Details

analyze1.9s (25.7%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.7%	0.3%	0
0%	99.7%	0.3%	1
0%	99.7%	0.3%	2
0%	99.7%	0.3%	3
0%	99.7%	0.3%	4
0%	99.7%	0.3%	5
0%	99.7%	0.3%	6
0%	99.7%	0.3%	7
0%	99.7%	0.3%	8
0%	99.7%	0.3%	9
0%	99.7%	0.3%	10
0%	99.7%	0.3%	11
0%	99.7%	0.3%	12
0.8%	98.9%	0.3%	13
1.2%	98.5%	0.3%	14

Compiler

Compiled 38 to 31 computations (18.4% saved)

sample37.0ms (0.5%)

Algorithm

1×

intervals

Results

21.0ms	256×	body	128	valid
2.0ms	22×	body	128	invalid

Compiler

Compiled 75 to 67 computations (10.7% saved)

simplify281.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4971	55
1	4971	55

prune4.0ms (0%)

Pruning

1 alts after pruning (1 fresh and 0 done)

	Pruned	Kept	Total
New	1	0	1
Fresh	0	1	1
Picked	0	0	0
Done	0	0	0
Total	1	1	2

Merged error: 28.7b

Counts

2 → 1

Compiler

Compiled 74 to 60 computations (18.9% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)
0.1b	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
2.9b	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
27.2b	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))

rewrite91.0ms (1.2%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_12829`
15×	`add-cbrt-cube_binary64_12843` `add-exp-log_binary64_12845`
12×	`*-un-lft-identity_binary64_12807` `add-cube-cbrt_binary64_12842`
10×	`pow1_binary64_12868`
9×	`associate-l_binary64_12748` `associate-r_binary64_12747`
5×	`flip3-+_binary64_12810` `flip-+_binary64_12781`
4×	`prod-exp_binary64_12856` `cbrt-unprod_binary64_12840` `associate-r/_binary64_12749` `associate-l/_binary64_12750` `add-log-exp_binary64_12846`
3×	`pow-prod-down_binary64_12878` `-commutative_binary64_12738` `times-frac_binary64_12813` `associate-/r_binary64_12751` `unswap-sqr_binary64_12775`
2×	`div-exp_binary64_12858` `associate-/r/_binary64_12753` `associate-/l/_binary64_12754` `cbrt-undiv_binary64_12841`
1×	`div-inv_binary64_12804` `clear-num_binary64_12806` `associate-/l*_binary64_12752` `distribute-rgt-in_binary64_12757` `frac-2neg_binary64_12818` `distribute-lft-in_binary64_12756`

Counts

4 → 87

Calls

4 calls:

33.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))
25.0ms	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
13.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)
8.0ms	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)

series1.3s (17.7%)

Counts

4 → 12

Calls

4 calls:

885.0ms	(/.f64 (.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))
327.0ms	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
73.0ms	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
37.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z)

simplify86.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (54.0ms)

Iter	Nodes	Cost
0	5136	3033

prune647.0ms (8.7%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	90	9	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	91	9	100

Merged error: 0.5b

Counts

100 → 9

Compiler

Compiled 14801 to 11013 computations (25.6% saved)

localize5.0ms (0.1%)

Local error

Found 2 expressions with local error:

0.0b	(+.f64 x (.f64 (.f64 y b) 4503599627370496/2737158995491925))
0.4b	(.f64 (.f64 y b) 4503599627370496/2737158995491925)

rewrite11.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`add-cbrt-cube_binary64_12843` `pow1_binary64_12868` `add-exp-log_binary64_12845`
4×	`add-log-exp_binary64_12846`
3×	`-un-lft-identity_binary64_12807` `pow-prod-down_binary64_12878` `prod-exp_binary64_12856` `cbrt-unprod_binary64_12840` `add-sqr-sqrt_binary64_12829` `add-cube-cbrt_binary64_12842` `associate-r*_binary64_12747`
1×	`-commutative_binary64_12738` `associate-l*_binary64_12748` `flip3-+_binary64_12810` `sum-log_binary64_12898` `flip-+_binary64_12781` `+-commutative_binary64_12737`

Counts

2 → 29

Calls

2 calls:

5.0ms	(.f64 (.f64 y b) 4503599627370496/2737158995491925)
4.0ms	(+.f64 x (.f64 (.f64 y b) 4503599627370496/2737158995491925))

series96.0ms (1.3%)

Counts

2 → 6

Calls

2 calls:

65.0ms	(+.f64 x (.f64 (.f64 y b) 4503599627370496/2737158995491925))
31.0ms	(.f64 (.f64 y b) 4503599627370496/2737158995491925)

simplify98.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4757	381
1	4757	381

prune172.0ms (2.3%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	32	3	35
Fresh	2	6	8
Picked	1	0	1
Done	0	0	0
Total	35	9	44

Merged error: 0.5b

Counts

44 → 9

Compiler

Compiled 3511 to 2842 computations (19.1% saved)

localize5.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 x (.f64 y (.f64 b 4503599627370496/2737158995491925)))
0.2b	(.f64 y (.f64 b 4503599627370496/2737158995491925))
0.4b	(*.f64 b 4503599627370496/2737158995491925)

rewrite16.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-cbrt-cube_binary64_12843` `pow1_binary64_12868` `add-exp-log_binary64_12845`
8×	`add-sqr-sqrt_binary64_12829`
6×	`-un-lft-identity_binary64_12807` `associate-l*_binary64_12748` `add-cube-cbrt_binary64_12842`
5×	`add-log-exp_binary64_12846`
4×	`pow-prod-down_binary64_12878` `prod-exp_binary64_12856` `cbrt-unprod_binary64_12840` `associate-r_binary64_12747`
2×	`*-commutative_binary64_12738`
1×	`flip3-+_binary64_12810` `sum-log_binary64_12898` `flip-+_binary64_12781` `+-commutative_binary64_12737` `unswap-sqr_binary64_12775`

Counts

3 → 47

Calls

3 calls:

5.0ms	(.f64 y (.f64 b 4503599627370496/2737158995491925))
4.0ms	(*.f64 b 4503599627370496/2737158995491925)
4.0ms	(+.f64 x (.f64 y (.f64 b 4503599627370496/2737158995491925)))

series121.0ms (1.6%)

Counts

3 → 9

Calls

3 calls:

68.0ms	(+.f64 x (.f64 y (.f64 b 4503599627370496/2737158995491925)))
29.0ms	(.f64 y (.f64 b 4503599627370496/2737158995491925))
24.0ms	(*.f64 b 4503599627370496/2737158995491925)

simplify72.0ms (1%)

Algorithm

1×	egg-herbie

Counts

56 → 56

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	4945	509
1	4945	509

prune125.0ms (1.7%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	56	0	56
Fresh	0	8	8
Picked	0	1	1
Done	0	0	0
Total	56	9	65

Merged error: 0.5b

Counts

65 → 9

Compiler

Compiled 2434 to 1949 computations (19.9% saved)

localize7.0ms (0.1%)

Local error

Found 3 expressions with local error:

0.0b

(+.f64 x (*.f64 (*.f64 (*.f64 y b) (sqrt.f64 4503599627370496/2737158995491925)) (sqrt.f64 4503599627370496/2737158995491925)))

0.2b

(*.f64 (*.f64 y b) (sqrt.f64 4503599627370496/2737158995491925))

0.3b

(*.f64 (*.f64 (*.f64 y b) (sqrt.f64 4503599627370496/2737158995491925)) (sqrt.f64 4503599627370496/2737158995491925))

rewrite28.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

17×	`add-cbrt-cube_binary64_12843` `pow1_binary64_12868` `add-exp-log_binary64_12845`
12×	`associate-r_binary64_12747`
9×	`pow-prod-down_binary64_12878` `prod-exp_binary64_12856` `cbrt-unprod_binary64_12840`
7×	`*-un-lft-identity_binary64_12807` `add-sqr-sqrt_binary64_12829` `add-cube-cbrt_binary64_12842`
6×	`sqrt-prod_binary64_12823`
5×	`add-log-exp_binary64_12846`
2×	`-commutative_binary64_12738` `associate-l*_binary64_12748`
1×	`flip3-+_binary64_12810` `sum-log_binary64_12898` `flip-+_binary64_12781` `+-commutative_binary64_12737`

Counts

3 → 56

Calls

3 calls:

13.0ms

(*.f64 (*.f64 (*.f64 y b) (sqrt.f64 4503599627370496/2737158995491925)) (sqrt.f64 4503599627370496/2737158995491925))

7.0ms

(*.f64 (*.f64 y b) (sqrt.f64 4503599627370496/2737158995491925))

4.0ms

(+.f64 x (*.f64 (*.f64 (*.f64 y b) (sqrt.f64 4503599627370496/2737158995491925)) (sqrt.f64 4503599627370496/2737158995491925)))

series246.0ms (3.3%)

Counts

3 → 9

Calls

3 calls:

117.0ms

(+.f64 x (*.f64 (*.f64 (*.f64 y b) (sqrt.f64 4503599627370496/2737158995491925)) (sqrt.f64 4503599627370496/2737158995491925)))

77.0ms

(*.f64 (*.f64 (*.f64 y b) (sqrt.f64 4503599627370496/2737158995491925)) (sqrt.f64 4503599627370496/2737158995491925))

52.0ms

(*.f64 (*.f64 y b) (sqrt.f64 4503599627370496/2737158995491925))

simplify78.0ms (1%)

Algorithm

1×	egg-herbie

Counts

65 → 65

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4916	705
1	4916	705

prune67.0ms (0.9%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	64	1	65
Fresh	0	7	7
Picked	1	0	1
Done	1	0	1
Total	66	8	74

Merged error: 0.5b

Counts

74 → 8

Compiler

Compiled 1132 to 795 computations (29.8% saved)

regimes435.0ms (5.8%)

Compiler: Compiled 1770 to 1536 computations (13.2% saved)

bsearch78.0ms (1%)

Steps

Iters	Range		Point
10	7.317459805983961e+27	4.072634537553549e+40	4.974259772593562e+39
7	-1.6442048761342146e+69	-4.647464072227077e+67	-4.702036921833592e+67

Compiler

Compiled 1 to 6 computations (-500% saved)

simplify3.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	71	91
1	71	91

end0.0ms (0%)

sample1.4s (18.7%)

Algorithm

1×

intervals

Results

683.0ms	8000×	body	128	valid
75.0ms	883×	body	128	invalid

Compiler

Compiled 471 to 383 computations (18.7% saved)

Details

analyze1.9s (25.7%)

sample37.0ms (0.5%)

simplify281.0ms (3.8%)

prune4.0ms (0%)

localize25.0ms (0.3%)

rewrite91.0ms (1.2%)

series1.3s (17.7%)

simplify86.0ms (1.2%)

prune647.0ms (8.7%)

localize5.0ms (0.1%)

rewrite11.0ms (0.2%)

series96.0ms (1.3%)

simplify98.0ms (1.3%)

prune172.0ms (2.3%)

localize5.0ms (0.1%)

rewrite16.0ms (0.2%)

series121.0ms (1.6%)

simplify72.0ms (1%)

prune125.0ms (1.7%)

localize7.0ms (0.1%)

rewrite28.0ms (0.4%)

series246.0ms (3.3%)

simplify78.0ms (1%)

prune67.0ms (0.9%)

regimes435.0ms (5.8%)

bsearch78.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.4s (18.7%)

Profiling