Details

analyze2.0s (23.7%)

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)

sample39.0ms (0.5%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	128	valid
2.0ms	27×	body	128	invalid

Compiler

Compiled 75 to 67 computations (10.7% saved)

simplify121.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (114.0ms)

Iter	Nodes	Cost
0	4970	55
1	4970	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: 29.7b

Counts

2 → 1

Compiler

Compiled 74 to 60 computations (18.9% saved)

localize30.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
0.1b	(.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z)
3.8b	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
28.2b	(/.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))

rewrite87.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
12×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
10×	`pow1_binary64`
9×	`associate-r_binary64` `associate-l_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `associate-r/_binary64` `prod-exp_binary64` `associate-l/_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `unswap-sqr_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-/r/_binary64` `div-exp_binary64`
1×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 87

Calls

4 calls:

34.0ms	(/.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))
19.0ms	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
15.0ms	(.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z)
8.0ms	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)

series1.3s (15.6%)

Counts

4 → 12

Calls

4 calls:

871.0ms	(/.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))
324.0ms	(.f64 y (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (*.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z) b))
76.0ms	(.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z)
70.0ms	(.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 z 7049496828096731/2251799813685248) 3143161857605767/281474976710656) z) t) z) a) z)

simplify92.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

99 → 99

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	5110	3162

prune584.0ms (6.8%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	91	8	99
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	92	8	100

Merged error: 0.0b

Counts

100 → 8

Compiler

Compiled 13552 to 10008 computations (26.2% saved)

localize15.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(*.f64 (+.f64 z 4288183283079449/281474976710656) z)
0.0b	(.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z)
0.0b	(.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z)
4.3b	(/.f64 (.f64 y (+.f64 0 b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))

rewrite63.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
14×	`*-un-lft-identity_binary64`
12×	`add-cube-cbrt_binary64`
10×	`pow1_binary64` `associate-l_binary64`
9×	`associate-r_binary64`
6×	`associate-*l/_binary64`
5×	`flip3-+_binary64` `flip-+_binary64`
4×	`add-log-exp_binary64` `cbrt-unprod_binary64` `prod-exp_binary64`
3×	`pow-prod-down_binary64` `associate-/r_binary64` `unswap-sqr_binary64` `times-frac_binary64` `-commutative_binary64`
2×	`associate-/l/_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `associate-/r/_binary64` `div-exp_binary64`
1×	`distribute-lft-out_binary64` `clear-num_binary64` `frac-2neg_binary64` `associate-/l*_binary64` `div-inv_binary64`

Counts

4 → 86

Calls

4 calls:

22.0ms	(/.f64 (.f64 y (+.f64 0 b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))
14.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z)
11.0ms	(.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z)
7.0ms	(*.f64 (+.f64 z 4288183283079449/281474976710656) z)

series530.0ms (6.2%)

Counts

4 → 12

Calls

4 calls:

407.0ms	(/.f64 (.f64 y (+.f64 0 b)) (+.f64 (.f64 (+.f64 (.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z) 2737158995491925/4503599627370496))
61.0ms	(*.f64 (+.f64 z 4288183283079449/281474976710656) z)
36.0ms	(.f64 (+.f64 (.f64 (+.f64 (*.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z) 3360836715704971/281474976710656) z)
26.0ms	(.f64 (+.f64 (.f64 (+.f64 z 4288183283079449/281474976710656) z) 4428869650076171/140737488355328) z)

simplify68.0ms (0.8%)

Algorithm

1×	egg-herbie

Counts

98 → 98

Iterations

Useful iterations: 0 (43.0ms)

Iter	Nodes	Cost
0	4897	2055
1	4897	2055

prune258.0ms (3%)

Pruning

8 alts after pruning (8 fresh and 0 done)

	Pruned	Kept	Total
New	97	1	98
Fresh	0	7	7
Picked	1	0	1
Done	0	0	0
Total	98	8	106

Merged error: 0.0b

Counts

106 → 8

Compiler

Compiled 5609 to 4201 computations (25.1% saved)

localize14.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.0b	(.f64 z (+.f64 (.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656))
0.0b	(.f64 z (+.f64 (.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328))
1.4b	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496) b)
2.7b	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496) b))

rewrite81.0ms (0.9%)

Algorithm

1×	rewrite-expression-head

Rules

84×	`times-frac_binary64`
62×	`add-sqr-sqrt_binary64`
58×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
16×	`associate-/r*_binary64`
15×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`pow1_binary64`
6×	`associate-r_binary64` `associate-l_binary64` `associate-/l*_binary64` `div-inv_binary64`
4×	`add-log-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `div-exp_binary64`
3×	`flip3-+_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `cbrt-unprod_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `*-commutative_binary64`
1×	`associate-/r/_binary64`

Counts

4 → 143

Calls

4 calls:

21.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496) b)
16.0ms	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496) b))
14.0ms	(.f64 z (+.f64 (.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656))
12.0ms	(.f64 z (+.f64 (.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328))

series446.0ms (5.2%)

Counts

4 → 12

Calls

4 calls:

313.0ms	(/.f64 y (/.f64 (+.f64 (.f64 z (+.f64 (.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496) b))
73.0ms	(/.f64 (+.f64 (.f64 z (+.f64 (.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656)) 2737158995491925/4503599627370496) b)
33.0ms	(.f64 z (+.f64 (.f64 z (+.f64 (*.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328)) 3360836715704971/281474976710656))
26.0ms	(.f64 z (+.f64 (.f64 z (+.f64 z 4288183283079449/281474976710656)) 4428869650076171/140737488355328))

simplify115.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

155 → 155

Iterations

Useful iterations: 0 (59.0ms)

Iter	Nodes	Cost
0	4938	5640
1	4938	5640

prune296.0ms (3.4%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	155	0	155
Fresh	0	7	7
Picked	0	1	1
Done	0	0	0
Total	155	8	163

Merged error: 0.0b

Counts

163 → 8

Compiler

Compiled 6136 to 4208 computations (31.4% 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 (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

7×	`pow1_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64`
3×	`pow-prod-down_binary64` `-un-lft-identity_binary64` `cbrt-unprod_binary64` `associate-r*_binary64` `add-cube-cbrt_binary64` `prod-exp_binary64` `add-sqr-sqrt_binary64`
1×	`flip3-+_binary64` `associate-l_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64` `*-commutative_binary64`

Counts

2 → 29

Calls

2 calls:

6.0ms	(.f64 (.f64 y b) 4503599627370496/2737158995491925)
4.0ms	(+.f64 x (.f64 (.f64 y b) 4503599627370496/2737158995491925))

series95.0ms (1.1%)

Counts

2 → 6

Calls

2 calls:

63.0ms	(+.f64 x (.f64 (.f64 y b) 4503599627370496/2737158995491925))
32.0ms	(.f64 (.f64 y b) 4503599627370496/2737158995491925)

simplify97.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

35 → 35

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4766	381
1	4766	381

prune157.0ms (1.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	35	0	35
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	35	8	43

Merged error: 0.0b

Counts

43 → 8

Compiler

Compiled 3369 to 2628 computations (22% saved)

regimes374.0ms (4.4%)

Compiler: Compiled 2520 to 2070 computations (17.9% saved)

bsearch83.0ms (1%)

Steps

Iters	Range		Point
9	7.865682598617256e+51	3.666770787434822e+59	4.171617838415009e+58
9	-1.2419353201447695e+18	-15920181451230.178	-1.2236199774931236e+18

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	67	111
1	67	111

end0.0ms (0%)

sample1.5s (17.9%)

Algorithm

1×

intervals

Results

752.0ms	8000×	body	128	valid
83.0ms	850×	body	128	invalid

Compiler

Compiled 610 to 478 computations (21.6% saved)

Details

analyze2.0s (23.7%)

sample39.0ms (0.5%)

simplify121.0ms (1.4%)

prune4.0ms (0%)

localize30.0ms (0.4%)

rewrite87.0ms (1%)

series1.3s (15.6%)

simplify92.0ms (1.1%)

prune584.0ms (6.8%)

localize15.0ms (0.2%)

rewrite63.0ms (0.7%)

series530.0ms (6.2%)

simplify68.0ms (0.8%)

prune258.0ms (3%)

localize14.0ms (0.2%)

rewrite81.0ms (0.9%)

series446.0ms (5.2%)

simplify115.0ms (1.3%)

prune296.0ms (3.4%)

localize5.0ms (0.1%)

rewrite11.0ms (0.1%)

series95.0ms (1.1%)

simplify97.0ms (1.1%)

prune157.0ms (1.8%)

regimes374.0ms (4.4%)

bsearch83.0ms (1%)

simplify3.0ms (0%)

end0.0ms (0%)

sample1.5s (17.9%)

Profiling