Details

analyze1.0s (13.1%)

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
0%	99.8%	0.2%	9
1.8%	98%	0.2%	10
7.7%	92.1%	0.2%	11
10.4%	89.3%	0.2%	12
12.2%	87.5%	0.2%	13
21.9%	77.7%	0.4%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample29.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	213×	body	128	valid
2.0ms	15×	body	1024	valid
2.0ms	41×	body	128	invalid
1.0ms	13×	body	512	valid
1.0ms	15×	body	256	valid

Compiler

Compiled 27 to 28 computations (-3.7% saved)

simplify161.0ms (2%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (68.0ms)

Iter	Nodes	Cost
0	4973	19
1	4973	19

prune2.0ms (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

14.9b

Counts

2 → 1

Compiler

Compiled 26 to 22 computations (15.4% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 t x) (-.f64 a z))
3.4b	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
4.8b	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))

rewrite46.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

78×	`add-sqr-sqrt_binary64_3510`
73×	`*-un-lft-identity_binary64_3488`
51×	`times-frac_binary64_3494`
31×	`associate-r_binary64_3428`
27×	`add-cube-cbrt_binary64_3523`
23×	`difference-of-squares_binary64_3457` `distribute-lft-out--_binary64_3440`
10×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526`
5×	`associate-/r_binary64_3432` `flip3--_binary64_3492` `associate-/l_binary64_3433` `associate-l_binary64_3429` `add-log-exp_binary64_3527` `flip--_binary64_3463` `pow1_binary64_3549`
4×	`associate-/r/_binary64_3434`
2×	`associate-*l/_binary64_3431` `unswap-sqr_binary64_3456` `associate-/l/_binary64_3435` `cbrt-unprod_binary64_3521` `frac-times_binary64_3498` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522` `div-inv_binary64_3485` `prod-exp_binary64_3537`
1×	`clear-num_binary64_3487` `flip-+_binary64_3462` `flip3-+_binary64_3491` `+-commutative_binary64_3418` `associate-r/_binary64_3430` `pow-prod-down_binary64_3559` `frac-2neg_binary64_3499` `-commutative_binary64_3419` `sum-log_binary64_3579` `div-sub_binary64_3493`

Counts

3 → 119

Calls

3 calls:

23.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
8.0ms	(/.f64 (-.f64 t x) (-.f64 a z))
4.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))

series438.0ms (5.5%)

Counts

3 → 9

Calls

3 calls:

221.0ms	(+.f64 x (*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z))))
163.0ms	(*.f64 (-.f64 y z) (/.f64 (-.f64 t x) (-.f64 a z)))
54.0ms	(/.f64 (-.f64 t x) (-.f64 a z))

simplify70.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

128 → 128

Iterations

Useful iterations: 0 (44.0ms)

Iter	Nodes	Cost
0	5823	2420

prune140.0ms (1.8%)

Pruning

17 alts after pruning (16 fresh and 1 done)

	Pruned	Kept	Total
New	112	16	128
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	112	17	129

Error

4.3b

Counts

129 → 17

Compiler

Compiled 3019 to 700 computations (76.8% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a z))
0.5b	(cbrt.f64 (-.f64 a z))
0.5b	(cbrt.f64 (-.f64 a z))
9.1b	(+.f64 x (.f64 (.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))

rewrite23.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`cbrt-prod_binary64_3519`
13×	`add-sqr-sqrt_binary64_3510` `*-un-lft-identity_binary64_3488`
7×	`add-cube-cbrt_binary64_3523`
6×	`add-log-exp_binary64_3527` `cbrt-div_binary64_3520`
4×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `pow1_binary64_3549`
3×	`difference-of-squares_binary64_3457` `distribute-lft-out--_binary64_3440` `flip3--_binary64_3492` `flip--_binary64_3463` `pow1/3_binary64_3570`
1×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `+-commutative_binary64_3418` `sum-log_binary64_3579`

Counts

4 → 56

Calls

4 calls:

5.0ms	(cbrt.f64 (-.f64 a z))
5.0ms	(+.f64 x (.f64 (.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))
3.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))

series562.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

247.0ms	(+.f64 x (.f64 (.f64 (-.f64 y z) (/.f64 (.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 t x))) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z))))) (/.f64 (cbrt.f64 (-.f64 t x)) (cbrt.f64 (-.f64 a z)))))
109.0ms	(cbrt.f64 (-.f64 a z))
106.0ms	(cbrt.f64 (-.f64 a z))
101.0ms	(cbrt.f64 (-.f64 a z))

simplify59.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5681	1067

prune84.0ms (1.1%)

Pruning

17 alts after pruning (15 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	15	15
Picked	0	1	1
Done	0	1	1
Total	68	17	85

Error

4.3b

Counts

85 → 17

Compiler

Compiled 2932 to 652 computations (77.8% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 a z))
0.5b	(cbrt.f64 (-.f64 a z))
1.7b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
8.3b	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))

rewrite68.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64_3510`
59×	`*-un-lft-identity_binary64_3488`
52×	`times-frac_binary64_3494`
46×	`associate-r_binary64_3428`
37×	`cbrt-prod_binary64_3519`
27×	`add-cube-cbrt_binary64_3523`
25×	`add-exp-log_binary64_3526`
18×	`add-cbrt-cube_binary64_3524` `cbrt-div_binary64_3520`
17×	`associate-l_binary64_3429`
16×	`difference-of-squares_binary64_3457` `distribute-lft-out--_binary64_3440`
10×	`associate-/r/_binary64_3434`
9×	`flip3--_binary64_3492` `flip--_binary64_3463`
8×	`cbrt-unprod_binary64_3521` `prod-exp_binary64_3537`
7×	`div-exp_binary64_3539` `cbrt-undiv_binary64_3522`
6×	`unswap-sqr_binary64_3456` `add-log-exp_binary64_3527` `pow1_binary64_3549`
5×	`frac-times_binary64_3498`
3×	`associate-l/_binary64_3431` `associate-r/_binary64_3430`
2×	`pow1/3_binary64_3570` `div-inv_binary64_3485`
1×	`flip-+_binary64_3462` `flip3-+_binary64_3491` `+-commutative_binary64_3418` `pow-prod-down_binary64_3559` `*-commutative_binary64_3419` `sum-log_binary64_3579`

Counts

4 → 134

Calls

4 calls:

41.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
4.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
3.0ms	(cbrt.f64 (-.f64 a z))
3.0ms	(cbrt.f64 (-.f64 a z))

series797.0ms (10.1%)

Counts

4 → 12

Calls

4 calls:

334.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z))))
232.0ms	(+.f64 x (.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 (-.f64 t x) (cbrt.f64 (-.f64 a z)))))
119.0ms	(cbrt.f64 (-.f64 a z))
112.0ms	(cbrt.f64 (-.f64 a z))

simplify68.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

146 → 146

Iterations

Useful iterations: 0 (32.0ms)

Iter	Nodes	Cost
0	5605	3915

prune152.0ms (1.9%)

Pruning

16 alts after pruning (14 fresh and 2 done)

	Pruned	Kept	Total
New	142	4	146
Fresh	4	10	14
Picked	0	1	1
Done	1	1	2
Total	147	16	163

Error

4.3b

Counts

163 → 16

Compiler

Compiled 4758 to 924 computations (80.6% saved)

localize10.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 (-.f64 a z) (-.f64 t x))
3.9b	(+.f64 x (pow.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) 1))
5.0b	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))

rewrite131.0ms (1.7%)

Algorithm

1×	rewrite-expression-head

Rules

330×	`times-frac_binary64_3494`
323×	`*-un-lft-identity_binary64_3488`
321×	`add-sqr-sqrt_binary64_3510`
113×	`add-cube-cbrt_binary64_3523`
104×	`difference-of-squares_binary64_3457` `distribute-lft-out--_binary64_3440`
36×	`associate-/r*_binary64_3432`
15×	`associate-/r/_binary64_3434`
10×	`add-cbrt-cube_binary64_3524` `add-exp-log_binary64_3526` `associate-/l*_binary64_3433`
9×	`flip3--_binary64_3492` `flip--_binary64_3463`
8×	`div-inv_binary64_3485`
5×	`add-log-exp_binary64_3527`
4×	`associate-/l/_binary64_3435` `div-exp_binary64_3539` `cbrt-undiv_binary64_3522`
3×	`pow1_binary64_3549`
2×	`clear-num_binary64_3487` `frac-2neg_binary64_3499` `div-sub_binary64_3493`
1×	`distribute-lft-out_binary64_3439` `flip-+_binary64_3462` `flip3-+_binary64_3491` `+-commutative_binary64_3418` `sum-log_binary64_3579`

Counts

3 → 273

Calls

3 calls:

64.0ms	(+.f64 x (pow.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) 1))
17.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))
9.0ms	(/.f64 (-.f64 a z) (-.f64 t x))

series796.0ms (10.1%)

Counts

3 → 9

Calls

3 calls:

426.0ms	(+.f64 x (pow.f64 (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x))) 1))
317.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) (-.f64 t x)))
53.0ms	(/.f64 (-.f64 a z) (-.f64 t x))

simplify120.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

282 → 282

Iterations

Useful iterations: 0 (48.0ms)

Iter	Nodes	Cost
0	5063	8387

prune223.0ms (2.8%)

Pruning

15 alts after pruning (13 fresh and 2 done)

	Pruned	Kept	Total
New	276	6	282
Fresh	6	7	13
Picked	0	1	1
Done	1	1	2
Total	283	15	298

Error

4.0b

Counts

298 → 15

Compiler

Compiled 7451 to 1507 computations (79.8% saved)

regimes994.0ms (12.6%)

Accuracy

Total 3.4b remaining (50.9%)

Threshold costs 0b (0%)

Compiler

Compiled 9129 to 5989 computations (34.4% saved)

bsearch5.0ms (0.1%)

Compiler: Compiled 13 to 11 computations (15.4% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	81	138
1	81	138

end0.0ms (0%)

sample1.8s (23.4%)

Algorithm

1×

intervals

Results

283.0ms	6732×	body	128	valid
56.0ms	1246×	body	128	invalid
54.0ms	377×	body	1024	valid
51.0ms	474×	body	512	valid
32.0ms	346×	body	256	valid
13.0ms	71×	body	2048	valid

Compiler

Compiled 1604 to 1027 computations (36% saved)

Details

analyze1.0s (13.1%)

sample29.0ms (0.4%)

simplify161.0ms (2%)

prune2.0ms (0%)

localize9.0ms (0.1%)

rewrite46.0ms (0.6%)

series438.0ms (5.5%)

simplify70.0ms (0.9%)

prune140.0ms (1.8%)

localize17.0ms (0.2%)

rewrite23.0ms (0.3%)

series562.0ms (7.1%)

simplify59.0ms (0.7%)

prune84.0ms (1.1%)

localize13.0ms (0.2%)

rewrite68.0ms (0.9%)

series797.0ms (10.1%)

simplify68.0ms (0.9%)

prune152.0ms (1.9%)

localize10.0ms (0.1%)

rewrite131.0ms (1.7%)

series796.0ms (10.1%)

simplify120.0ms (1.5%)

prune223.0ms (2.8%)

regimes994.0ms (12.6%)

bsearch5.0ms (0.1%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.8s (23.4%)

Profiling