Details

analyze496.0ms (4.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
50%	50%	0%	2
50%	50%	0%	3
62.5%	37.5%	0%	4
68.7%	31.2%	0%	5
71.8%	28.1%	0%	6
73.4%	26.5%	0%	7
74.2%	25.8%	0%	8
74.6%	25.4%	0%	9
74.8%	25.2%	0%	10
74.9%	25.1%	0%	11
74.9%	25%	0%	12
74.9%	25%	0%	13
75%	25%	0%	14

Compiler

Compiled 10 to 8 computations (20% saved)

sample127.0ms (1.1%)

Algorithm

1×

intervals

Results

49.0ms	71×	body	1024	valid
30.0ms	49×	body	2048	valid
20.0ms	53×	body	512	valid
6.0ms	71×	body	128	valid
3.0ms	3×	body	4096	valid
2.0ms	9×	body	256	valid

Compiler

Compiled 19 to 16 computations (15.8% saved)

simplify184.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	11	14
1	11	14

prune5.0ms (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

Error

54.3b

Counts

2 → 1

Compiler

Compiled 18 to 14 computations (22.2% saved)

localize14.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.5b	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
3.0b	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
16.2b	(sqrt.f64 (+.f64 (*.f64 x x) 1))

rewrite137.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Error

54.2b

Rules

9×	`*-un-lft-identity_binary64_4170`
6×	`add-sqr-sqrt_binary64_4192`
5×	`pow1_binary64_4231` `add-log-exp_binary64_4209` `add-cube-cbrt_binary64_4205`
4×	`add-exp-log_binary64_4208` `log-prod_binary64_4256`
3×	`add-cbrt-cube_binary64_4206` `flip3-+_binary64_4173` `flip-+_binary64_4144` `sqrt-prod_binary64_4186`
2×	`sqrt-div_binary64_4187` `log-div_binary64_4257` `distribute-lft-out_binary64_4121`
1×	`pow1/2_binary64_4250` `sqrt-pow1_binary64_4188` `rem-sqrt-square_binary64_4183` `log-pow_binary64_4259` `rem-log-exp_binary64_4211` `sum-log_binary64_4261` `+-commutative_binary64_4100`

Counts

3 → 42

Calls

3 calls:

14.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
13.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
9.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 766 to 464 computations (39.4% saved)

series408.0ms (3.7%)

Error

0.0b

Counts

3 → 31

Calls

3 calls:

158.0ms	(log.f64 (+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1))))
102.0ms	(+.f64 x (sqrt.f64 (+.f64 (*.f64 x x) 1)))
83.0ms	(sqrt.f64 (+.f64 (*.f64 x x) 1))

Compiler

Compiled 878 to 750 computations (14.6% saved)

simplify123.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

73 → 73

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	5319	1102

prune118.0ms (1.1%)

Pruning

4 alts after pruning (4 fresh and 0 done)

	Pruned	Kept	Total
New	69	4	73
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	70	4	74

Error

0.0b

Counts

74 → 4

Compiler

Compiled 1010 to 675 computations (33.2% saved)

localize31.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 5/112 (pow.f64 x 7))
0.1b	(*.f64 (pow.f64 x 5) 3/40)
0.3b	(*.f64 (pow.f64 x 3) 1/6)
22.6b	(-.f64 (+.f64 x (.f64 (pow.f64 x 5) 3/40)) (+.f64 (.f64 (pow.f64 x 3) 1/6) (*.f64 5/112 (pow.f64 x 7))))

rewrite486.0ms (4.4%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

34×	`add-sqr-sqrt_binary64_4192`
22×	`associate-l_binary64_4111`
19×	`add-exp-log_binary64_4208`
17×	`*-un-lft-identity_binary64_4170`
16×	`add-log-exp_binary64_4209`
15×	`add-cube-cbrt_binary64_4205`
13×	`associate-r_binary64_4110`
12×	`unpow-prod-down_binary64_4249`
10×	`add-cbrt-cube_binary64_4206` `unswap-sqr_binary64_4138`
9×	`prod-exp_binary64_4219`
6×	`sqr-pow_binary64_4142`
4×	`sum-log_binary64_4261` `diff-log_binary64_4262` `pow1_binary64_4231` `flip3-+_binary64_4173` `frac-sub_binary64_4179` `flip-+_binary64_4144` `cube-prod_binary64_4198`
3×	`cancel-sign-sub-inv_binary64_4136` `pow-to-exp_binary64_4239` `pow-exp_binary64_4238` `cbrt-unprod_binary64_4203` `*-commutative_binary64_4101`
1×	`flip3--_binary64_4174` `sub-neg_binary64_4163` `flip--_binary64_4145` `difference-of-squares_binary64_4139` `distribute-lft-out--_binary64_4122` `associate--l+_binary64_4107` `associate--r+_binary64_4106` `unpow3_binary64_4236` `cube-mult_binary64_4200`

Counts

4 → 106

Calls

4 calls:

23.0ms	(-.f64 (+.f64 x (.f64 (pow.f64 x 5) 3/40)) (+.f64 (.f64 (pow.f64 x 3) 1/6) (*.f64 5/112 (pow.f64 x 7))))
12.0ms	(*.f64 (pow.f64 x 3) 1/6)
11.0ms	(*.f64 5/112 (pow.f64 x 7))
11.0ms	(*.f64 (pow.f64 x 5) 3/40)

Compiler

Compiled 3201 to 2555 computations (20.2% saved)

series365.0ms (3.3%)

Error

0.0b

Counts

4 → 17

Calls

4 calls:

97.0ms	(*.f64 5/112 (pow.f64 x 7))
97.0ms	(-.f64 (+.f64 x (.f64 (pow.f64 x 5) 3/40)) (+.f64 (.f64 (pow.f64 x 3) 1/6) (*.f64 5/112 (pow.f64 x 7))))
82.0ms	(*.f64 (pow.f64 x 5) 3/40)
60.0ms	(*.f64 (pow.f64 x 3) 1/6)

Compiler

Compiled 691 to 574 computations (16.9% saved)

simplify174.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

123 → 123

Iterations

Useful iterations: 0 (122.0ms)

Iter	Nodes	Cost
0	4923	2212
1	4923	2212

prune397.0ms (3.6%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	123	0	123
Fresh	0	3	3
Picked	0	1	1
Done	0	0	0
Total	123	4	127

Error

0.0b

Counts

127 → 4

Compiler

Compiled 3141 to 2489 computations (20.8% saved)

localize25.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(/.f64 1/16 (pow.f64 x 5))
0.3b	(/.f64 1/8 (pow.f64 x 3))
17.0b	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
20.2b	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))

rewrite862.0ms (7.8%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

75×	`*-un-lft-identity_binary64_4170`
73×	`add-sqr-sqrt_binary64_4192` `times-frac_binary64_4176`
47×	`add-cube-cbrt_binary64_4205`
26×	`unpow-prod-down_binary64_4249`
19×	`associate-/r*_binary64_4114`
15×	`add-exp-log_binary64_4208`
14×	`cube-prod_binary64_4198`
11×	`log-prod_binary64_4256`
10×	`difference-of-squares_binary64_4139` `sqr-pow_binary64_4142`
9×	`add-log-exp_binary64_4209`
8×	`add-cbrt-cube_binary64_4206`
6×	`frac-sub_binary64_4179` `distribute-lft-out_binary64_4121` `distribute-lft-out--_binary64_4122` `div-exp_binary64_4221` `associate-/l*_binary64_4115`
5×	`pow1_binary64_4231` `cancel-sign-sub-inv_binary64_4136` `log-div_binary64_4257`
4×	`unpow3_binary64_4236` `cube-mult_binary64_4200`
2×	`diff-log_binary64_4262` `frac-add_binary64_4178` `flip3-+_binary64_4173` `flip-+_binary64_4144` `flip3--_binary64_4174` `flip--_binary64_4145` `pow-to-exp_binary64_4239` `pow-exp_binary64_4238` `cbrt-undiv_binary64_4204` `frac-2neg_binary64_4181` `clear-num_binary64_4169` `div-inv_binary64_4167`
1×	`sum-log_binary64_4261` `sub-neg_binary64_4163` `associate--r+_binary64_4106` `log-pow_binary64_4259` `rem-log-exp_binary64_4211`

Counts

4 → 164

Calls

4 calls:

89.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
89.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
11.0ms	(/.f64 1/8 (pow.f64 x 3))
9.0ms	(/.f64 1/16 (pow.f64 x 5))

Compiler

Compiled 4463 to 3632 computations (18.6% saved)

series402.0ms (3.6%)

Error

0.0b

Counts

4 → 18

Calls

4 calls:

147.0ms	(-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5))))
94.0ms	(log.f64 (-.f64 (/.f64 1/8 (pow.f64 x 3)) (+.f64 (/.f64 1/2 x) (/.f64 1/16 (pow.f64 x 5)))))
71.0ms	(/.f64 1/16 (pow.f64 x 5))
64.0ms	(/.f64 1/8 (pow.f64 x 3))

Compiler

Compiled 697 to 616 computations (11.6% saved)

simplify190.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

182 → 182

Iterations

Useful iterations: 0 (93.0ms)

Iter	Nodes	Cost
0	5168	3684

prune540.0ms (4.9%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	182	0	182
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	182	4	186

Error

0.0b

Counts

186 → 4

Compiler

Compiled 4182 to 3329 computations (20.4% saved)

localize12.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
0.0b	(+.f64 x (/.f64 1/2 x))
0.0b	(+.f64 x (+.f64 x (/.f64 1/2 x)))

rewrite121.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Error

0.0b

Rules

16×	`*-un-lft-identity_binary64_4170`
10×	`add-log-exp_binary64_4209`
7×	`distribute-lft-out_binary64_4121`
5×	`log-prod_binary64_4256`
4×	`sum-log_binary64_4261` `pow1_binary64_4231` `add-exp-log_binary64_4208` `add-cube-cbrt_binary64_4205` `add-sqr-sqrt_binary64_4192`
3×	`add-cbrt-cube_binary64_4206` `flip3-+_binary64_4173` `flip-+_binary64_4144`
2×	`+-commutative_binary64_4100` `log-div_binary64_4257`
1×	`associate-+r+_binary64_4102` `log-pow_binary64_4259` `rem-log-exp_binary64_4211`

Counts

3 → 43

Calls

3 calls:

17.0ms	(+.f64 x (+.f64 x (/.f64 1/2 x)))
16.0ms	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
12.0ms	(+.f64 x (/.f64 1/2 x))

Compiler

Compiled 683 to 458 computations (32.9% saved)

series255.0ms (2.3%)

Error

0.0b

Counts

3 → 17

Calls

3 calls:

97.0ms	(+.f64 x (+.f64 x (/.f64 1/2 x)))
68.0ms	(log.f64 (+.f64 x (+.f64 x (/.f64 1/2 x))))
68.0ms	(+.f64 x (/.f64 1/2 x))

Compiler

Compiled 377 to 316 computations (16.2% saved)

simplify119.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

60 → 60

Iterations

Useful iterations: 0 (95.0ms)

Iter	Nodes	Cost
0	5106	740

prune73.0ms (0.7%)

Pruning

4 alts after pruning (1 fresh and 3 done)

	Pruned	Kept	Total
New	60	0	60
Fresh	0	1	1
Picked	0	1	1
Done	0	2	2
Total	60	4	64

Error

0.0b

Counts

64 → 4

Compiler

Compiled 685 to 423 computations (38.2% saved)

regimes490.0ms (4.4%)

Accuracy

Total 0.1b remaining (86%)

Threshold costs 0.1b (86%)

Compiler

Compiled 1793 to 1343 computations (25.1% saved)

bsearch83.0ms (0.7%)

Steps

Iters	Range		Point
10	0.40645441100929564	4.2565398279645896e+18	1.0766709768647007
8	-251.49049503104322	-0.009872165400500623	-1.0686534996162853

Compiler

Compiled 1 to 1 computations (0% saved)

simplify11.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (6.0ms)

Iter	Nodes	Cost
0	221	88
1	221	88

end0.0ms (0%)

sample4.9s (43.8%)

Algorithm

1×

intervals

Results

1.6s	2457×	body	1024	valid
711.0ms	1193×	body	2048	valid
486.0ms	1294×	body	512	valid
203.0ms	2343×	body	128	valid
147.0ms	673×	body	256	valid
32.0ms	40×	body	4096	valid

Compiler

Compiled 606 to 461 computations (23.9% saved)

Details

analyze496.0ms (4.5%)

sample127.0ms (1.1%)

simplify184.0ms (1.7%)

prune5.0ms (0%)

localize14.0ms (0.1%)

rewrite137.0ms (1.2%)

series408.0ms (3.7%)

simplify123.0ms (1.1%)

prune118.0ms (1.1%)

localize31.0ms (0.3%)

rewrite486.0ms (4.4%)

series365.0ms (3.3%)

simplify174.0ms (1.6%)

prune397.0ms (3.6%)

localize25.0ms (0.2%)

rewrite862.0ms (7.8%)

series402.0ms (3.6%)

simplify190.0ms (1.7%)

prune540.0ms (4.9%)

localize12.0ms (0.1%)

rewrite121.0ms (1.1%)

series255.0ms (2.3%)

simplify119.0ms (1.1%)

prune73.0ms (0.7%)

regimes490.0ms (4.4%)

bsearch83.0ms (0.7%)

simplify11.0ms (0.1%)

end0.0ms (0%)

sample4.9s (43.8%)

Profiling