Details

analyze932.0ms (15.9%)

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)

sample29.0ms (0.5%)

Algorithm

1×

intervals

Results

15.0ms	256×	body	128	valid
1.0ms	30×	body	128	invalid

Compiler

Compiled 23 to 26 computations (-13% saved)

simplify122.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (116.0ms)

Iter	Nodes	Cost
0	4955	16
1	4955	16

prune3.0ms (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))

rewrite32.0ms (0.5%)

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` `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 → 63

Calls

3 calls:

10.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
9.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
7.0ms	(*.f64 (-.f64 y z) t)

series459.0ms (7.8%)

Counts

3 → 9

Calls

3 calls:

248.0ms	(+.f64 x (/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z)))
154.0ms	(/.f64 (*.f64 (-.f64 y z) t) (-.f64 a z))
56.0ms	(*.f64 (-.f64 y z) t)

simplify56.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	5866	1014

prune156.0ms (2.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	66	6	72
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	67	6	73

Merged error: 0.0b

Counts

73 → 6

Compiler

Compiled 2883 to 1465 computations (49.2% saved)

localize15.0ms (0.3%)

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))))

rewrite82.0ms (1.4%)

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`
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 → 163

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))

series918.0ms (15.7%)

Counts

4 → 12

Calls

4 calls:

261.0ms	(.f64 (/.f64 (-.f64 y z) (.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))) (/.f64 t (cbrt.f64 (-.f64 a z))))
236.0ms	(*.f64 (cbrt.f64 (-.f64 a z)) (cbrt.f64 (-.f64 a z)))
213.0ms	(cbrt.f64 (-.f64 a z))
207.0ms	(cbrt.f64 (-.f64 a z))

simplify105.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

175 → 175

Iterations

Useful iterations: 0 (66.0ms)

Iter	Nodes	Cost
0	4966	3577
1	4966	3577

prune200.0ms (3.4%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	173	2	175
Fresh	1	4	5
Picked	0	1	1
Done	0	0	0
Total	174	7	181

Merged error: 0b

Counts

181 → 7

Compiler

Compiled 5183 to 1504 computations (71% saved)

localize11.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (pow.f64 (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))) 1))
0.0b	(/.f64 (-.f64 y z) (-.f64 a z))
2.0b	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))

rewrite46.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
73×	`*-un-lft-identity_binary64`
51×	`times-frac_binary64`
31×	`associate-r_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-l_binary64` `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` `distribute-lft-out_binary64` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 114

Calls

3 calls:

18.0ms	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
10.0ms	(/.f64 (-.f64 y z) (-.f64 a z))
5.0ms	(+.f64 x (pow.f64 (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))) 1))

series517.0ms (8.8%)

Counts

3 → 9

Calls

3 calls:

258.0ms	(+.f64 x (pow.f64 (*.f64 t (/.f64 (-.f64 y z) (-.f64 a z))) 1))
172.0ms	(*.f64 t (/.f64 (-.f64 y z) (-.f64 a z)))
86.0ms	(/.f64 (-.f64 y z) (-.f64 a z))

simplify79.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	6245	2072

prune110.0ms (1.9%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	122	1	123
Fresh	1	4	5
Picked	0	1	1
Done	0	1	1
Total	123	7	130

Merged error: 0b

Counts

130 → 7

Compiler

Compiled 2640 to 829 computations (68.6% saved)

localize17.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 t)
0.6b	(cbrt.f64 t)
1.0b	(.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (cbrt.f64 t)))
1.3b	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (cbrt.f64 t))

rewrite53.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

49×	`add-sqr-sqrt_binary64`
39×	`*-un-lft-identity_binary64`
32×	`associate-l_binary64`
30×	`add-exp-log_binary64`
27×	`times-frac_binary64`
19×	`add-cube-cbrt_binary64`
18×	`pow1_binary64` `add-cbrt-cube_binary64`
15×	`cbrt-unprod_binary64` `prod-exp_binary64`
11×	`cbrt-prod_binary64`
10×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
9×	`pow-prod-down_binary64`
7×	`associate-r_binary64`
4×	`add-log-exp_binary64` `unswap-sqr_binary64`
3×	`cbrt-undiv_binary64` `div-exp_binary64`
2×	`pow1/3_binary64` `associate-/r/_binary64` `associate-l/_binary64` `-commutative_binary64`
1×	`flip3--_binary64` `associate-*r/_binary64` `div-inv_binary64` `flip--_binary64`

Counts

4 → 104

Calls

4 calls:

19.0ms	(.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (cbrt.f64 t)))
18.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (cbrt.f64 t))
1.0ms	(cbrt.f64 t)
1.0ms	(cbrt.f64 t)

series789.0ms (13.5%)

Counts

4 → 12

Calls

4 calls:

297.0ms	(*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (cbrt.f64 t))
200.0ms	(.f64 (.f64 (cbrt.f64 t) (cbrt.f64 t)) (*.f64 (/.f64 (-.f64 y z) (-.f64 a z)) (cbrt.f64 t)))
148.0ms	(cbrt.f64 t)
143.0ms	(cbrt.f64 t)

simplify73.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	4991	1604
1	4991	1604

prune103.0ms (1.8%)

Pruning

7 alts after pruning (4 fresh and 3 done)

	Pruned	Kept	Total
New	116	0	116
Fresh	0	4	4
Picked	0	1	1
Done	0	2	2
Total	116	7	123

Merged error: 0b

Counts

123 → 7

Compiler

Compiled 2755 to 771 computations (72% saved)

regimes92.0ms (1.6%)

Compiler: Compiled 505 to 455 computations (9.9% saved)

bsearch39.0ms (0.7%)

Steps

Iters	Range		Point
6	8.377404403182764e-277	4.673275644615207e-276	1.409003184810671e-276
9	-2.1922524971763953e-61	-2.347376533172402e-67	-4.388866292847462e-64

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	41	63
1	41	63

end0.0ms (0%)

sample802.0ms (13.7%)

Algorithm

1×

intervals

Results

319.0ms	8000×	body	128	valid
29.0ms	777×	body	128	invalid

Compiler

Compiled 195 to 137 computations (29.7% saved)

Details

analyze932.0ms (15.9%)

sample29.0ms (0.5%)

simplify122.0ms (2.1%)

prune3.0ms (0%)

localize9.0ms (0.2%)

rewrite32.0ms (0.5%)

series459.0ms (7.8%)

simplify56.0ms (0.9%)

prune156.0ms (2.7%)

localize15.0ms (0.3%)

rewrite82.0ms (1.4%)

series918.0ms (15.7%)

simplify105.0ms (1.8%)

prune200.0ms (3.4%)

localize11.0ms (0.2%)

rewrite46.0ms (0.8%)

series517.0ms (8.8%)

simplify79.0ms (1.4%)

prune110.0ms (1.9%)

localize17.0ms (0.3%)

rewrite53.0ms (0.9%)

series789.0ms (13.5%)

simplify73.0ms (1.2%)

prune103.0ms (1.8%)

regimes92.0ms (1.6%)

bsearch39.0ms (0.7%)

simplify2.0ms (0%)

end0.0ms (0%)

sample802.0ms (13.7%)

Profiling