Details

analyze911.0ms (15.7%)

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
2.3%	97.4%	0.2%	9
4.7%	95.1%	0.2%	10
12.7%	87.1%	0.2%	11
15.9%	83.9%	0.2%	12
24.9%	74.9%	0.2%	13
33.2%	66.5%	0.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample25.0ms (0.4%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
1.0ms	23×	body	128	invalid

Compiler

Compiled 23 to 26 computations (-13% saved)

simplify123.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (117.0ms)

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: 10.9b

Counts

2 → 1

Compiler

Compiled 22 to 20 computations (9.1% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
0.0b	(*.f64 y (-.f64 z t))
10.4b	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))

rewrite34.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-cube-cbrt_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`associate-/r_binary64` `add-log-exp_binary64` `pow1_binary64` `associate-r*_binary64` `times-frac_binary64`
4×	`associate-*r/_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
3×	`flip3--_binary64` `associate-l_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
2×	`associate-/l/_binary64` `sub-neg_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 → 71

Calls

3 calls:

11.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))
9.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
8.0ms	(*.f64 y (-.f64 z t))

series683.0ms (11.8%)

Counts

3 → 9

Calls

3 calls:

379.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a))
238.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 z a)))
66.0ms	(*.f64 y (-.f64 z t))

simplify57.0ms (1%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (42.0ms)

Iter	Nodes	Cost
0	5668	1097

prune158.0ms (2.7%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	73	7	80
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	7	81

Merged error: 0.0b

Counts

81 → 7

Compiler

Compiled 2926 to 1527 computations (47.8% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
0.0b	(/.f64 (-.f64 z t) (-.f64 z a))
1.7b	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))

rewrite42.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

76×	`add-sqr-sqrt_binary64`
71×	`*-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` `associate-r/_binary64` `div-sub_binary64` `clear-num_binary64` `frac-2neg_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `-commutative_binary64`

Counts

3 → 113

Calls

3 calls:

18.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
10.0ms	(/.f64 (-.f64 z t) (-.f64 z a))
4.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))

series470.0ms (8.1%)

Counts

3 → 9

Calls

3 calls:

243.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 z a))))
159.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 z a)))
67.0ms	(/.f64 (-.f64 z t) (-.f64 z a))

simplify74.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	6358	2068

prune97.0ms (1.7%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	122	0	122
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	122	7	129

Merged error: 0.0b

Counts

129 → 7

Compiler

Compiled 2444 to 600 computations (75.5% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
0.0b	(/.f64 (-.f64 z a) (-.f64 z t))
1.8b	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))

rewrite87.0ms (1.5%)

Algorithm

1×	rewrite-expression-head

Rules

218×	`times-frac_binary64`
197×	`*-un-lft-identity_binary64`
195×	`add-sqr-sqrt_binary64`
91×	`add-cube-cbrt_binary64`
52×	`difference-of-squares_binary64` `distribute-lft-out--_binary64`
36×	`associate-/r*_binary64`
11×	`associate-/r/_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`associate-/l*_binary64`
6×	`flip3--_binary64` `div-inv_binary64` `flip--_binary64`
5×	`add-log-exp_binary64`
4×	`cbrt-undiv_binary64` `div-exp_binary64`
3×	`pow1_binary64`
2×	`associate-/l/_binary64` `clear-num_binary64` `frac-2neg_binary64`
1×	`flip3-+_binary64` `distribute-lft-out_binary64` `div-sub_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

3 → 206

Calls

3 calls:

38.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
15.0ms	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))
10.0ms	(/.f64 (-.f64 z a) (-.f64 z t))

series555.0ms (9.6%)

Counts

3 → 9

Calls

3 calls:

256.0ms	(/.f64 y (/.f64 (-.f64 z a) (-.f64 z t)))
231.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 z a) (-.f64 z t))))
67.0ms	(/.f64 (-.f64 z a) (-.f64 z t))

simplify98.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5121	5192

prune189.0ms (3.3%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	214	1	215
Fresh	3	2	5
Picked	0	1	1
Done	0	1	1
Total	217	5	222

Merged error: 0b

Counts

222 → 5

Compiler

Compiled 4997 to 1073 computations (78.5% saved)

localize13.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (-.f64 z a))
0.5b	(cbrt.f64 (-.f64 z a))
0.5b	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
7.5b	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))

rewrite92.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

97×	`add-sqr-sqrt_binary64`
79×	`*-un-lft-identity_binary64`
65×	`cbrt-prod_binary64`
54×	`associate-r_binary64`
50×	`times-frac_binary64`
35×	`add-cube-cbrt_binary64`
30×	`cbrt-div_binary64`
27×	`add-exp-log_binary64`
23×	`associate-l_binary64`
21×	`distribute-lft-out--_binary64`
19×	`difference-of-squares_binary64`
18×	`add-cbrt-cube_binary64`
15×	`flip3--_binary64` `flip--_binary64`
13×	`pow1_binary64`
10×	`swap-sqr_binary64` `associate-/r/_binary64` `unswap-sqr_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 → 177

Calls

4 calls:

43.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))
15.0ms	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
4.0ms	(cbrt.f64 (-.f64 z a))
4.0ms	(cbrt.f64 (-.f64 z a))

series910.0ms (15.7%)

Counts

4 → 12

Calls

4 calls:

261.0ms	(.f64 (/.f64 y (.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))) (/.f64 (-.f64 z t) (cbrt.f64 (-.f64 z a))))
228.0ms	(*.f64 (cbrt.f64 (-.f64 z a)) (cbrt.f64 (-.f64 z a)))
211.0ms	(cbrt.f64 (-.f64 z a))
210.0ms	(cbrt.f64 (-.f64 z a))

simplify105.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

189 → 189

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4967	3946
1	4967	3946

prune176.0ms (3%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	189	0	189
Fresh	0	2	2
Picked	0	1	1
Done	0	2	2
Total	189	5	194

Merged error: 0b

Counts

194 → 5

Compiler

Compiled 5192 to 1243 computations (76.1% saved)

regimes75.0ms (1.3%)

Compiler: Compiled 355 to 325 computations (8.5% saved)

bsearch27.0ms (0.5%)

Steps

Iters	Range		Point
7	7.407852436638179e-37	1.8689691769614195e-35	1.63191112146173e-35
4	-1.0241820647375369e+18	-5.345805779970715e+17	-5.4288497895092806e+17

Compiler

Compiled 1 to 5 computations (-400% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	64	63
1	64	63

end0.0ms (0%)

sample753.0ms (13%)

Algorithm

1×

intervals

Results

317.0ms	7999×	body	128	valid
27.0ms	730×	body	128	invalid
0.0ms	1×	body	1024	valid

Compiler

Compiled 135 to 102 computations (24.4% saved)

Details

analyze911.0ms (15.7%)

sample25.0ms (0.4%)

simplify123.0ms (2.1%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite34.0ms (0.6%)

series683.0ms (11.8%)

simplify57.0ms (1%)

prune158.0ms (2.7%)

localize10.0ms (0.2%)

rewrite42.0ms (0.7%)

series470.0ms (8.1%)

simplify74.0ms (1.3%)

prune97.0ms (1.7%)

localize8.0ms (0.1%)

rewrite87.0ms (1.5%)

series555.0ms (9.6%)

simplify98.0ms (1.7%)

prune189.0ms (3.3%)

localize13.0ms (0.2%)

rewrite92.0ms (1.6%)

series910.0ms (15.7%)

simplify105.0ms (1.8%)

prune176.0ms (3%)

regimes75.0ms (1.3%)

bsearch27.0ms (0.5%)

simplify3.0ms (0%)

end0.0ms (0%)

sample753.0ms (13%)

Profiling