Details

analyze1.9s (25.3%)

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
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 (20.4%)

Results

1.1s	8256×	body	128	valid
246.0ms	361×	body	8192	exit
51.0ms	401×	body	128	invalid

Compiler

Compiled 33 to 21 computations (36.4% saved)

simplify119.0ms (1.6%)

Algorithm

1×	egg-herbie

Rules

1894×	`fma-neg_binary64`
843×	`div-sub_binary64`
750×	`fma-def_binary64`
582×	`times-frac_binary64`
397×	`sub-neg_binary64`

Counts

1 → 2

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	11	16
1	18	16
2	37	14
3	78	14
4	163	14
5	295	14
6	645	14
7	1554	14
8	3040	14
9	3228	14
10	3469	14
11	3370	14
12	3363	14
13	3398	14
14	4949	14

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

0.1b

Counts

3 → 2

Alt Table

Status	Error	Program
	10.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
▶	1.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

Compiler

Compiled 88 to 50 computations (43.2% saved)

localize7.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(/.f64 (-.f64 z t) (-.f64 a t))
✓	1.5b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

series62.0ms (0.8%)

Counts

2 → 96

Calls

2 calls:

41.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
21.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

rewrite13.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64`
38×	`add-sqr-sqrt_binary64`
25×	`times-frac_binary64`
14×	`add-cube-cbrt_binary64`
12×	`distribute-lft-out--_binary64`

Counts

2 → 64

Calls

2 calls:

9.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
0.0ms	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)

simplify303.0ms (4.1%)

Algorithm

1×	egg-herbie

Rules

690×	`cancel-sign-sub-inv_binary64`
647×	`times-frac_binary64`
542×	`fma-neg_binary64`
354×	`sub-neg_binary64`
188×	`neg-mul-1_binary64`

Counts

160 → 138

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	267	4118
1	740	4035
2	2434	3427
3	4231	3410
4	4964	3410

prune109.0ms (1.5%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	135	3	138
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	135	5	140

Error

0.0b

Counts

140 → 5

Alt Table

Status	Error	Program
	41.6b	(cbrt.f64 (.f64 (.f64 (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x) (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)) (fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)))
	10.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
▶	2.4b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	1.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	13.8b	(fma.f64 y (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 z t) (-.f64 a t)) (/.f64 (-.f64 z t) (-.f64 a t))) (/.f64 (-.f64 z t) (-.f64 a t)))) x)

Compiler

Compiled 3419 to 1128 computations (67% saved)

localize9.0ms (0.1%)

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))

series51.0ms (0.7%)

Counts

2 → 72

Calls

2 calls:

34.0ms	(*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t))
17.0ms	(/.f64 y (-.f64 a t))

rewrite24.0ms (0.3%)

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))

simplify156.0ms (2.1%)

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

prune164.0ms (2.2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	201	2	203
Fresh	1	2	3
Picked	0	1	1
Done	0	1	1
Total	202	6	208

Error

0.0b

Counts

208 → 6

Alt Table

Status	Error	Program
	10.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	2.4b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
▶	6.8b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t))))
✓	1.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	16.8b	(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 y (-.f64 a t)) 3)) (-.f64 z t)))
	13.8b	(fma.f64 y (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 z t) (-.f64 a t)) (/.f64 (-.f64 z t) (-.f64 a t))) (/.f64 (-.f64 z t) (-.f64 a t)))) x)

Compiler

Compiled 5223 to 1520 computations (70.9% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.5b	(cbrt.f64 (-.f64 a t))
✓	0.5b	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
✓	3.0b	(*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t))
✓	6.0b	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t)))

series597.0ms (8.1%)

Counts

4 → 144

Calls

4 calls:

484.0ms	(*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t))
39.0ms	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
38.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t)))
35.0ms	(cbrt.f64 (-.f64 a t))

rewrite89.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

107×	`add-sqr-sqrt_binary64`
97×	`*-un-lft-identity_binary64`
89×	`add-exp-log_binary64`
73×	`add-cube-cbrt_binary64`
65×	`distribute-lft-in_binary64`

Counts

4 → 280

Calls

4 calls:

24.0ms	(.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t)))
14.0ms	(*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t))
11.0ms	(*.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))
2.0ms	(cbrt.f64 (-.f64 a t))

simplify230.0ms (3.1%)

Algorithm

1×	egg-herbie

Rules

471×	`times-frac_binary64`
452×	`fma-def_binary64`
317×	`*-commutative_binary64`
286×	`associate-/l*_binary64`
181×	`associate-r_binary64`

Counts

424 → 516

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	850	13543
1	2205	11564
2	5029	11564

prune628.0ms (8.5%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	621	1	622
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	621	7	628

Error

Counts

628 → 7

Alt Table

Status	Error	Program
▶	10.1b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
✓	2.4b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	6.8b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t))))
✓	1.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	22.4b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (.f64 (.f64 z y) (cbrt.f64 (/.f64 1 a)))))
	16.8b	(+.f64 x (*.f64 (cbrt.f64 (pow.f64 (/.f64 y (-.f64 a t)) 3)) (-.f64 z t)))
	13.8b	(fma.f64 y (cbrt.f64 (.f64 (.f64 (/.f64 (-.f64 z t) (-.f64 a t)) (/.f64 (-.f64 z t) (-.f64 a t))) (/.f64 (-.f64 z t) (-.f64 a t)))) x)

Compiler

Compiled 26105 to 9127 computations (65% saved)

localize8.0ms (0.1%)

Local error

Found 2 expressions with local error:

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

series47.0ms (0.6%)

Counts

2 → 84

Calls

2 calls:

40.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
7.0ms	(*.f64 y (-.f64 z t))

rewrite21.0ms (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:

10.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
6.0ms	(*.f64 y (-.f64 z t))

simplify124.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

784×	`cancel-sign-sub-inv_binary64`
329×	`fma-neg_binary64`
245×	`sub-neg_binary64`
232×	`associate-/l*_binary64`
200×	`times-frac_binary64`

Counts

165 → 150

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	264	2954
1	628	2771
2	2830	2693
3	4707	2690
4	4973	2690
5	4932	2690

prune134.0ms (1.8%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	148	2	150
Fresh	3	0	3
Picked	1	0	1
Done	0	3	3
Total	152	5	157

Error

Counts

157 → 5

Alt Table

Status	Error	Program
✓	2.4b	(+.f64 x (*.f64 (/.f64 y (-.f64 a t)) (-.f64 z t)))
✓	6.8b	(+.f64 x (.f64 (/.f64 1 (.f64 (cbrt.f64 (-.f64 a t)) (cbrt.f64 (-.f64 a t)))) (*.f64 (/.f64 y (cbrt.f64 (-.f64 a t))) (-.f64 z t))))
✓	1.6b	(fma.f64 y (/.f64 (-.f64 z t) (-.f64 a t)) x)
	1.2b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
	10.2b	(+.f64 x (/.f64 1 (/.f64 (-.f64 a t) (*.f64 y (-.f64 z t)))))

Compiler

Compiled 3611 to 1109 computations (69.3% saved)

regimes1.0s (13.6%)

Accuracy

Total 0.7b remaining (98.5%)

Threshold costs 0.7b (98.5%)

Counts

101 → 3

Compiler

Compiled 15430 to 8731 computations (43.4% saved)

bsearch3.0ms (0%)

Compiler: Compiled 14 to 9 computations (35.7% saved)

simplify5.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	27	95
1	42	93
2	52	93
3	60	93
4	65	93
5	68	93
6	69	93
7	69	93

end77.0ms (1%)

Compiler: Compiled 230 to 104 computations (54.8% saved)

Details

analyze1.9s (25.3%)

sample1.5s (20.4%)

simplify119.0ms (1.6%)

prune4.0ms (0%)

localize7.0ms (0.1%)

series62.0ms (0.8%)

rewrite13.0ms (0.2%)

simplify303.0ms (4.1%)

prune109.0ms (1.5%)

localize9.0ms (0.1%)

series51.0ms (0.7%)

rewrite24.0ms (0.3%)

simplify156.0ms (2.1%)

prune164.0ms (2.2%)

localize14.0ms (0.2%)

series597.0ms (8.1%)

rewrite89.0ms (1.2%)

simplify230.0ms (3.1%)

prune628.0ms (8.5%)

localize8.0ms (0.1%)

series47.0ms (0.6%)

rewrite21.0ms (0.3%)

simplify124.0ms (1.7%)

prune134.0ms (1.8%)

regimes1.0s (13.6%)

bsearch3.0ms (0%)

simplify5.0ms (0.1%)

end77.0ms (1%)

Profiling