Details

analyze7.0ms (0.2%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
50%	50%	0%	3
50%	25%	25%	4
62.5%	12.5%	25%	5
68.7%	6.2%	25%	6
71.8%	3.1%	25%	7
73.4%	1.6%	25%	8
74.2%	0.8%	25%	9
74.6%	0.4%	25%	10
74.8%	0.2%	25%	11
74.9%	0.1%	25%	12
74.9%	0%	25.1%	13
74.9%	0%	25.1%	14

Compiler

Compiled 14 to 12 computations (14.3% saved)

sample14.0ms (0.4%)

Algorithm

1×

intervals

Results

8.0ms

256×

body

128

valid

Compiler

Compiled 27 to 24 computations (11.1% saved)

simplify127.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	617	13
1	617	13

prune4.0ms (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

0.0b

Counts

2 → 2

Compiler

Compiled 31 to 27 computations (12.9% saved)

localize6.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 x (+.f64 12 (.f64 x -9)))
0.0b	(+.f64 12 (*.f64 x -9))
0.0b	(+.f64 12 (*.f64 x -9))
0.1b	(.f64 x (+.f64 12 (.f64 x -9)))

rewrite12.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

6×	`add-sqr-sqrt_binary64_14079`
4×	`*-un-lft-identity_binary64_14057` `add-cube-cbrt_binary64_14092` `pow1_binary64_14118` `add-exp-log_binary64_14095` `add-log-exp_binary64_14096` `add-cbrt-cube_binary64_14093`
3×	`associate-r_binary64_13997` `associate-l_binary64_13998`
2×	`associate-*r/_binary64_13999` `flip-+_binary64_14031` `flip3-+_binary64_14060`
1×	`pow-prod-down_binary64_14128` `unswap-sqr_binary64_14025` `sum-log_binary64_14148` `distribute-rgt-in_binary64_14007` `+-commutative_binary64_13987` `*-commutative_binary64_13988` `prod-exp_binary64_14106` `cbrt-unprod_binary64_14090` `distribute-lft-in_binary64_14006`

Counts

2 → 33

Calls

4 calls:

6.0ms	(.f64 x (+.f64 12 (.f64 x -9)))
3.0ms	(+.f64 12 (*.f64 x -9))
0.0ms	(+.f64 12 (*.f64 x -9))
0.0ms	(.f64 x (+.f64 12 (.f64 x -9)))

series275.0ms (7.8%)

Counts

2 → 12

Calls

2 calls:

246.0ms	(.f64 x (+.f64 12 (.f64 x -9)))
30.0ms	(+.f64 12 (*.f64 x -9))

Compiler

Compiled 158 to 144 computations (8.9% saved)

simplify66.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

45 → 45

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5181	482

prune55.0ms (1.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	41	4	45
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	41	6	47

Error

0.0b

Counts

47 → 6

Compiler

Compiled 659 to 523 computations (20.6% saved)

localize8.0ms (0.2%)

Local error

Found 6 expressions with local error:

0.2b	(.f64 (.f64 x 3) x)
0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
0.0b	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
0.0b	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
0.1b	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
0.2b	(.f64 (.f64 x 3) x)

rewrite28.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`pow1_binary64_14118` `add-exp-log_binary64_14095` `add-cbrt-cube_binary64_14093`
8×	`*-un-lft-identity_binary64_14057` `add-sqr-sqrt_binary64_14079`
7×	`associate-r_binary64_13997`
6×	`add-cube-cbrt_binary64_14092`
5×	`add-log-exp_binary64_14096`
4×	`pow-prod-down_binary64_14128` `associate-l_binary64_13998` `prod-exp_binary64_14106` `cbrt-unprod_binary64_14090`
2×	`associate-r/_binary64_13999` `-commutative_binary64_13988`
1×	`unswap-sqr_binary64_14025` `flip-+_binary64_14031` `distribute-rgt-in_binary64_14007` `distribute-lft-out_binary64_14008` `flip3-+_binary64_14060` `flip3--_binary64_14061` `diff-log_binary64_14149` `flip--_binary64_14032` `sub-neg_binary64_14050` `distribute-lft-in_binary64_14006` `cancel-sign-sub-inv_binary64_14023`

Counts

3 → 53

Calls

6 calls:

10.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
8.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
5.0ms	(.f64 (.f64 x 3) x)
0.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
0.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))

series164.0ms (4.7%)

Counts

3 → 18

Calls

3 calls:

83.0ms	(.f64 3 (+.f64 (-.f64 (.f64 (.f64 x 3) x) (.f64 x 4)) 1))
56.0ms	(-.f64 (.f64 (.f64 x 3) x) (*.f64 x 4))
25.0ms	(.f64 (.f64 x 3) x)

Compiler

Compiled 281 to 262 computations (6.8% saved)

simplify57.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	5022	905

prune71.0ms (2%)

Pruning

5 alts after pruning (3 fresh and 2 done)

	Pruned	Kept	Total
New	70	1	71
Fresh	2	2	4
Picked	0	1	1
Done	0	1	1
Total	72	5	77

Error

Counts

77 → 5

Compiler

Compiled 1170 to 943 computations (19.4% saved)

localize11.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(/.f64 (-.f64 144 (.f64 x (.f64 x 81))) (-.f64 12 (*.f64 x -9)))
0.1b	(.f64 x (.f64 x 81))
0.1b	(.f64 x (/.f64 (-.f64 144 (.f64 x (.f64 x 81))) (-.f64 12 (.f64 x -9))))
0.0b	(-.f64 12 (*.f64 x -9))
0.0b	(-.f64 12 (*.f64 x -9))
0.1b	(.f64 x (/.f64 (-.f64 144 (.f64 x (.f64 x 81))) (-.f64 12 (.f64 x -9))))
0.1b	(.f64 x (.f64 x 81))
0.2b	(/.f64 (-.f64 144 (.f64 x (.f64 x 81))) (-.f64 12 (*.f64 x -9)))

rewrite37.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`add-sqr-sqrt_binary64_14079`
21×	`*-un-lft-identity_binary64_14057` `add-cube-cbrt_binary64_14092`
19×	`times-frac_binary64_14063`
16×	`associate-r_binary64_13997` `add-exp-log_binary64_14095` `add-cbrt-cube_binary64_14093`
11×	`pow1_binary64_14118`
6×	`associate-l_binary64_13998` `add-log-exp_binary64_14096`
5×	`prod-exp_binary64_14106` `cbrt-unprod_binary64_14090`
4×	`pow-prod-down_binary64_14128` `flip3--_binary64_14061` `flip--_binary64_14032` `associate-/r/_binary64_14003`
3×	`associate-/r_binary64_14001` `associate-/l_binary64_14002`
2×	`unswap-sqr_binary64_14025` `div-exp_binary64_14108` `*-commutative_binary64_13988` `cbrt-undiv_binary64_14091` `associate-/l/_binary64_14004` `div-inv_binary64_14054`
1×	`associate-*r/_binary64_13999` `frac-2neg_binary64_14068` `div-sub_binary64_14062` `clear-num_binary64_14056` `diff-log_binary64_14149` `sub-neg_binary64_14050` `cancel-sign-sub-inv_binary64_14023`

Counts

4 → 96

Calls

8 calls:

10.0ms	(.f64 x (/.f64 (-.f64 144 (.f64 x (.f64 x 81))) (-.f64 12 (.f64 x -9))))
7.0ms	(.f64 x (.f64 x 81))
7.0ms	(/.f64 (-.f64 144 (.f64 x (.f64 x 81))) (-.f64 12 (*.f64 x -9)))
3.0ms	(-.f64 12 (*.f64 x -9))
0.0ms	(-.f64 12 (*.f64 x -9))

series209.0ms (5.9%)

Counts

4 → 21

Calls

4 calls:

90.0ms	(.f64 x (/.f64 (-.f64 144 (.f64 x (.f64 x 81))) (-.f64 12 (.f64 x -9))))
64.0ms	(/.f64 (-.f64 144 (.f64 x (.f64 x 81))) (-.f64 12 (*.f64 x -9)))
31.0ms	(-.f64 12 (*.f64 x -9))
25.0ms	(.f64 x (.f64 x 81))

Compiler

Compiled 405 to 353 computations (12.8% saved)

simplify49.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

117 → 117

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	5009	2144

prune146.0ms (4.1%)

Pruning

5 alts after pruning (2 fresh and 3 done)

	Pruned	Kept	Total
New	116	1	117
Fresh	1	1	2
Picked	0	1	1
Done	0	2	2
Total	117	5	122

Error

Counts

122 → 5

Compiler

Compiled 2703 to 2118 computations (21.6% saved)

localize11.0ms (0.3%)

Local error

Found 8 expressions with local error:

0.2b	(.f64 (.f64 x x) 81)
0.2b	(/.f64 (-.f64 144 (.f64 (.f64 x x) 81)) (-.f64 12 (*.f64 x -9)))
0.1b	(.f64 x (/.f64 (-.f64 144 (.f64 (.f64 x x) 81)) (-.f64 12 (.f64 x -9))))
0.0b	(-.f64 12 (*.f64 x -9))
0.0b	(-.f64 12 (*.f64 x -9))
0.1b	(.f64 x (/.f64 (-.f64 144 (.f64 (.f64 x x) 81)) (-.f64 12 (.f64 x -9))))
0.2b	(/.f64 (-.f64 144 (.f64 (.f64 x x) 81)) (-.f64 12 (*.f64 x -9)))
0.2b	(.f64 (.f64 x x) 81)

rewrite38.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64_14079`
21×	`*-un-lft-identity_binary64_14057` `add-cube-cbrt_binary64_14092`
19×	`times-frac_binary64_14063`
18×	`associate-r_binary64_13997`
16×	`add-exp-log_binary64_14095` `add-cbrt-cube_binary64_14093`
11×	`pow1_binary64_14118`
6×	`add-log-exp_binary64_14096`
5×	`prod-exp_binary64_14106` `cbrt-unprod_binary64_14090`
4×	`pow-prod-down_binary64_14128` `flip3--_binary64_14061` `associate-l_binary64_13998` `flip--_binary64_14032` `associate-/r/_binary64_14003`
3×	`unswap-sqr_binary64_14025` `associate-/r_binary64_14001` `associate-/l_binary64_14002`
2×	`div-exp_binary64_14108` `*-commutative_binary64_13988` `cbrt-undiv_binary64_14091` `associate-/l/_binary64_14004` `div-inv_binary64_14054`
1×	`associate-*r/_binary64_13999` `frac-2neg_binary64_14068` `div-sub_binary64_14062` `clear-num_binary64_14056` `diff-log_binary64_14149` `sub-neg_binary64_14050` `cancel-sign-sub-inv_binary64_14023`

Counts

4 → 97

Calls

8 calls:

10.0ms	(.f64 x (/.f64 (-.f64 144 (.f64 (.f64 x x) 81)) (-.f64 12 (.f64 x -9))))
7.0ms	(/.f64 (-.f64 144 (.f64 (.f64 x x) 81)) (-.f64 12 (*.f64 x -9)))
6.0ms	(.f64 (.f64 x x) 81)
3.0ms	(-.f64 12 (*.f64 x -9))
0.0ms	(-.f64 12 (*.f64 x -9))

series210.0ms (6%)

Counts

4 → 21

Calls

4 calls:

92.0ms	(.f64 x (/.f64 (-.f64 144 (.f64 (.f64 x x) 81)) (-.f64 12 (.f64 x -9))))
65.0ms	(/.f64 (-.f64 144 (.f64 (.f64 x x) 81)) (-.f64 12 (*.f64 x -9)))
29.0ms	(-.f64 12 (*.f64 x -9))
25.0ms	(.f64 (.f64 x x) 81)

Compiler

Compiled 405 to 353 computations (12.8% saved)

simplify68.0ms (1.9%)

Algorithm

1×	egg-herbie

Counts

118 → 118

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4960	2149
1	4960	2149

prune137.0ms (3.9%)

Pruning

5 alts after pruning (1 fresh and 4 done)

	Pruned	Kept	Total
New	118	0	118
Fresh	0	1	1
Picked	0	1	1
Done	0	3	3
Total	118	5	123

Error

Counts

123 → 5

Compiler

Compiled 2675 to 1969 computations (26.4% saved)

simplify36.0ms (1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	1099	428
1	1099	428

regimes39.0ms (1.1%)

Accuracy

Total 0.1b remaining (96.8%)

Threshold costs 0.1b (96.8%)

Compiler

Compiled 293 to 252 computations (14% saved)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	76	16
1	76	16

end0.0ms (0%)

sample1.6s (46.4%)

Algorithm

1×

intervals

Results

254.0ms	8000×	body	128	valid
0.0ms	2×	body	128	invalid

Compiler

Compiled 898 to 772 computations (14% saved)

Pareto

0.5778357990231406

Details

analyze7.0ms (0.2%)

sample14.0ms (0.4%)

simplify127.0ms (3.6%)

prune4.0ms (0.1%)

localize6.0ms (0.2%)

rewrite12.0ms (0.3%)

series275.0ms (7.8%)

simplify66.0ms (1.9%)

prune55.0ms (1.6%)

localize8.0ms (0.2%)

rewrite28.0ms (0.8%)

series164.0ms (4.7%)

simplify57.0ms (1.6%)

prune71.0ms (2%)

localize11.0ms (0.3%)

rewrite37.0ms (1%)

series209.0ms (5.9%)

simplify49.0ms (1.4%)

prune146.0ms (4.1%)

localize11.0ms (0.3%)

rewrite38.0ms (1.1%)

series210.0ms (6%)

simplify68.0ms (1.9%)

prune137.0ms (3.9%)

simplify36.0ms (1%)

regimes39.0ms (1.1%)

bsearch0.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.6s (46.4%)

Profiling