (50.9% saved)

localize36.0ms (0.2%)

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	(cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))))
	3.4b	(.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t))
	5.2b	(/.f64 x (*.f64 y z))

prune407.0ms (2.4%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	218	0	218
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	218	3	221

Error

Counts

221 → 3

Alt Table

Status	Error	Program
✓	1.0b	(.f64 1/3 (acos.f64 (.f64 x (/.f64 (/.f64 (sqrt.f64 t) z) (*.f64 y 18)))))
✓	1.0b	(log.f64 (pow.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t))))) 1/3))
✓	0.0b	(log.f64 (.f64 (pow.f64 (cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (.f64 y z)) (sqrt.f64 t)))))) 2/3) (cbrt.f64 (cbrt.f64 (exp.f64 (acos.f64 (.f64 1/18 (.f64 (/.f64 x (*.f64 y z)) (sqrt.f64 t)))))))))

Compiler

Compiled 8325 to 3931 computations (52.8% saved)

regimes235.0ms (1.4%)

Accuracy

Total 0.2b remaining (96.5%)

Threshold costs 0.2b (96.5%)

Counts

5 → 1

Compiler

Compiled 1726 to 1310 computations (24.1% saved)

simplify6.0ms (0%)

Algorithm

1×	egg-herbie

Rules

4×	`*-commutative_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	19	51
1	23	51
2	23	51

end173.0ms (1%)

Remove: (sort y z)
Compiler: Compiled 211 to 143 computations (32.2% saved)

Details

analyze1.9s (11.2%)

sample5.7s (34.2%)

simplify114.0ms (0.7%)

prune3.0ms (0%)

localize13.0ms (0.1%)

series213.0ms (1.3%)

rewrite52.0ms (0.3%)

simplify469.0ms (2.8%)

prune151.0ms (0.9%)

localize20.0ms (0.1%)

series3.6s (21.8%)

rewrite42.0ms (0.3%)

simplify81.0ms (0.5%)

prune131.0ms (0.8%)

localize19.0ms (0.1%)

series3.0s (17.8%)

rewrite7.0ms (0%)

simplify170.0ms (1%)

prune146.0ms (0.9%)

localize36.0ms (0.2%)

prune407.0ms (2.4%)

regimes235.0ms (1.4%)

simplify6.0ms (0%)

end173.0ms (1%)

Profiling