Details

analyze706.0ms (14.2%)

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
9.4%	90.4%	0.2%	8
9.4%	90.4%	0.2%	9
10.9%	88.9%	0.2%	10
25.9%	73.9%	0.2%	11
47.1%	52.7%	0.2%	12
55.3%	44.5%	0.2%	13
59.2%	40.6%	0.2%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample24.0ms (0.5%)

Algorithm

1×

intervals

Results

14.0ms

256×

body

128

valid

Compiler

Compiled 35 to 33 computations (5.7% saved)

simplify230.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4903	19
1	4903	19

prune9.0ms (0.2%)

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: 1.5b

Counts

2 → 2

Compiler

Compiled 73 to 61 computations (16.4% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
0.0b	(-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)
4.2b	(/.f64 (.f64 y t) (.f64 2 z))
5.3b	(/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))

rewrite49.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`*-un-lft-identity_binary64_14183`
25×	`add-sqr-sqrt_binary64_14205`
18×	`add-cbrt-cube_binary64_14219` `add-exp-log_binary64_14221`
16×	`times-frac_binary64_14189`
15×	`add-cube-cbrt_binary64_14218`
8×	`add-log-exp_binary64_14222`
6×	`associate-/r*_binary64_14127`
5×	`cbrt-undiv_binary64_14217` `difference-of-squares_binary64_14152` `div-exp_binary64_14234` `distribute-lft-out--_binary64_14135`
4×	`prod-exp_binary64_14232` `associate-/l*_binary64_14128` `pow1_binary64_14244` `cbrt-unprod_binary64_14216`
3×	`cancel-sign-sub-inv_binary64_14149`
2×	`clear-num_binary64_14182` `flip--_binary64_14158` `div-inv_binary64_14180` `flip3--_binary64_14187` `frac-2neg_binary64_14194` `associate-/r/_binary64_14129`
1×	`sub-neg_binary64_14176` `distribute-lft-out_binary64_14134` `flip3-+_binary64_14186` `diff-log_binary64_14275` `sum-log_binary64_14274` `flip-+_binary64_14157` `+-commutative_binary64_14113`

Counts

4 → 86

Calls

4 calls:

16.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
11.0ms	(/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
9.0ms	(-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)
7.0ms	(/.f64 (.f64 y t) (.f64 2 z))

series399.0ms (8%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z))
123.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)))
95.0ms	(-.f64 (/.f64 (.f64 y t) (.f64 2 z)) z)
42.0ms	(/.f64 (.f64 y t) (.f64 2 z))

simplify83.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4945	1905
1	4945	1905

prune248.0ms (5%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	92	6	98
Fresh	0	1	1
Picked	1	0	1
Done	0	0	0
Total	93	7	100

Merged error: 0.5b

Counts

100 → 7

Compiler

Compiled 4585 to 3039 computations (33.7% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z)
0.3b	(/.f64 2 (/.f64 t z))
5.3b	(/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z))
7.4b	(/.f64 y (/.f64 2 (/.f64 t z)))

rewrite183.0ms (3.7%)

Algorithm

1×	rewrite-expression-head

Rules

525×	`times-frac_binary64_14189`
315×	`add-sqr-sqrt_binary64_14205`
255×	`*-un-lft-identity_binary64_14183`
245×	`add-cube-cbrt_binary64_14218`
65×	`associate-/r*_binary64_14127`
23×	`div-inv_binary64_14180`
20×	`add-cbrt-cube_binary64_14219` `difference-of-squares_binary64_14152` `add-exp-log_binary64_14221`
10×	`cbrt-undiv_binary64_14217` `div-exp_binary64_14234`
9×	`associate-/l*_binary64_14128`
8×	`associate-/r/_binary64_14129`
6×	`add-log-exp_binary64_14222`
5×	`distribute-lft-out--_binary64_14135`
4×	`pow1_binary64_14244`
3×	`clear-num_binary64_14182` `cancel-sign-sub-inv_binary64_14149` `frac-2neg_binary64_14194`
2×	`flip--_binary64_14158` `flip3--_binary64_14187`
1×	`sub-neg_binary64_14176` `diff-log_binary64_14275`

Counts

4 → 334

Calls

4 calls:

62.0ms	(-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z)
49.0ms	(/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z))
14.0ms	(/.f64 y (/.f64 2 (/.f64 t z)))
7.0ms	(/.f64 2 (/.f64 t z))

series285.0ms (5.7%)

Counts

4 → 12

Calls

4 calls:

118.0ms	(/.f64 y (-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z))
94.0ms	(-.f64 (/.f64 y (/.f64 2 (/.f64 t z))) z)
45.0ms	(/.f64 y (/.f64 2 (/.f64 t z)))
28.0ms	(/.f64 2 (/.f64 t z))

simplify133.0ms (2.7%)

Algorithm

1×	egg-herbie

Counts

346 → 346

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4942	8126
1	4942	8126

prune414.0ms (8.3%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	344	2	346
Fresh	3	3	6
Picked	1	0	1
Done	0	0	0
Total	348	5	353

Merged error: 0.5b

Counts

353 → 5

Compiler

Compiled 8715 to 4169 computations (52.2% saved)

localize12.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 y (-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z)))
0.0b	(-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z)
5.3b	(/.f64 y (-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z))
7.4b	(/.f64 y (*.f64 2 (/.f64 z t)))

rewrite54.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`*-un-lft-identity_binary64_14183`
27×	`add-sqr-sqrt_binary64_14205`
18×	`times-frac_binary64_14189`
17×	`add-cube-cbrt_binary64_14218`
15×	`add-cbrt-cube_binary64_14219` `add-exp-log_binary64_14221`
8×	`add-log-exp_binary64_14222`
6×	`associate-/l_binary64_14128` `associate-/r_binary64_14127`
5×	`cbrt-undiv_binary64_14217` `difference-of-squares_binary64_14152` `div-exp_binary64_14234` `distribute-lft-out--_binary64_14135`
4×	`pow1_binary64_14244`
3×	`cancel-sign-sub-inv_binary64_14149` `associate-/r/_binary64_14129`
2×	`clear-num_binary64_14182` `flip--_binary64_14158` `prod-exp_binary64_14232` `div-inv_binary64_14180` `flip3--_binary64_14187` `frac-2neg_binary64_14194` `cbrt-unprod_binary64_14216`
1×	`sub-neg_binary64_14176` `distribute-lft-out_binary64_14134` `associate-*r/_binary64_14125` `flip3-+_binary64_14186` `diff-log_binary64_14275` `sum-log_binary64_14274` `flip-+_binary64_14157` `+-commutative_binary64_14113`

Counts

4 → 89

Calls

4 calls:

17.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z)))
13.0ms	(/.f64 y (-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z))
10.0ms	(-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z)
7.0ms	(/.f64 y (*.f64 2 (/.f64 z t)))

series508.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

242.0ms	(/.f64 y (-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z))
139.0ms	(+.f64 x (/.f64 y (-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z)))
76.0ms	(-.f64 (/.f64 y (*.f64 2 (/.f64 z t))) z)
50.0ms	(/.f64 y (*.f64 2 (/.f64 z t)))

simplify86.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

101 → 101

Iterations

Useful iterations: 0 (63.0ms)

Iter	Nodes	Cost
0	4944	1940
1	4944	1940

prune95.0ms (1.9%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	100	1	101
Fresh	3	1	4
Picked	0	1	1
Done	0	0	0
Total	103	3	106

Merged error: 0b

Counts

106 → 3

Compiler

Compiled 2065 to 1057 computations (48.8% saved)

localize9.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(+.f64 x (/.f64 1 (-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y))))
0.0b	(-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y))
0.3b	(/.f64 1/2 (/.f64 z t))
1.1b	(/.f64 1 (-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y)))

rewrite155.0ms (3.1%)

Algorithm

1×	rewrite-expression-head

Rules

174×	`add-sqr-sqrt_binary64_14205`
172×	`times-frac_binary64_14189`
102×	`*-un-lft-identity_binary64_14183`
69×	`add-cube-cbrt_binary64_14218`
30×	`difference-of-squares_binary64_14152`
24×	`associate-/r*_binary64_14127`
13×	`cancel-sign-sub-inv_binary64_14149` `add-exp-log_binary64_14221`
11×	`add-cbrt-cube_binary64_14219`
10×	`distribute-lft-out--_binary64_14135`
8×	`div-inv_binary64_14180` `add-log-exp_binary64_14222`
6×	`associate-/l*_binary64_14128`
5×	`div-exp_binary64_14234` `pow1_binary64_14244`
4×	`cbrt-undiv_binary64_14217` `associate-/r/_binary64_14129`
2×	`clear-num_binary64_14182` `flip--_binary64_14158` `distribute-lft-out_binary64_14134` `flip3--_binary64_14187` `frac-2neg_binary64_14194` `frac-sub_binary64_14192`
1×	`sub-neg_binary64_14176` `inv-pow_binary64_14268` `flip3-+_binary64_14186` `diff-log_binary64_14275` `sum-log_binary64_14274` `1-exp_binary64_14227` `pow-flip_binary64_14257` `rec-exp_binary64_14233` `flip-+_binary64_14157` `+-commutative_binary64_14113`

Counts

4 → 182

Calls

4 calls:

45.0ms	(+.f64 x (/.f64 1 (-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y))))
42.0ms	(/.f64 1 (-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y)))
41.0ms	(-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y))
6.0ms	(/.f64 1/2 (/.f64 z t))

series197.0ms (3.9%)

Counts

4 → 12

Calls

4 calls:

69.0ms	(+.f64 x (/.f64 1 (-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y))))
60.0ms	(/.f64 1 (-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y)))
42.0ms	(-.f64 (/.f64 1/2 (/.f64 z t)) (/.f64 z y))
26.0ms	(/.f64 1/2 (/.f64 z t))

simplify99.0ms (2%)

Algorithm

1×	egg-herbie

Counts

194 → 194

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5016	4105

prune199.0ms (4%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	194	0	194
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	194	3	197

Merged error: 0b

Counts

197 → 3

Compiler

Compiled 4144 to 1997 computations (51.8% saved)

regimes67.0ms (1.3%)

Compiler: Compiled 330 to 308 computations (6.7% saved)

bsearch0.0ms (0%)

simplify2.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	31	19
1	31	19

end0.0ms (0%)

sample719.0ms (14.4%)

Algorithm

1×

intervals

Results

389.0ms

8000×

body

128

valid

Compiler

Compiled 87 to 80 computations (8% saved)

Details

analyze706.0ms (14.2%)

sample24.0ms (0.5%)

simplify230.0ms (4.6%)

prune9.0ms (0.2%)

localize9.0ms (0.2%)

rewrite49.0ms (1%)

series399.0ms (8%)

simplify83.0ms (1.7%)

prune248.0ms (5%)

localize12.0ms (0.2%)

rewrite183.0ms (3.7%)

series285.0ms (5.7%)

simplify133.0ms (2.7%)

prune414.0ms (8.3%)

localize12.0ms (0.2%)

rewrite54.0ms (1.1%)

series508.0ms (10.2%)

simplify86.0ms (1.7%)

prune95.0ms (1.9%)

localize9.0ms (0.2%)

rewrite155.0ms (3.1%)

series197.0ms (3.9%)

simplify99.0ms (2%)

prune199.0ms (4%)

regimes67.0ms (1.3%)

bsearch0.0ms (0%)

simplify2.0ms (0%)

end0.0ms (0%)

sample719.0ms (14.4%)

Profiling