Details

analyze1.1s (17.5%)

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
24.9%	74.9%	0.2%	13
26.2%	73.6%	0.2%	14

Compiler

Compiled 12 to 11 computations (8.3% saved)

sample22.0ms (0.4%)

Algorithm

1×

intervals

Results

10.0ms	256×	body	128	valid
1.0ms	20×	body	128	invalid

Compiler

Compiled 23 to 26 computations (-13% saved)

simplify153.0ms (2.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (142.0ms)

Iter	Nodes	Cost
0	5714	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: 11.1b

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 a t)))
0.0b	(*.f64 y (-.f64 z t))
11.5b	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))

rewrite34.0ms (0.5%)

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

series516.0ms (8.4%)

Counts

3 → 9

Calls

3 calls:

264.0ms	(+.f64 x (/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t)))
188.0ms	(/.f64 (*.f64 y (-.f64 z t)) (-.f64 a t))
64.0ms	(*.f64 y (-.f64 z t))

simplify54.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

80 → 80

Iterations

Useful iterations: 0 (40.0ms)

Iter	Nodes	Cost
0	5685	1097

prune132.0ms (2.1%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	75	5	80
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	75	6	81

Merged error: 0.0b

Counts

81 → 6

Compiler

Compiled 2488 to 1177 computations (52.7% saved)

localize9.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
0.0b	(/.f64 (-.f64 a t) (-.f64 z t))
2.1b	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))

rewrite86.0ms (1.4%)

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:

35.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
15.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))
10.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

series745.0ms (12.1%)

Counts

3 → 9

Calls

3 calls:

331.0ms	(+.f64 x (/.f64 y (/.f64 (-.f64 a t) (-.f64 z t))))
324.0ms	(/.f64 y (/.f64 (-.f64 a t) (-.f64 z t)))
90.0ms	(/.f64 (-.f64 a t) (-.f64 z t))

simplify94.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

215 → 215

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	5090	5201

prune340.0ms (5.5%)

Pruning

7 alts after pruning (6 fresh and 1 done)

	Pruned	Kept	Total
New	211	4	215
Fresh	2	2	4
Picked	1	0	1
Done	0	1	1
Total	214	7	221

Merged error: 0b

Counts

221 → 7

Compiler

Compiled 7863 to 2885 computations (63.3% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 (-.f64 a t))
0.6b	(cbrt.f64 (-.f64 a t))
0.6b	(cbrt.f64 (-.f64 a t))
0.6b	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))

rewrite38.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

43×	`cbrt-prod_binary64`
37×	`add-sqr-sqrt_binary64`
35×	`*-un-lft-identity_binary64`
18×	`cbrt-div_binary64`
15×	`add-cube-cbrt_binary64`
11×	`pow1_binary64`
10×	`swap-sqr_binary64`
9×	`flip3--_binary64` `pow1/3_binary64` `distribute-lft-out--_binary64` `flip--_binary64`
8×	`associate-r_binary64` `associate-l_binary64`
7×	`difference-of-squares_binary64`
6×	`add-exp-log_binary64`
4×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `unswap-sqr_binary64` `frac-times_binary64`
2×	`pow-prod-down_binary64` `pow-prod-up_binary64` `associate-r/_binary64` `pow-sqr_binary64` `associate-l/_binary64`
1×	`cbrt-unprod_binary64` `pow-plus_binary64` `prod-exp_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 101

Calls

4 calls:

13.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
4.0ms	(cbrt.f64 (-.f64 a t))
4.0ms	(cbrt.f64 (-.f64 a t))
3.0ms	(cbrt.f64 (-.f64 a t))

series887.0ms (14.4%)

Counts

4 → 12

Calls

4 calls:

240.0ms	(*.f64 (cbrt.f64 (-.f64 z t)) (cbrt.f64 (-.f64 z t)))
228.0ms	(cbrt.f64 (-.f64 a t))
216.0ms	(cbrt.f64 (-.f64 a t))
202.0ms	(cbrt.f64 (-.f64 a t))

simplify131.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

113 → 113

Iterations

Useful iterations: 0 (111.0ms)

Iter	Nodes	Cost
0	4825	1656
1	4825	1656

prune128.0ms (2.1%)

Pruning

7 alts after pruning (5 fresh and 2 done)

	Pruned	Kept	Total
New	113	0	113
Fresh	0	5	5
Picked	0	1	1
Done	0	1	1
Total	113	7	120

Merged error: 0b

Counts

120 → 7

Compiler

Compiled 4436 to 905 computations (79.6% saved)

localize8.0ms (0.1%)

Local error

Found 3 expressions with local error:

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

rewrite46.0ms (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:

21.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
9.0ms	(/.f64 (-.f64 z t) (-.f64 a t))
4.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))

series530.0ms (8.6%)

Counts

3 → 9

Calls

3 calls:

264.0ms	(+.f64 x (*.f64 y (/.f64 (-.f64 z t) (-.f64 a t))))
172.0ms	(*.f64 y (/.f64 (-.f64 z t) (-.f64 a t)))
94.0ms	(/.f64 (-.f64 z t) (-.f64 a t))

simplify76.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (53.0ms)

Iter	Nodes	Cost
0	6268	2068

prune123.0ms (2%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	121	1	122
Fresh	1	3	4
Picked	1	0	1
Done	0	2	2
Total	123	6	129

Merged error: 0b

Counts

129 → 6

Compiler

Compiled 2659 to 719 computations (73% saved)

regimes118.0ms (1.9%)

Compiler: Compiled 914 to 639 computations (30.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	30	52
1	30	52

end0.0ms (0%)

sample798.0ms (12.9%)

Algorithm

1×

intervals

Results

330.0ms	7999×	body	128	valid
28.0ms	722×	body	128	invalid
0.0ms	1×	body	512	valid

Compiler

Compiled 172 to 115 computations (33.1% saved)

Details

analyze1.1s (17.5%)

sample22.0ms (0.4%)

simplify153.0ms (2.5%)

prune2.0ms (0%)

localize8.0ms (0.1%)

rewrite34.0ms (0.5%)

series516.0ms (8.4%)

simplify54.0ms (0.9%)

prune132.0ms (2.1%)

localize9.0ms (0.1%)

rewrite86.0ms (1.4%)

series745.0ms (12.1%)

simplify94.0ms (1.5%)

prune340.0ms (5.5%)

localize16.0ms (0.3%)

rewrite38.0ms (0.6%)

series887.0ms (14.4%)

simplify131.0ms (2.1%)

prune128.0ms (2.1%)

localize8.0ms (0.1%)

rewrite46.0ms (0.7%)

series530.0ms (8.6%)

simplify76.0ms (1.2%)

prune123.0ms (2%)

regimes118.0ms (1.9%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample798.0ms (12.9%)

Profiling