Details

analyze1.7s (28%)

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
0%	99.8%	0.2%	9
0%	99.8%	0.2%	10
0%	99.8%	0.2%	11
0%	99.8%	0.2%	12
0%	99.8%	0.2%	13
0%	99.8%	0.2%	14

Compiler

Compiled 17 to 11 computations (35.3% saved)

sample1.5s (25.4%)

Results

1.1s	8256×	body	128	valid
262.0ms	361×	body	8192	exit
53.0ms	401×	body	128	invalid

Compiler

Compiled 33 to 21 computations (36.4% saved)

simplify122.0ms (2.1%)

Algorithm

1×	egg-herbie

Rules

1627×	`fma-def_binary64`
927×	`div-sub_binary64`
619×	`times-frac_binary64`
541×	`fma-neg_binary64`
386×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	21	14
2	40	14
3	78	14
4	161	14
5	302	14
6	659	14
7	1591	14
8	3045	14
9	3070	14
10	3380	14
11	3469	14
12	3480	14
13	4892	14
14	5124	14

prune3.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Error

1.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	1.6b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

Compiler

Compiled 58 to 31 computations (46.6% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	2.3b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))

series57.0ms (1%)

Counts

2 → 84

Calls

2 calls:

34.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
22.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite27.0ms (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:

11.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
8.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

simplify132.0ms (2.2%)

Algorithm

1×	egg-herbie

Rules

737×	`cancel-sign-sub-inv_binary64`
386×	`sub-neg_binary64`
263×	`fma-neg_binary64`
194×	`associate-/l*_binary64`
184×	`div-sub_binary64`

Counts

190 → 184

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	290	4483
1	807	4312
2	3067	4264
3	4766	4260
4	5066	4260

prune146.0ms (2.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	178	6	184
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	178	7	185

Error

0.0b

Counts

185 → 7

Alt Table

Status	Error	Program
	13.8b	(+.f64 x (*.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3))))
	10.2b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 (-.f64 a t))))
✓	1.6b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
▶	2.3b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))))
	19.4b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))))
	32.9b	(+.f64 x (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (/.f64 (-.f64 z t) (-.f64 a t)))))
	10.1b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 4846 to 1547 computations (68.1% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.3b	(/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))
✓	0.5b	(cbrt.f64 (-.f64 a t))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
✓	6.8b	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))

series251.0ms (4.2%)

Counts

4 → 132

Calls

4 calls:

139.0ms	(/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))
40.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))
39.0ms	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
32.0ms	(cbrt.f64 (-.f64 a t))

rewrite75.0ms (1.3%)

Algorithm

1×	rewrite-expression-head

Rules

145×	`add-sqr-sqrt_binary64`
127×	`*-un-lft-identity_binary64`
90×	`times-frac_binary64`
90×	`cbrt-prod_binary64`
55×	`add-cube-cbrt_binary64`

Counts

4 → 240

Calls

4 calls:

26.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t))))
10.0ms	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
7.0ms	(/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))
2.0ms	(cbrt.f64 (-.f64 a t))

simplify240.0ms (4%)

Algorithm

1×	egg-herbie

Rules

348×	`fma-def_binary64`
291×	`associate-/l*_binary64`
287×	`times-frac_binary64`
263×	`associate-/r*_binary64`
214×	`*-commutative_binary64`

Counts

372 → 421

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	677	11675
1	2000	10759
2	4999	10759
3	4983	10759

prune449.0ms (7.5%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	525	0	525
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	525	7	532

Error

0.0b

Counts

532 → 7

Alt Table

Status	Error	Program
	13.8b	(+.f64 x (*.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3))))
	10.2b	(+.f64 x (.f64 (.f64 y (-.f64 z t)) (/.f64 1 (-.f64 a t))))
✓	1.6b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
✓	2.3b	(+.f64 x (.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 a t)))))
	19.4b	(+.f64 x (.f64 (.f64 y (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))) (sqrt.f64 (/.f64 (-.f64 z t) (-.f64 a t)))))
	32.9b	(+.f64 x (.f64 (sqrt.f64 y) (.f64 (sqrt.f64 y) (/.f64 (-.f64 z t) (-.f64 a t)))))
▶	10.1b	(+.f64 x (/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t)))

Compiler

Compiled 20207 to 7105 computations (64.8% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(*.f64 (-.f64 z t) y)
✓	10.2b	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))

series56.0ms (0.9%)

Counts

2 → 60

Calls

2 calls:

48.0ms	(/.f64 (*.f64 (-.f64 z t) y) (-.f64 a t))
8.0ms	(*.f64 (-.f64 z t) y)

rewrite14.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

14×	`add-sqr-sqrt_binary64`
12×	`*-un-lft-identity_binary64`
9×	`add-cbrt-cube_binary64`
9×	`add-exp-log_binary64`
6×	`add-cube-cbrt_binary64`

Counts

2 → 55

Calls

2 calls:

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

simplify84.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

611×	`fma-def_binary64`
550×	`cancel-sign-sub-inv_binary64`
360×	`div-sub_binary64`
329×	`fma-neg_binary64`
296×	`distribute-rgt-in_binary64`

Counts

115 → 124

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	199	2430
1	555	2202
2	2168	1959
3	4400	1957
4	5131	1957

prune95.0ms (1.6%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	121	3	124
Fresh	3	1	4
Picked	1	0	1
Done	2	0	2
Total	127	4	131

Error

Counts

131 → 4

Alt Table

Status	Error	Program
	13.8b	(+.f64 x (*.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3))))
	2.4b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
	10.2b	(+.f64 x (/.f64 1 (/.f64 (-.f64 a t) (*.f64 (-.f64 z t) y))))
▶	2.4b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 2842 to 929 computations (67.3% saved)

localize9.0ms (0.2%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 y (-.f64 a t))
✓	9.9b	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))

series54.0ms (0.9%)

Counts

2 → 72

Calls

2 calls:

35.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
18.0ms	(/.f64 y (-.f64 a t))

rewrite23.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

57×	`add-sqr-sqrt_binary64`
52×	`*-un-lft-identity_binary64`
36×	`add-cube-cbrt_binary64`
31×	`times-frac_binary64`
21×	`associate-l_binary64`

Counts

2 → 113

Calls

2 calls:

10.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
4.0ms	(/.f64 y (-.f64 a t))

simplify161.0ms (2.7%)

Algorithm

1×	egg-herbie

Rules

766×	`cancel-sign-sub-inv_binary64`
366×	`fma-neg_binary64`
238×	`sub-neg_binary64`
178×	`times-frac_binary64`
174×	`associate-/l*_binary64`

Counts

185 → 203

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	340	4235
1	810	4049
2	3050	3971
3	4777	3970
4	4973	3970
5	4980	3970

prune125.0ms (2.1%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	203	0	203
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	203	4	207

Error

Counts

207 → 4

Alt Table

Status	Error	Program
	13.8b	(+.f64 x (*.f64 y (cbrt.f64 (pow.f64 (/.f64 (-.f64 z t) (-.f64 a t)) 3))))
	2.4b	(+.f64 x (/.f64 (-.f64 z t) (/.f64 (-.f64 a t) y)))
	10.2b	(+.f64 x (/.f64 1 (/.f64 (-.f64 a t) (*.f64 (-.f64 z t) y))))
✓	2.4b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))

Compiler

Compiled 5069 to 1446 computations (71.5% saved)

regimes564.0ms (9.5%)

Accuracy

Total 0.5b remaining (95.3%)

Threshold costs 0.5b (95.3%)

Counts

74 → 1

Compiler

Compiled 11712 to 7148 computations (39% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	17	52
1	23	52
2	29	52
3	31	52
4	32	52
5	32	52

end63.0ms (1.1%)

Compiler: Compiled 145 to 77 computations (46.9% saved)

Details

analyze1.7s (28%)

sample1.5s (25.4%)

simplify122.0ms (2.1%)

prune3.0ms (0.1%)

localize8.0ms (0.1%)

series57.0ms (1%)

rewrite27.0ms (0.5%)

simplify132.0ms (2.2%)

prune146.0ms (2.4%)

localize12.0ms (0.2%)

series251.0ms (4.2%)

rewrite75.0ms (1.3%)

simplify240.0ms (4%)

prune449.0ms (7.5%)

localize8.0ms (0.1%)

series56.0ms (0.9%)

rewrite14.0ms (0.2%)

simplify84.0ms (1.4%)

prune95.0ms (1.6%)

localize9.0ms (0.2%)

series54.0ms (0.9%)

rewrite23.0ms (0.4%)

simplify161.0ms (2.7%)

prune125.0ms (2.1%)

regimes564.0ms (9.5%)

simplify4.0ms (0.1%)

end63.0ms (1.1%)

Profiling