Details

analyze720.0ms (12.6%)

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
7%	92.8%	0.2%	8
19.1%	80.7%	0.2%	9
29.8%	70%	0.2%	10
31.3%	68.5%	0.2%	11
42.3%	57.2%	0.6%	12
53.3%	45.5%	1.2%	13
59.2%	39.3%	1.5%	14

Compiler

Compiled 14 to 9 computations (35.7% saved)

sample1.0s (18.1%)

Results

860.0ms	8256×	body	128	valid
70.0ms	676×	body	128	invalid

Compiler

Compiled 41 to 26 computations (36.6% saved)

simplify115.0ms (2%)

Algorithm

1×	egg-herbie

Rules

1630×	`fma-neg_binary64`
896×	`div-sub_binary64`
582×	`times-frac_binary64`
579×	`fma-def_binary64`
367×	`sub-neg_binary64`

Counts

1 → 1

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	9	13
1	15	13
2	34	13
3	74	13
4	145	13
5	245	13
6	572	13
7	1407	13
8	2937	13
9	2993	13
10	3292	13
11	3338	13
12	3355	13
13	3404	13
14	4948	13

prune1.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

14.8b

Counts

2 → 1

Alt Table

Status	Error	Program
▶	14.8b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

Compiler

Compiled 39 to 24 computations (38.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 x (-.f64 y z))
✓	14.0b	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))

series47.0ms (0.8%)

Counts

2 → 84

Calls

2 calls:

40.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
6.0ms	(*.f64 x (-.f64 y z))

rewrite17.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`prod-diff_binary64`
13×	`distribute-lft-in_binary64`

Counts

2 → 81

Calls

2 calls:

7.0ms	(/.f64 (*.f64 x (-.f64 y z)) (-.f64 t z))
5.0ms	(*.f64 x (-.f64 y z))

simplify97.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

526×	`cancel-sign-sub-inv_binary64`
513×	`fma-neg_binary64`
365×	`div-sub_binary64`
202×	`associate-/l*_binary64`
196×	`sub-neg_binary64`

Counts

165 → 145

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	244	2954
1	576	2753
2	2576	2555
3	4147	2552
4	5042	2552

prune102.0ms (1.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	137	8	145
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	138	8	146

Error

Counts

146 → 8

Alt Table

Status	Error	Program
▶	2.5b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
	14.8b	(-.f64 (/.f64 (.f64 y x) (-.f64 t z)) (/.f64 (.f64 z x) (-.f64 t z)))
	2.7b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
	33.3b	(-.f64 (+.f64 x (/.f64 (.f64 x t) z)) (.f64 (/.f64 x z) (+.f64 y (/.f64 (*.f64 y t) z))))
	32.4b	(*.f64 (/.f64 x (sqrt.f64 (-.f64 t z))) (/.f64 (-.f64 y z) (sqrt.f64 (-.f64 t z))))
	41.0b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (-.f64 y z) x) (-.f64 t z)) 3))
	15.2b	(/.f64 1 (/.f64 (-.f64 t z) (*.f64 x (-.f64 y z))))
	47.9b	(*.f64 (/.f64 x (+.f64 (sqrt.f64 t) (sqrt.f64 z))) (/.f64 (-.f64 y z) (-.f64 (sqrt.f64 t) (sqrt.f64 z))))

Compiler

Compiled 3325 to 1014 computations (69.5% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 t z) (-.f64 y z))
✓	2.4b	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))

series52.0ms (0.9%)

Counts

2 → 84

Calls

2 calls:

33.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
19.0ms	(/.f64 (-.f64 t z) (-.f64 y z))

rewrite38.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
194×	`*-un-lft-identity_binary64`
194×	`add-sqr-sqrt_binary64`
90×	`add-cube-cbrt_binary64`
52×	`distribute-lft-out--_binary64`

Counts

2 → 198

Calls

2 calls:

11.0ms	(/.f64 x (/.f64 (-.f64 t z) (-.f64 y z)))
6.0ms	(/.f64 (-.f64 t z) (-.f64 y z))

simplify159.0ms (2.8%)

Algorithm

1×	egg-herbie

Rules

562×	`cancel-sign-sub-inv_binary64`
374×	`sub-neg_binary64`
271×	`associate-/r/_binary64`
224×	`fma-neg_binary64`
198×	`associate-/l/_binary64`

Counts

282 → 300

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	408	7629
1	1057	7410
2	3983	7368
3	5298	7368

prune163.0ms (2.8%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	297	3	300
Fresh	3	4	7
Picked	1	0	1
Done	0	0	0
Total	301	7	308

Error

Counts

308 → 7

Alt Table

Status	Error	Program
	2.9b	(/.f64 x (/.f64 1 (*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))))
	41.0b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (-.f64 y z) x) (-.f64 t z)) 3))
	14.9b	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))
	14.8b	(-.f64 (/.f64 (.f64 y x) (-.f64 t z)) (/.f64 (.f64 z x) (-.f64 t z)))
▶	2.5b	(/.f64 x (-.f64 (/.f64 t (-.f64 y z)) (/.f64 z (-.f64 y z))))
	2.7b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
	15.2b	(/.f64 1 (/.f64 (-.f64 t z) (*.f64 x (-.f64 y z))))

Compiler

Compiled 7282 to 1737 computations (76.1% saved)

localize7.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(-.f64 (/.f64 t (-.f64 y z)) (/.f64 z (-.f64 y z)))
✓	0.0b	(/.f64 t (-.f64 y z))
✓	0.0b	(/.f64 z (-.f64 y z))
✓	2.4b	(/.f64 x (-.f64 (/.f64 t (-.f64 y z)) (/.f64 z (-.f64 y z))))

series165.0ms (2.9%)

Counts

4 → 111

Calls

4 calls:

116.0ms	(/.f64 x (-.f64 (/.f64 t (-.f64 y z)) (/.f64 z (-.f64 y z))))
22.0ms	(-.f64 (/.f64 t (-.f64 y z)) (/.f64 z (-.f64 y z)))
17.0ms	(/.f64 t (-.f64 y z))
9.0ms	(/.f64 z (-.f64 y z))

rewrite197.0ms (3.4%)

Algorithm

1×	rewrite-expression-head

Rules

863×	`*-un-lft-identity_binary64`
834×	`times-frac_binary64`
813×	`add-sqr-sqrt_binary64`
453×	`add-cube-cbrt_binary64`
441×	`prod-diff_binary64`

Counts

4 → 684

Calls

4 calls:

28.0ms	(-.f64 (/.f64 t (-.f64 y z)) (/.f64 z (-.f64 y z)))
22.0ms	(/.f64 x (-.f64 (/.f64 t (-.f64 y z)) (/.f64 z (-.f64 y z))))
4.0ms	(/.f64 z (-.f64 y z))
3.0ms	(/.f64 t (-.f64 y z))

simplify973.0ms (16.9%)

Algorithm

1×	egg-herbie

Rules

853×	`times-frac_binary64`
306×	`fma-udef_binary64`
263×	`unsub-neg_binary64`
237×	`fma-def_binary64`
197×	`sub-neg_binary64`

Counts

795 → 882

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	1006	47199
1	2724	42312
2	4809	42120
3	5008	42120

prune527.0ms (9.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	882	0	882
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	882	7	889

Error

Counts

889 → 7

Alt Table

Status	Error	Program
	2.9b	(/.f64 x (/.f64 1 (*.f64 (-.f64 y z) (/.f64 1 (-.f64 t z)))))
	41.0b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (-.f64 y z) x) (-.f64 t z)) 3))
	14.9b	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))
	14.8b	(-.f64 (/.f64 (.f64 y x) (-.f64 t z)) (/.f64 (.f64 z x) (-.f64 t z)))
✓	2.5b	(/.f64 x (-.f64 (/.f64 t (-.f64 y z)) (/.f64 z (-.f64 y z))))
▶	2.7b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
	15.2b	(/.f64 1 (/.f64 (-.f64 t z) (*.f64 x (-.f64 y z))))

Compiler

Compiled 44646 to 8283 computations (81.4% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 y z) (-.f64 t z))
✓	2.6b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))

series56.0ms (1%)

Counts

2 → 84

Calls

2 calls:

34.0ms	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
21.0ms	(/.f64 (-.f64 y z) (-.f64 t z))

rewrite26.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
70×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_binary64`
26×	`add-cube-cbrt_binary64`

Counts

2 → 106

Calls

2 calls:

10.0ms	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
7.0ms	(/.f64 (-.f64 y z) (-.f64 t z))

simplify100.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

906×	`fma-def_binary64`
511×	`cancel-sign-sub-inv_binary64`
372×	`sub-neg_binary64`
220×	`fma-neg_binary64`
164×	`associate-/l*_binary64`

Counts

190 → 181

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	283	4489
1	786	4288
2	2972	4076
3	5031	4076

prune112.0ms (2%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	180	1	181
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	181	7	188

Error

Counts

188 → 7

Alt Table

Status	Error	Program
	14.9b	(*.f64 (/.f64 1 (-.f64 t z)) (/.f64 x (/.f64 1 (-.f64 y z))))
	14.8b	(-.f64 (/.f64 (.f64 y x) (-.f64 t z)) (/.f64 (.f64 z x) (-.f64 t z)))
✓	2.5b	(/.f64 x (-.f64 (/.f64 t (-.f64 y z)) (/.f64 z (-.f64 y z))))
✓	2.7b	(*.f64 x (/.f64 (-.f64 y z) (-.f64 t z)))
	41.0b	(cbrt.f64 (pow.f64 (/.f64 (*.f64 (-.f64 y z) x) (-.f64 t z)) 3))
	2.8b	(.f64 x (.f64 (-.f64 y z) (/.f64 1 (-.f64 t z))))
	15.2b	(/.f64 1 (/.f64 (-.f64 t z) (*.f64 x (-.f64 y z))))

Compiler

Compiled 4170 to 1214 computations (70.9% saved)

regimes879.0ms (15.3%)

Accuracy

Total 2.3b remaining (99.4%)

Threshold costs 0b (0%)

Counts

140 → 3

Compiler

Compiled 11415 to 7094 computations (37.9% saved)

bsearch41.0ms (0.7%)

Steps

Iters	Range		Point
5	1.6067246258723035e-175	5.378997592358505e-175	3.0222555522334117e-175
9	-5.884031482906643e-78	-3.0333340990339227e-83	-1.5964659875812437e-80

Compiler

Compiled 5 to 4 computations (20% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

5×	`+-commutative_binary64`
5×	`sub-neg_binary64`
4×	`*-commutative_binary64`
2×	`neg-sub0_binary64`
2×	`neg-mul-1_binary64`

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	24	57
1	33	57
2	42	57
3	46	57
4	48	57
5	47	57

end87.0ms (1.5%)

Compiler: Compiled 198 to 110 computations (44.4% saved)

Details

analyze720.0ms (12.6%)

sample1.0s (18.1%)

simplify115.0ms (2%)

prune1.0ms (0%)

localize6.0ms (0.1%)

series47.0ms (0.8%)

rewrite17.0ms (0.3%)

simplify97.0ms (1.7%)

prune102.0ms (1.8%)

localize6.0ms (0.1%)

series52.0ms (0.9%)

rewrite38.0ms (0.7%)

simplify159.0ms (2.8%)

prune163.0ms (2.8%)

localize7.0ms (0.1%)

series165.0ms (2.9%)

rewrite197.0ms (3.4%)

simplify973.0ms (16.9%)

prune527.0ms (9.2%)

localize6.0ms (0.1%)

series56.0ms (1%)

rewrite26.0ms (0.5%)

simplify100.0ms (1.7%)

prune112.0ms (2%)

regimes879.0ms (15.3%)

bsearch41.0ms (0.7%)

simplify4.0ms (0.1%)

end87.0ms (1.5%)

Profiling