Details

analyze970.0ms (17.2%)

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
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
18.4%	81.3%	0.2%	13
29.5%	70.3%	0.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample23.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	80	valid
1.0ms	30×	body	80	invalid

Compiler

Compiled 23 to 26 computations (-13% saved)

simplify193.0ms (3.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (177.0ms)

Iter	Nodes	Cost
0	4974	16
1	4974	16

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

Merged error: 9.9b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(*.f64 (-.f64 y z) t)
0.0b	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
10.3b	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`add-cube-cbrt_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-l*_binary64` `times-frac_binary64`
4×	`associate-*l/_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `insert-posit16` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `prod-exp_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `distribute-lft-out_binary64` `unswap-sqr_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l_binary64` `div-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 66

Calls

3 calls:

14.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
11.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
8.0ms	(*.f64 (-.f64 y z) t)

series425.0ms (7.5%)

Counts

3 → 9

Calls

3 calls:

225.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
137.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
63.0ms	(*.f64 (-.f64 y z) t)

simplify96.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	5883	1056

prune68.0ms (1.2%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	69	6	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	6	76

Merged error: 0.0b

Counts

76 → 6

Compiler

Compiled 1257 to 345 computations (72.6% saved)

localize12.0ms (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	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
3.9b	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))

rewrite69.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

75×	`add-sqr-sqrt_binary64`
57×	`*-un-lft-identity_binary64`
55×	`cbrt-prod_binary64`
38×	`associate-r_binary64`
36×	`times-frac_binary64`
31×	`add-cube-cbrt_binary64`
30×	`cbrt-div_binary64`
27×	`add-exp-log_binary64`
25×	`associate-l_binary64`
18×	`add-cbrt-cube_binary64`
15×	`flip3--_binary64` `flip--_binary64`
13×	`pow1_binary64`
12×	`distribute-lft-out--_binary64`
10×	`swap-sqr_binary64` `associate-/r/_binary64` `unswap-sqr_binary64` `difference-of-squares_binary64`
9×	`cbrt-unprod_binary64` `prod-exp_binary64` `frac-times_binary64`
8×	`pow1/3_binary64`
7×	`cbrt-undiv_binary64` `div-exp_binary64`
5×	`associate-r/_binary64` `associate-l/_binary64`
4×	`add-log-exp_binary64` `insert-posit16`
3×	`pow-prod-down_binary64`
2×	`pow-prod-up_binary64` `div-inv_binary64` `pow-sqr_binary64` `*-commutative_binary64`
1×	`pow-plus_binary64` `pow2_binary64`

Counts

4 → 167

Calls

4 calls:

38.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))
13.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
4.0ms	(cbrt.f64 (-.f64 a z))
4.0ms	(cbrt.f64 (-.f64 a z))

series892.0ms (15.8%)

Counts

4 → 12

Calls

4 calls:

243.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))
224.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
213.0ms	(cbrt.f64 (-.f64 a z))
211.0ms	(cbrt.f64 (-.f64 a z))

simplify137.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

179 → 179

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	5251	3607

prune179.0ms (3.2%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	178	1	179
Fresh	0	5	5
Picked	0	1	1
Done	0	0	0
Total	178	7	185

Merged error: 0b

Counts

185 → 7

Compiler

Compiled 4920 to 1230 computations (75% saved)

localize9.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t)))
0.0b	(/.f64 (-.f64 a z) t)
9.0b	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t))

rewrite68.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

200×	`times-frac_binary64`
173×	`*-un-lft-identity_binary64`
171×	`add-sqr-sqrt_binary64`
87×	`add-cube-cbrt_binary64`
42×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
22×	`associate-/r*_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
8×	`div-inv_binary64`
5×	`add-log-exp_binary64`
4×	`associate-/l/_binary64` `cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64` `div-sub_binary64` `insert-posit16`
2×	`flip3--_binary64` `clear-num_binary64` `frac-2neg_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `associate-+r-_binary64` `distribute-lft-out_binary64` `associate-/r/_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 191

Calls

3 calls:

32.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t)))
16.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t))
7.0ms	(/.f64 (-.f64 a z) t)

series489.0ms (8.7%)

Counts

3 → 9

Calls

3 calls:

223.0ms	(/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t))
218.0ms	(+.f64 x (/.f64 (-.f64 y z) (/.f64 (-.f64 a z) t)))
48.0ms	(/.f64 (-.f64 a z) t)

simplify143.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

200 → 200

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5766	4762

prune147.0ms (2.6%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	198	2	200
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	201	6	207

Merged error: 0b

Counts

207 → 6

Compiler

Compiled 4138 to 692 computations (83.3% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t))
0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
2.0b	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)

rewrite35.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
71×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-l_binary64`
27×	`add-cube-cbrt_binary64`
22×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-/l_binary64`
4×	`associate-/r/_binary64`
3×	`flip3--_binary64` `associate-r_binary64` `insert-posit16` `flip--_binary64`
2×	`associate-/l/_binary64` `cbrt-unprod_binary64` `cbrt-undiv_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `div-inv_binary64` `div-exp_binary64`
1×	`pow-prod-down_binary64` `flip3-+_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `associate-l/_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 116

Calls

3 calls:

15.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
10.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
5.0ms	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t))

series510.0ms (9%)

Counts

3 → 9

Calls

3 calls:

225.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t)
202.0ms	(+.f64 x (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) t))
83.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

simplify173.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (137.0ms)

Iter	Nodes	Cost
0	4863	2138
1	4863	2138

prune88.0ms (1.6%)

Pruning

6 alts after pruning (3 fresh and 3 done)

	Pruned	Kept	Total
New	125	0	125
Fresh	0	3	3
Picked	0	1	1
Done	0	2	2
Total	125	6	131

Merged error: 0b

Counts

131 → 6

Compiler

Compiled 2298 to 500 computations (78.2% saved)

regimes71.0ms (1.3%)

Compiler: Compiled 450 to 380 computations (15.6% saved)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	25	16
1	25	16

end0.0ms (0%)

sample784.0ms (13.9%)

Algorithm

1×

intervals

Results

319.0ms	7998×	body	80	valid
33.0ms	777×	body	80	invalid
0.0ms	2×	body	160	valid

Compiler

Compiled 152 to 111 computations (27% saved)

Details

analyze970.0ms (17.2%)

sample23.0ms (0.4%)

simplify193.0ms (3.4%)

prune2.0ms (0%)

localize9.0ms (0.2%)

rewrite36.0ms (0.6%)

series425.0ms (7.5%)

simplify96.0ms (1.7%)

prune68.0ms (1.2%)

localize12.0ms (0.2%)

rewrite69.0ms (1.2%)

series892.0ms (15.8%)

simplify137.0ms (2.4%)

prune179.0ms (3.2%)

localize9.0ms (0.2%)

rewrite68.0ms (1.2%)

series489.0ms (8.7%)

simplify143.0ms (2.5%)

prune147.0ms (2.6%)

localize10.0ms (0.2%)

rewrite35.0ms (0.6%)

series510.0ms (9%)

simplify173.0ms (3.1%)

prune88.0ms (1.6%)

regimes71.0ms (1.3%)

bsearch0.0ms (0%)

simplify8.0ms (0.1%)

end0.0ms (0%)

sample784.0ms (13.9%)

Profiling