Details

analyze705.0ms (12.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	99.9%	0.1%	0
0%	99.9%	0.1%	1
0%	99.9%	0.1%	2
0%	99.9%	0.1%	3
0%	99.9%	0.1%	4
0%	99.9%	0.1%	5
12.5%	87.4%	0.1%	6
20.3%	73.3%	6.4%	7
27.3%	66.3%	6.4%	8
38.2%	53%	8.7%	9
46%	40.6%	13.4%	10
49.9%	35.1%	15%	11
54.9%	26.9%	18.1%	12
57.4%	22%	20.6%	13
59.7%	18%	22.4%	14

Compiler

Compiled 39 to 27 computations (30.8% saved)

sample37.0ms (0.6%)

Algorithm

1×

intervals

Results

22.0ms	256×	body	128	valid
1.0ms	12×	body	128	nan
1.0ms	10×	body	128	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify266.0ms (4.6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	1224	54
1	1224	54

prune11.0ms (0.2%)

Pruning

1 alts after pruning (1 fresh and 0 done)

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

Merged error: 20.8b

Counts

2 → 1

Compiler

Compiled 146 to 101 computations (30.8% saved)

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

1.0b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
1.5b	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite26.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`*-un-lft-identity_binary64` `add-log-exp_binary64` `add-sqr-sqrt_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64` `sqrt-prod_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-div_binary64`
3×	`flip3--_binary64` `flip--_binary64`
2×	`pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`flip3-+_binary64` `sub-neg_binary64` `diff-log_binary64` `distribute-lft-out_binary64` `cancel-sign-sub-inv_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 54

Calls

4 calls:

7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
7.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
5.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series445.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

128.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
118.0ms	(+.f64 b (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))
73.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

simplify67.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

66 → 66

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	5234	1295

prune265.0ms (4.5%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	59	7	66
Fresh	0	0	0
Picked	0	1	1
Done	0	0	0
Total	59	8	67

Merged error: 10.1b

Counts

67 → 8

Compiler

Compiled 6191 to 3987 computations (35.6% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

9.0b	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite20.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

10×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
7×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`pow1/2_binary64` `flip3--_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `flip--_binary64`
1×	`flip3-+_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 56

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
3.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))

series490.0ms (8.4%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(+.f64 b (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
114.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify44.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (27.0ms)

Iter	Nodes	Cost
0	5547	1361

prune145.0ms (2.5%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	68	8	76

Merged error: 10.1b

Counts

76 → 8

Compiler

Compiled 3867 to 2340 computations (39.5% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

10.3b	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite36.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
9×	`sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
7×	`pow1_binary64`
6×	`add-log-exp_binary64` `sqrt-div_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64`
3×	`pow1/2_binary64` `cancel-sign-sub-inv_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `difference-of-squares_binary64`

Counts

4 → 60

Calls

4 calls:

19.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series486.0ms (8.3%)

Counts

4 → 12

Calls

4 calls:

142.0ms	(-.f64 (.f64 (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))) b)
117.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify65.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

72 → 72

Iterations

Useful iterations: 0 (46.0ms)

Iter	Nodes	Cost
0	4976	1417
1	4976	1417

prune176.0ms (3%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	72	0	72
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	72	8	80

Merged error: 10.1b

Counts

80 → 8

Compiler

Compiled 4393 to 2682 computations (38.9% saved)

localize27.0ms (0.5%)

Local error

Found 4 expressions with local error:

6.6b	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
23.8b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.6b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite19.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

8×	`add-sqr-sqrt_binary64`
7×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64`
6×	`add-log-exp_binary64` `cbrt-prod_binary64`
5×	`pow1_binary64`
4×	`cbrt-div_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64`
3×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
2×	`pow1/3_binary64` `sqrt-div_binary64`
1×	`flip3-+_binary64` `pow1/2_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `+-commutative_binary64` `flip-+_binary64` `sum-log_binary64`

Counts

4 → 52

Calls

4 calls:

5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
5.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
3.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))

series690.0ms (11.8%)

Counts

4 → 12

Calls

4 calls:

219.0ms	(+.f64 b (.f64 (fabs.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (.f64 4 a))))) (sqrt.f64 (cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))))))
173.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
165.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
133.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify71.0ms (1.2%)

Algorithm

1×	egg-herbie

Counts

64 → 64

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4918	1669
1	4918	1669

prune147.0ms (2.5%)

Pruning

8 alts after pruning (4 fresh and 4 done)

	Pruned	Kept	Total
New	64	0	64
Fresh	0	4	4
Picked	0	1	1
Done	0	3	3
Total	64	8	72

Merged error: 10.1b

Counts

72 → 8

Compiler

Compiled 3616 to 2195 computations (39.3% saved)

regimes161.0ms (2.8%)

Compiler: Compiled 993 to 702 computations (29.3% saved)

bsearch73.0ms (1.2%)

Steps

Iters	Range		Point
8	1.4848892700023645e+146	3.268889869395191e+149	2.468062116429859e+148
8	-2.605817302689682e+157	-1.5872384102599588e+153	-1.3305907505166363e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	137	170
1	137	170

end0.0ms (0%)

sample1.3s (21.9%)

Algorithm

1×

intervals

Results

670.0ms	8000×	body	128	valid
54.0ms	677×	body	128	nan
31.0ms	389×	body	128	invalid

Compiler

Compiled 482 to 329 computations (31.7% saved)

Details

analyze705.0ms (12.1%)

sample37.0ms (0.6%)

simplify266.0ms (4.6%)

prune11.0ms (0.2%)

localize31.0ms (0.5%)

rewrite26.0ms (0.4%)

series445.0ms (7.6%)

simplify67.0ms (1.2%)

prune265.0ms (4.5%)

localize27.0ms (0.5%)

rewrite20.0ms (0.3%)

series490.0ms (8.4%)

simplify44.0ms (0.7%)

prune145.0ms (2.5%)

localize24.0ms (0.4%)

rewrite36.0ms (0.6%)

series486.0ms (8.3%)

simplify65.0ms (1.1%)

prune176.0ms (3%)

localize27.0ms (0.5%)

rewrite19.0ms (0.3%)

series690.0ms (11.8%)

simplify71.0ms (1.2%)

prune147.0ms (2.5%)

regimes161.0ms (2.8%)

bsearch73.0ms (1.2%)

simplify4.0ms (0.1%)

end0.0ms (0%)

sample1.3s (21.9%)

Profiling