Details

analyze1.1s (16.1%)

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
6.2%	93.6%	0.2%	9
6.2%	82.7%	11.1%	10
12.5%	73.7%	13.8%	11
15.6%	59.5%	25%	12
17.9%	53.3%	28.8%	13
22.4%	47.2%	30.4%	14

Compiler

Compiled 18 to 12 computations (33.3% saved)

sample31.0ms (0.5%)

Algorithm

1×

intervals

Results

13.0ms	256×	body	128	valid
4.0ms	92×	body	128	invalid

Compiler

Compiled 39 to 27 computations (30.8% saved)

simplify70.0ms (1%)

Algorithm

1×	egg-herbie

Rules

853×	`fma-neg_binary64`
525×	`fma-def_binary64`
182×	`cancel-sign-sub-inv_binary64`
160×	`associate-l_binary64`
154×	`distribute-rgt-in_binary64`

Counts

1 → 2

Iterations

Useful iterations: 1 (0.0ms)

Iter	Nodes	Cost
0	12	19
1	25	17
2	72	17
3	227	17
4	512	17
5	1044	17
6	1436	17
7	1492	17
8	1573	17
9	1615	17
10	1631	17
11	1631	17
12	1550	17

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

7.6b

Counts

3 → 1

Alt Table

Status	Error	Program
▶	7.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 61 to 35 computations (42.6% saved)

localize8.0ms (0.1%)

Local error

Found 1 expressions with local error:

New	Error	Program
✓	7.1b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

rewrite12.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

5×	`add-cube-cbrt_binary64`
5×	`fma-udef_binary64`
4×	`pow1_binary64`
4×	`add-sqr-sqrt_binary64`
3×	`add-cbrt-cube_binary64`

Counts

1 → 33

Calls

1 calls:

10.0ms

(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

series71.0ms (1.1%)

Counts

1 → 48

Calls

1 calls:

71.0ms

(fma.f64 y (*.f64 4 (-.f64 t (*.f64 z z))) (*.f64 x x))

simplify91.0ms (1.4%)

Algorithm

1×	egg-herbie

Rules

850×	`fma-neg_binary64`
574×	`cancel-sign-sub-inv_binary64`
369×	`associate-l_binary64`
361×	`exp-prod_binary64`
328×	`associate-r_binary64`

Counts

81 → 144

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	61	1549
1	185	1283
2	527	1271
3	2244	1271
4	4110	1271
5	4969	1271

prune39.0ms (0.6%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	140	4	144
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	140	5	145

Error

6.8b

Counts

145 → 5

Alt Table

Status	Error	Program
	39.5b	(.f64 4 (.f64 y t))
	27.5b	(pow.f64 (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 2)
▶	19.6b	(fma.f64 x x (.f64 4 (.f64 y t)))
✓	7.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
	41.7b	(pow.f64 x 2)

Compiler

Compiled 1207 to 479 computations (60.3% saved)

localize6.0ms (0.1%)

Local error

Found 2 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 4 (.f64 y t)))
✓	0.0b	(.f64 4 (.f64 y t))

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`pow1_binary64`
12×	`add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64`
10×	`pow-prod-down_binary64`
9×	`add-cube-cbrt_binary64`

Counts

2 → 69

Calls

2 calls:

14.0ms	(.f64 4 (.f64 y t))
9.0ms	(fma.f64 x x (.f64 4 (.f64 y t)))

series55.0ms (0.8%)

Counts

2 → 36

Calls

2 calls:

34.0ms	(fma.f64 x x (.f64 4 (.f64 y t)))
21.0ms	(.f64 4 (.f64 y t))

simplify81.0ms (1.2%)

Algorithm

1×	egg-herbie

Rules

992×	`fma-neg_binary64`
554×	`associate-l_binary64`
457×	`associate-r_binary64`
348×	`cancel-sign-sub-inv_binary64`
332×	`distribute-rgt-neg-in_binary64`

Counts

105 → 165

Iterations

Useful iterations: 2 (0.0ms)

Iter	Nodes	Cost
0	77	1010
1	185	959
2	547	955
3	2151	955
4	4124	955
5	5021	955

prune67.0ms (1%)

Pruning

11 alts after pruning (10 fresh and 1 done)

	Pruned	Kept	Total
New	158	7	165
Fresh	0	3	3
Picked	1	0	1
Done	0	1	1
Total	159	11	170

Error

6.8b

Counts

170 → 11

Alt Table

Status	Error	Program
	41.7b	(pow.f64 x 2)
	40.8b	(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 4 (.f64 y t)) (.f64 4 (.f64 y t)))) (-.f64 (.f64 x x) (.f64 4 (*.f64 y t))))
	39.5b	(.f64 4 (.f64 y t))
	45.7b	(sqrt.f64 (.f64 (fma.f64 x x (.f64 4 (.f64 y t))) (fma.f64 x x (.f64 4 (*.f64 y t)))))
	46.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 x x (.f64 4 (.f64 y t))) (fma.f64 x x (.f64 4 (.f64 y t)))) (fma.f64 x x (.f64 4 (.f64 y t)))))
	27.5b	(pow.f64 (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 2)
	35.5b	(exp.f64 (log.f64 (fma.f64 4 (.f64 y t) (.f64 x x))))
	52.5b	(pow.f64 (.f64 (.f64 (fma.f64 x x (.f64 4 (.f64 y t))) (fma.f64 x x (.f64 4 (.f64 y t)))) (fma.f64 x x (.f64 4 (.f64 y t)))) 1/3)
	20.4b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t)))) 3)
✓	7.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))
▶	20.1b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t))))

Compiler

Compiled 1581 to 828 computations (47.6% saved)

localize9.0ms (0.1%)

Local error

Found 4 expressions with local error:

New	Error	Program
✓	0.0b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t))))
✓	0.2b	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t)))
✓	0.3b	(.f64 (cbrt.f64 4) (.f64 y t))
✓	1.0b	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

rewrite64.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-exp-log_binary64`
23×	`add-sqr-sqrt_binary64`
19×	`add-cube-cbrt_binary64`
18×	`pow1/3_binary64`
16×	`pow1_binary64`

Counts

4 → 145

Calls

4 calls:

21.0ms	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t)))
14.0ms	(.f64 (cbrt.f64 4) (.f64 y t))
13.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
10.0ms	(fma.f64 x x (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t))))

series194.0ms (2.9%)

Counts

4 → 60

Calls

4 calls:

79.0ms	(fma.f64 x x (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t))))
72.0ms	(.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t)))
43.0ms	(.f64 (cbrt.f64 4) (.f64 y t))
0.0ms	(*.f64 (cbrt.f64 4) (cbrt.f64 4))

simplify168.0ms (2.5%)

Algorithm

1×	egg-herbie

Rules

561×	`unswap-sqr_binary64`
549×	`fma-neg_binary64`
457×	`*-commutative_binary64`
401×	`log-prod_binary64`
367×	`exp-prod_binary64`

Counts

205 → 340

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	129	1821
1	294	1613
2	1114	1605
3	3273	1594
4	4376	1594
5	4869	1594
6	4992	1594
7	4920	1594

prune138.0ms (2.1%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	337	3	340
Fresh	1	8	9
Picked	1	0	1
Done	0	1	1
Total	339	12	351

Error

6.8b

Counts

351 → 12

Alt Table

Status	Error	Program
▶	20.1b	(fma.f64 x x (pow.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t)))) 3))
	46.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 x x (.f64 4 (.f64 y t))) (fma.f64 x x (.f64 4 (.f64 y t)))) (fma.f64 x x (.f64 4 (.f64 y t)))))
	41.7b	(pow.f64 x 2)
	40.8b	(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 4 (.f64 y t)) (.f64 4 (.f64 y t)))) (-.f64 (.f64 x x) (.f64 4 (*.f64 y t))))
	39.5b	(.f64 4 (.f64 y t))
	27.5b	(pow.f64 (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 2)
	35.5b	(exp.f64 (log.f64 (fma.f64 4 (.f64 y t) (.f64 x x))))
	36.6b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (sqrt.f64 (pow.f64 (.f64 (cbrt.f64 4) (.f64 y t)) 2))))
	52.5b	(pow.f64 (.f64 (.f64 (fma.f64 x x (.f64 4 (.f64 y t))) (fma.f64 x x (.f64 4 (.f64 y t)))) (fma.f64 x x (.f64 4 (.f64 y t)))) 1/3)
	20.4b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t)))) 3)
	39.9b	(.f64 (pow.f64 (cbrt.f64 4) 3) (.f64 y t))
✓	7.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 3794 to 2580 computations (32% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

New	Error	Program
	0.3b	(.f64 (cbrt.f64 4) (.f64 y t))
✓	0.6b	(pow.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t)))) 3)
	1.0b	(*.f64 (cbrt.f64 4) (cbrt.f64 4))
✓	10.1b	(cbrt.f64 (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t))))

rewrite31.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

11×	`add-cube-cbrt_binary64`
8×	`add-sqr-sqrt_binary64`
7×	`pow1/3_binary64`
6×	`log1p-expm1-u_binary64`
6×	`expm1-log1p-u_binary64`

Counts

2 → 76

Calls

2 calls:

15.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t)))) 3)
12.0ms	(cbrt.f64 (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t))))

series1.2s (17.7%)

Counts

2 → 48

Calls

2 calls:

634.0ms	(pow.f64 (cbrt.f64 (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t)))) 3)
551.0ms	(cbrt.f64 (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (.f64 (cbrt.f64 4) (.f64 y t))))

simplify114.0ms (1.7%)

Algorithm

1×	egg-herbie

Rules

729×	`associate-l_binary64`
666×	`associate-r_binary64`
577×	`fma-def_binary64`
381×	`log-prod_binary64`
278×	`exp-prod_binary64`

Counts

124 → 214

Iterations

Useful iterations: 3 (0.0ms)

Iter	Nodes	Cost
0	109	1676
1	243	1587
2	599	1467
3	3024	1105
4	4649	1105
5	5111	1105

prune189.0ms (2.8%)

Pruning

14 alts after pruning (13 fresh and 1 done)

	Pruned	Kept	Total
New	326	3	329
Fresh	0	10	10
Picked	1	0	1
Done	0	1	1
Total	327	14	341

Error

6.8b

Counts

341 → 14

Alt Table

Status	Error	Program
	36.6b	(fma.f64 x x (sqrt.f64 (pow.f64 (cbrt.f64 (.f64 4 (.f64 y t))) 6)))
	20.4b	(pow.f64 (cbrt.f64 (fma.f64 x x (.f64 4 (.f64 y t)))) 3)
	41.7b	(pow.f64 x 2)
	40.8b	(/.f64 (-.f64 (.f64 (.f64 x x) (.f64 x x)) (.f64 (.f64 4 (.f64 y t)) (.f64 4 (.f64 y t)))) (-.f64 (.f64 x x) (.f64 4 (*.f64 y t))))
	39.5b	(.f64 4 (.f64 y t))
	46.9b	(cbrt.f64 (.f64 (.f64 (fma.f64 x x (.f64 4 (.f64 y t))) (fma.f64 x x (.f64 4 (.f64 y t)))) (fma.f64 x x (.f64 4 (.f64 y t)))))
	27.5b	(pow.f64 (sqrt.f64 (fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))) 2)
	35.5b	(exp.f64 (log.f64 (fma.f64 4 (.f64 y t) (.f64 x x))))
	36.6b	(fma.f64 x x (.f64 (.f64 (cbrt.f64 4) (cbrt.f64 4)) (sqrt.f64 (pow.f64 (.f64 (cbrt.f64 4) (.f64 y t)) 2))))
	52.5b	(pow.f64 (.f64 (.f64 (fma.f64 x x (.f64 4 (.f64 y t))) (fma.f64 x x (.f64 4 (.f64 y t)))) (fma.f64 x x (.f64 4 (.f64 y t)))) 1/3)
	33.1b	(fma.f64 x x (pow.f64 (sqrt.f64 (pow.f64 (cbrt.f64 (cbrt.f64 (.f64 4 (.f64 y t)))) 6)) 3))
	39.9b	(.f64 (pow.f64 (cbrt.f64 4) 3) (.f64 y t))
	50.9b	(fma.f64 x x (pow.f64 (.f64 (cbrt.f64 4) (.f64 (cbrt.f64 -1) (exp.f64 (*.f64 1/3 (-.f64 (log.f64 y) (log.f64 (/.f64 -1 t))))))) 3))
✓	7.6b	(fma.f64 y (.f64 4 (-.f64 t (.f64 z z))) (*.f64 x x))

Compiler

Compiled 4070 to 3004 computations (26.2% saved)

regimes983.0ms (14.7%)

Accuracy

Total 0.8b remaining (13.9%)

Threshold costs 0.8b (13.9%)

Compiler

Compiled 10320 to 7199 computations (30.2% saved)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Rules

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

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	11	17
1	17	17
2	24	17
3	28	17
4	30	17
5	30	17

end1.0ms (0%)

Compiler: Compiled 16 to 10 computations (37.5% saved)

sample2.0s (29.2%)

Algorithm

1×

intervals

Results

715.0ms	8000×	body	128	valid
272.0ms	2944×	body	128	invalid

Compiler

Compiled 308 to 211 computations (31.5% saved)

Details

analyze1.1s (16.1%)

sample31.0ms (0.5%)

simplify70.0ms (1%)

prune3.0ms (0%)

localize8.0ms (0.1%)

rewrite12.0ms (0.2%)

series71.0ms (1.1%)

simplify91.0ms (1.4%)

prune39.0ms (0.6%)

localize6.0ms (0.1%)

rewrite26.0ms (0.4%)

series55.0ms (0.8%)

simplify81.0ms (1.2%)

prune67.0ms (1%)

localize9.0ms (0.1%)

rewrite64.0ms (1%)

series194.0ms (2.9%)

simplify168.0ms (2.5%)

prune138.0ms (2.1%)

localize13.0ms (0.2%)

rewrite31.0ms (0.5%)

series1.2s (17.7%)

simplify114.0ms (1.7%)

prune189.0ms (2.8%)

regimes983.0ms (14.7%)

simplify8.0ms (0.1%)

end1.0ms (0%)

sample2.0s (29.2%)

Profiling