Details

analyze528.0ms (8.3%)

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)

sample38.0ms (0.6%)

Algorithm

1×

intervals

Results

23.0ms	256×	body	80	valid
1.0ms	17×	body	80	nan
1.0ms	8×	body	80	invalid

Compiler

Compiled 77 to 56 computations (27.3% saved)

simplify253.0ms (4%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	1225	54
1	1225	54

prune9.0ms (0.1%)

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: 20.1b

Counts

2 → 1

Compiler

Compiled 72 to 50 computations (30.6% saved)

localize24.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.8b	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
0.9b	(-.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))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite225.0ms (3.5%)

Algorithm

1×	rewrite-expression-head

Rules

12×	`add-sqr-sqrt_binary64`
8×	`*-un-lft-identity_binary64` `add-log-exp_binary64`
7×	`sqrt-prod_binary64`
6×	`pow1_binary64` `add-cube-cbrt_binary64`
4×	`flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `insert-posit16` `flip--_binary64` `sqrt-div_binary64`
2×	`sub-neg_binary64` `pow1/2_binary64` `diff-log_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `difference-of-squares_binary64`
1×	`distribute-lft-out--_binary64`

Counts

4 → 59

Calls

4 calls:

200.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
11.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
6.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series457.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

140.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
127.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))) b)
125.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
64.0ms	(-.f64 (.f64 b b) (.f64 c (*.f64 4 a)))

simplify112.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

71 → 71

Iterations

Useful iterations: 0 (83.0ms)

Iter	Nodes	Cost
0	4889	1448
1	4889	1448

prune155.0ms (2.4%)

Pruning

7 alts after pruning (7 fresh and 0 done)

	Pruned	Kept	Total
New	64	7	71
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	65	7	72

Merged error: 9.2b

Counts

72 → 7

Compiler

Compiled 3299 to 1995 computations (39.5% saved)

localize30.0ms (0.5%)

Local error

Found 4 expressions with local error:

7.5b	(+.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))))
24.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite24.0ms (0.4%)

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` `insert-posit16`
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 → 56

Calls

4 calls:

6.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
6.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(+.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)))))))

series700.0ms (11%)

Counts

4 → 12

Calls

4 calls:

233.0ms	(+.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)))))))
182.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
170.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
115.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify132.0ms (2.1%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (100.0ms)

Iter	Nodes	Cost
0	4971	1776
1	4971	1776

prune174.0ms (2.7%)

Pruning

8 alts after pruning (7 fresh and 1 done)

	Pruned	Kept	Total
New	67	1	68
Fresh	0	6	6
Picked	0	1	1
Done	0	0	0
Total	67	8	75

Merged error: 9.2b

Counts

75 → 8

Compiler

Compiled 4129 to 2530 computations (38.7% saved)

localize27.0ms (0.4%)

Local error

Found 4 expressions with local error:

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))))
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

12×	`add-sqr-sqrt_binary64` `sqrt-prod_binary64`
8×	`*-un-lft-identity_binary64` `pow1_binary64` `add-cube-cbrt_binary64` `sqrt-div_binary64`
4×	`add-log-exp_binary64` `pow1/2_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `insert-posit16` `flip--_binary64`

Counts

4 → 64

Calls

4 calls:

6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

series483.0ms (7.6%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
124.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
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))))

simplify116.0ms (1.8%)

Algorithm

1×	egg-herbie

Counts

76 → 76

Iterations

Useful iterations: 0 (87.0ms)

Iter	Nodes	Cost
0	4928	1472
1	4928	1472

prune244.0ms (3.8%)

Pruning

8 alts after pruning (6 fresh and 2 done)

	Pruned	Kept	Total
New	76	0	76
Fresh	0	6	6
Picked	0	1	1
Done	0	1	1
Total	76	8	84

Merged error: 9.2b

Counts

84 → 8

Compiler

Compiled 5350 to 3223 computations (39.8% saved)

localize31.0ms (0.5%)

Local error

Found 4 expressions with local error:

16.0b	(+.f64 b (.f64 (fabs.f64 (exp.f64 (log.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))))
24.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
24.5b	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

Compiler

Compiled 765 to 1275 computations (-66.7% saved)

rewrite23.0ms (0.4%)

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` `insert-posit16`
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 → 56

Calls

4 calls:

6.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
6.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
6.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
4.0ms	(+.f64 b (.f64 (fabs.f64 (exp.f64 (log.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)))))))

series674.0ms (10.6%)

Counts

4 → 12

Calls

4 calls:

213.0ms	(+.f64 b (.f64 (fabs.f64 (exp.f64 (log.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)))))))
176.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
174.0ms	(cbrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))
111.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 c (*.f64 4 a))))

simplify129.0ms (2%)

Algorithm

1×	egg-herbie

Counts

68 → 68

Iterations

Useful iterations: 0 (97.0ms)

Iter	Nodes	Cost
0	5014	1776

prune170.0ms (2.7%)

Pruning

8 alts after pruning (5 fresh and 3 done)

	Pruned	Kept	Total
New	68	0	68
Fresh	0	5	5
Picked	0	1	1
Done	0	2	2
Total	68	8	76

Merged error: 9.2b

Counts

76 → 8

Compiler

Compiled 3942 to 2434 computations (38.3% saved)

regimes137.0ms (2.2%)

Compiler: Compiled 1050 to 741 computations (29.4% saved)

bsearch78.0ms (1.2%)

Steps

Iters	Range		Point
7	1.6762673790377155e+148	1.0528540730496156e+150	1.706114356957086e+148
9	-5.895480744837128e+158	-7.147211645958943e+151	-1.3625547103425625e+154

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify9.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (4.0ms)

Iter	Nodes	Cost
0	146	188
1	146	188

end0.0ms (0%)

sample1.4s (21.4%)

Algorithm

1×

intervals

Results

700.0ms	8000×	body	80	valid
57.0ms	656×	body	80	nan
32.0ms	385×	body	80	invalid

Compiler

Compiled 512 to 349 computations (31.8% saved)

Details

analyze528.0ms (8.3%)

sample38.0ms (0.6%)

simplify253.0ms (4%)

prune9.0ms (0.1%)

localize24.0ms (0.4%)

rewrite225.0ms (3.5%)

series457.0ms (7.2%)

simplify112.0ms (1.8%)

prune155.0ms (2.4%)

localize30.0ms (0.5%)

rewrite24.0ms (0.4%)

series700.0ms (11%)

simplify132.0ms (2.1%)

prune174.0ms (2.7%)

localize27.0ms (0.4%)

rewrite26.0ms (0.4%)

series483.0ms (7.6%)

simplify116.0ms (1.8%)

prune244.0ms (3.8%)

localize31.0ms (0.5%)

rewrite23.0ms (0.4%)

series674.0ms (10.6%)

simplify129.0ms (2%)

prune170.0ms (2.7%)

regimes137.0ms (2.2%)

bsearch78.0ms (1.2%)

simplify9.0ms (0.1%)

end0.0ms (0%)

sample1.4s (21.4%)

Profiling