Details

analyze379.0ms (11.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
0%	99.9%	0.1%	6
25%	74.9%	0.1%	7
31.2%	68.6%	0.1%	8
35.9%	64%	0.1%	9
47.6%	49.9%	2.5%	10
49.1%	46.8%	4%	11
51.1%	44.1%	4.8%	12
60.2%	29.9%	9.9%	13
60.6%	27.9%	11.6%	14

Compiler

Compiled 12 to 10 computations (16.7% saved)

sample20.0ms (0.6%)

Algorithm

1×

intervals

Results

9.0ms	256×	body	128	valid
2.0ms	52×	body	128	invalid

Compiler

Compiled 23 to 22 computations (4.3% saved)

simplify186.0ms (5.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (89.0ms)

Iter	Nodes	Cost
0	5346	16

prune2.0ms (0.1%)

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

10.9b

Counts

2 → 1

Compiler

Compiled 22 to 18 computations (18.2% saved)

localize7.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.1b	(.f64 (.f64 z z) (+.f64 z 1))
10.5b	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))

rewrite22.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

28×	`add-cbrt-cube_binary64_9321` `add-exp-log_binary64_9323`
12×	`cbrt-unprod_binary64_9318` `prod-exp_binary64_9334`
7×	`pow1_binary64_9346`
6×	`div-exp_binary64_9336` `cbrt-undiv_binary64_9319`
5×	`*-un-lft-identity_binary64_9285`
4×	`add-sqr-sqrt_binary64_9307` `associate-r_binary64_9225` `associate-*r/_binary64_9227`
3×	`pow-prod-down_binary64_9356` `add-cube-cbrt_binary64_9320`
2×	`flip-+_binary64_9259` `add-log-exp_binary64_9324` `associate-/r/_binary64_9231` `flip3-+_binary64_9288`
1×	`clear-num_binary64_9284` `distribute-lft-in_binary64_9234` `distribute-rgt-in_binary64_9235` `unswap-sqr_binary64_9253` `associate-l_binary64_9226` `times-frac_binary64_9291` `frac-2neg_binary64_9296` `-commutative_binary64_9216` `associate-/l_binary64_9230` `distribute-lft-out_binary64_9236` `associate-/r*_binary64_9229` `div-inv_binary64_9282`

Counts

2 → 51

Calls

2 calls:

10.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
8.0ms	(.f64 (.f64 z z) (+.f64 z 1))

series93.0ms (2.7%)

Counts

2 → 6

Calls

2 calls:

59.0ms	(/.f64 (.f64 x y) (.f64 (*.f64 z z) (+.f64 z 1)))
34.0ms	(.f64 (.f64 z z) (+.f64 z 1))

simplify76.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

57 → 57

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4973	858
1	4973	858

prune58.0ms (1.7%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	51	6	57
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	52	6	58

Error

1.6b

Counts

58 → 6

Compiler

Compiled 911 to 451 computations (50.5% saved)

localize7.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (+.f64 z 1))
4.0b	(.f64 (/.f64 x (.f64 z z)) (/.f64 y (+.f64 z 1)))
8.8b	(/.f64 x (*.f64 z z))

rewrite31.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`*-un-lft-identity_binary64_9285`
34×	`add-sqr-sqrt_binary64_9307` `times-frac_binary64_9291`
31×	`add-cbrt-cube_binary64_9321` `add-exp-log_binary64_9323`
24×	`add-cube-cbrt_binary64_9320`
18×	`associate-r_binary64_9225`
10×	`div-exp_binary64_9336` `cbrt-undiv_binary64_9319`
9×	`cbrt-unprod_binary64_9318` `prod-exp_binary64_9334`
7×	`associate-l_binary64_9226` `distribute-lft-out_binary64_9236`
6×	`associate-/l*_binary64_9230`
5×	`pow1_binary64_9346` `associate-/r*_binary64_9229`
4×	`unswap-sqr_binary64_9253` `associate-/r/_binary64_9231` `div-inv_binary64_9282`
3×	`add-log-exp_binary64_9324`
2×	`clear-num_binary64_9284` `flip-+_binary64_9259` `frac-2neg_binary64_9296` `flip3-+_binary64_9288`
1×	`associate-l/_binary64_9228` `frac-times_binary64_9295` `pow-prod-down_binary64_9356` `associate-r/_binary64_9227` `*-commutative_binary64_9216`

Counts

3 → 107

Calls

3 calls:

14.0ms	(.f64 (/.f64 x (.f64 z z)) (/.f64 y (+.f64 z 1)))
5.0ms	(/.f64 y (+.f64 z 1))
4.0ms	(/.f64 x (*.f64 z z))

series101.0ms (3%)

Counts

3 → 9

Calls

3 calls:

54.0ms	(.f64 (/.f64 x (.f64 z z)) (/.f64 y (+.f64 z 1)))
28.0ms	(/.f64 y (+.f64 z 1))
19.0ms	(/.f64 x (*.f64 z z))

simplify72.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

116 → 116

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4962	1772
1	4962	1772

prune104.0ms (3.1%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	109	7	116
Fresh	1	4	5
Picked	1	0	1
Done	0	0	0
Total	111	11	122

Error

Counts

122 → 11

Compiler

Compiled 2055 to 973 computations (52.7% saved)

localize8.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 y (+.f64 z 1))
0.8b	(.f64 (/.f64 1 z) (.f64 (/.f64 x z) (/.f64 y (+.f64 z 1))))
3.1b	(*.f64 (/.f64 x z) (/.f64 y (+.f64 z 1)))

rewrite49.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

94×	`add-exp-log_binary64_9323`
58×	`add-cbrt-cube_binary64_9321`
48×	`*-un-lft-identity_binary64_9285`
46×	`add-sqr-sqrt_binary64_9307` `times-frac_binary64_9291`
40×	`prod-exp_binary64_9334`
34×	`add-cube-cbrt_binary64_9320`
31×	`div-exp_binary64_9336`
26×	`associate-l_binary64_9226`
22×	`cbrt-unprod_binary64_9318`
19×	`associate-r_binary64_9225`
18×	`cbrt-undiv_binary64_9319`
10×	`pow1_binary64_9346`
7×	`distribute-lft-out_binary64_9236`
6×	`frac-times_binary64_9295` `associate-*r/_binary64_9227`
5×	`rec-exp_binary64_9335` `1-exp_binary64_9329`
4×	`associate-l/_binary64_9228` `pow-prod-down_binary64_9356` `unswap-sqr_binary64_9253` `associate-/r/_binary64_9231` `associate-/r_binary64_9229` `div-inv_binary64_9282`
3×	`add-log-exp_binary64_9324` `associate-/l*_binary64_9230`
2×	`flip-+_binary64_9259` `*-commutative_binary64_9216` `flip3-+_binary64_9288`
1×	`clear-num_binary64_9284` `frac-2neg_binary64_9296`

Counts

3 → 149

Calls

3 calls:

14.0ms	(.f64 (/.f64 1 z) (.f64 (/.f64 x z) (/.f64 y (+.f64 z 1))))
14.0ms	(*.f64 (/.f64 x z) (/.f64 y (+.f64 z 1)))
5.0ms	(/.f64 y (+.f64 z 1))

series109.0ms (3.2%)

Counts

3 → 9

Calls

3 calls:

44.0ms	(*.f64 (/.f64 x z) (/.f64 y (+.f64 z 1)))
39.0ms	(.f64 (/.f64 1 z) (.f64 (/.f64 x z) (/.f64 y (+.f64 z 1))))
25.0ms	(/.f64 y (+.f64 z 1))

simplify73.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

158 → 158

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5041	2588

prune136.0ms (4%)

Pruning

10 alts after pruning (9 fresh and 1 done)

	Pruned	Kept	Total
New	155	3	158
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	159	10	169

Error

Counts

169 → 10

Compiler

Compiled 2911 to 1346 computations (53.8% saved)

localize9.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(/.f64 y (+.f64 z 1))
0.8b	(.f64 (/.f64 1 z) (/.f64 (.f64 x (/.f64 y (+.f64 z 1))) z))
3.1b	(/.f64 (*.f64 x (/.f64 y (+.f64 z 1))) z)
3.3b	(*.f64 x (/.f64 y (+.f64 z 1)))

rewrite54.0ms (1.6%)

Algorithm

1×	rewrite-expression-head

Rules

80×	`add-exp-log_binary64_9323`
52×	`add-cbrt-cube_binary64_9321`
48×	`*-un-lft-identity_binary64_9285`
45×	`add-sqr-sqrt_binary64_9307`
42×	`times-frac_binary64_9291`
33×	`add-cube-cbrt_binary64_9320`
30×	`div-exp_binary64_9336`
28×	`prod-exp_binary64_9334`
25×	`associate-r_binary64_9225`
18×	`cbrt-undiv_binary64_9319`
16×	`cbrt-unprod_binary64_9318` `associate-l_binary64_9226`
8×	`pow1_binary64_9346`
7×	`distribute-lft-out_binary64_9236` `associate-/r*_binary64_9229`
5×	`unswap-sqr_binary64_9253` `div-inv_binary64_9282`
4×	`rec-exp_binary64_9335` `add-log-exp_binary64_9324` `associate-/l*_binary64_9230` `associate-/r/_binary64_9231` `1-exp_binary64_9329`
3×	`associate-*r/_binary64_9227`
2×	`clear-num_binary64_9284` `pow-prod-down_binary64_9356` `flip-+_binary64_9259` `frac-2neg_binary64_9296` `*-commutative_binary64_9216` `flip3-+_binary64_9288`
1×	`associate-/l/_binary64_9232` `associate-*l/_binary64_9228` `frac-times_binary64_9295`

Counts

4 → 153

Calls

4 calls:

15.0ms	(.f64 (/.f64 1 z) (/.f64 (.f64 x (/.f64 y (+.f64 z 1))) z))
11.0ms	(*.f64 x (/.f64 y (+.f64 z 1)))
8.0ms	(/.f64 (*.f64 x (/.f64 y (+.f64 z 1))) z)
5.0ms	(/.f64 y (+.f64 z 1))

series158.0ms (4.6%)

Counts

4 → 12

Calls

4 calls:

52.0ms	(/.f64 (*.f64 x (/.f64 y (+.f64 z 1))) z)
44.0ms	(*.f64 x (/.f64 y (+.f64 z 1)))
38.0ms	(.f64 (/.f64 1 z) (/.f64 (.f64 x (/.f64 y (+.f64 z 1))) z))
23.0ms	(/.f64 y (+.f64 z 1))

simplify106.0ms (3.1%)

Algorithm

1×	egg-herbie

Counts

165 → 165

Iterations

Useful iterations: 0 (75.0ms)

Iter	Nodes	Cost
0	4937	2633
1	4937	2633

prune141.0ms (4.1%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	164	1	165
Fresh	1	7	8
Picked	1	0	1
Done	0	1	1
Total	166	9	175

Error

Counts

175 → 9

Compiler

Compiled 2953 to 1738 computations (41.1% saved)

regimes350.0ms (10.3%)

Accuracy

Total 1.3b remaining (99.6%)

Threshold costs 0b (0%)

Compiler

Compiled 3547 to 2693 computations (24.1% saved)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	17	28
1	17	28

end0.0ms (0%)

sample1.1s (31.1%)

Algorithm

1×

intervals

Results

278.0ms	8000×	body	128	valid
50.0ms	1548×	body	128	invalid

Compiler

Compiled 599 to 450 computations (24.9% saved)

Details

analyze379.0ms (11.1%)

sample20.0ms (0.6%)

simplify186.0ms (5.4%)

prune2.0ms (0.1%)

localize7.0ms (0.2%)

rewrite22.0ms (0.6%)

series93.0ms (2.7%)

simplify76.0ms (2.2%)

prune58.0ms (1.7%)

localize7.0ms (0.2%)

rewrite31.0ms (0.9%)

series101.0ms (3%)

simplify72.0ms (2.1%)

prune104.0ms (3.1%)

localize8.0ms (0.2%)

rewrite49.0ms (1.4%)

series109.0ms (3.2%)

simplify73.0ms (2.1%)

prune136.0ms (4%)

localize9.0ms (0.3%)

rewrite54.0ms (1.6%)

series158.0ms (4.6%)

simplify106.0ms (3.1%)

prune141.0ms (4.1%)

regimes350.0ms (10.3%)

bsearch0.0ms (0%)

simplify2.0ms (0.1%)

end0.0ms (0%)

sample1.1s (31.1%)

Profiling