Details

analyze447.0ms (8.7%)

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
12.5%	87.4%	0.1%	5
18.7%	81.1%	0.1%	6
21.8%	71.8%	6.4%	7
31.2%	62.4%	6.4%	8
35.9%	55.4%	8.7%	9
37.8%	48.8%	13.4%	10
42.7%	42.3%	15%	11
47.7%	34.2%	18.1%	12
49.1%	30.4%	20.5%	13
51.9%	25.8%	22.3%	14

Compiler

Compiled 18 to 15 computations (16.7% saved)

sample41.0ms (0.8%)

Algorithm

1×

intervals

Results

9.0ms	171×	body	128	valid
7.0ms	26×	body	2048	valid
5.0ms	16×	body	4096	valid
5.0ms	25×	body	1024	valid
4.0ms	12×	body	512	valid
1.0ms	21×	body	128	nan
1.0ms	15×	body	128	invalid
1.0ms	6×	body	256	valid

Compiler

Compiled 35 to 32 computations (8.6% saved)

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	927	24
1	927	24

prune4.0ms (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: 33.5b

Counts

2 → 1

Compiler

Compiled 32 to 26 computations (18.8% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite36.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`add-sqr-sqrt_binary64`
13×	`*-un-lft-identity_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`add-cube-cbrt_binary64`
6×	`difference-of-squares_binary64` `associate-/l*_binary64` `times-frac_binary64` `sqrt-prod_binary64`
5×	`pow1_binary64`
4×	`flip3--_binary64` `flip--_binary64`
3×	`distribute-lft-out--_binary64`
2×	`associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `div-exp_binary64` `sqrt-div_binary64`
1×	`associate-/r*_binary64` `pow1/2_binary64` `cbrt-unprod_binary64` `sqrt-pow1_binary64` `div-sub_binary64` `rem-sqrt-square_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `div-inv_binary64`

Counts

4 → 70

Calls

4 calls:

12.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series506.0ms (9.8%)

Counts

4 → 12

Calls

4 calls:

200.0ms	(/.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (.f64 a 2))
123.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
121.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
63.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify70.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

82 → 82

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4930	1975
1	4930	1975

prune130.0ms (2.5%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	71	11	82
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	72	11	83

Merged error: 7.0b

Counts

83 → 11

Compiler

Compiled 2172 to 1202 computations (44.7% saved)

localize10.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))
0.2b	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite42.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

27×	`add-sqr-sqrt_binary64`
17×	`*-un-lft-identity_binary64`
13×	`associate-r_binary64` `add-cube-cbrt_binary64`
10×	`times-frac_binary64`
9×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
8×	`add-log-exp_binary64`
7×	`pow1_binary64`
6×	`associate-l_binary64`
5×	`flip3--_binary64` `flip--_binary64` `sqrt-prod_binary64`
4×	`difference-of-squares_binary64`
2×	`sub-neg_binary64` `diff-log_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `distribute-lft-out--_binary64` `frac-times_binary64` `sqrt-div_binary64` `associate-*l/_binary64`
1×	`pow-prod-down_binary64` `pow1/2_binary64` `cbrt-undiv_binary64` `associate-r/_binary64` `sqrt-pow1_binary64` `rem-sqrt-square_binary64` `div-inv_binary64` `div-exp_binary64` `-commutative_binary64`

Counts

4 → 79

Calls

4 calls:

17.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
4.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

series524.0ms (10.2%)

Counts

4 → 12

Calls

4 calls:

206.0ms	(.f64 (-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (.f64 a c)))) b) (/.f64 1/2 a))
132.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
121.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
64.0ms	(-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))

simplify55.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

91 → 91

Iterations

Useful iterations: 0 (34.0ms)

Iter	Nodes	Cost
0	4995	2223
1	4995	2223

prune106.0ms (2%)

Pruning

9 alts after pruning (8 fresh and 1 done)

	Pruned	Kept	Total
New	89	2	91
Fresh	4	6	10
Picked	0	1	1
Done	0	0	0
Total	93	9	102

Merged error: 7.0b

Counts

102 → 9

Compiler

Compiled 2321 to 1269 computations (45.3% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
23.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite35.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 58

Calls

4 calls:

9.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
7.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

series475.0ms (9.2%)

Counts

4 → 12

Calls

4 calls:

126.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
124.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
113.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
112.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

simplify69.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

70 → 70

Iterations

Useful iterations: 0 (52.0ms)

Iter	Nodes	Cost
0	5072	1536

prune109.0ms (2.1%)

Pruning

9 alts after pruning (7 fresh and 2 done)

	Pruned	Kept	Total
New	70	0	70
Fresh	0	7	7
Picked	0	1	1
Done	0	1	1
Total	70	9	79

Merged error: 7.0b

Counts

79 → 9

Compiler

Compiled 2785 to 1509 computations (45.8% saved)

localize16.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 a)
0.6b	(cbrt.f64 a)
1.2b	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
23.1b	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))

rewrite21.0ms (0.4%)

Algorithm

1×	rewrite-expression-head

Rules

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

Counts

4 → 51

Calls

4 calls:

8.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)
5.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
1.0ms	(cbrt.f64 a)
1.0ms	(cbrt.f64 a)

series568.0ms (11%)

Counts

4 → 12

Calls

4 calls:

161.0ms	(cbrt.f64 a)
158.0ms	(cbrt.f64 a)
126.0ms	(sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c))))
123.0ms	(-.f64 (sqrt.f64 (-.f64 (.f64 b b) (.f64 4 (*.f64 a c)))) b)

simplify83.0ms (1.6%)

Algorithm

1×	egg-herbie

Counts

63 → 63

Iterations

Useful iterations: 0 (70.0ms)

Iter	Nodes	Cost
0	4803	938
1	4803	938

prune87.0ms (1.7%)

Pruning

10 alts after pruning (7 fresh and 3 done)

	Pruned	Kept	Total
New	62	1	63
Fresh	0	6	6
Picked	0	1	1
Done	0	2	2
Total	62	10	72

Merged error: 7.0b

Counts

72 → 10

Compiler

Compiled 2026 to 1037 computations (48.8% saved)

regimes150.0ms (2.9%)

Compiler: Compiled 642 to 471 computations (26.6% saved)

bsearch39.0ms (0.7%)

Steps

Iters	Range		Point
6	7.67427418572736e-104	3.2024989368253016e-103	1.334581102480234e-103
5	-7.759370691277719e+56	-2.4813958126622977e+56	-7.6543743217375666e+56

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	52
1	93	52

end0.0ms (0%)

sample1.4s (27.9%)

Algorithm

1×

intervals

Results

291.0ms	1141×	body	2048	valid
271.0ms	5165×	body	128	valid
147.0ms	746×	body	1024	valid
131.0ms	406×	body	4096	valid
54.0ms	358×	body	512	valid
36.0ms	646×	body	128	nan
23.0ms	394×	body	128	invalid
18.0ms	184×	body	256	valid

Compiler

Compiled 307 to 219 computations (28.7% saved)

Details

analyze447.0ms (8.7%)

sample41.0ms (0.8%)

simplify69.0ms (1.3%)

prune4.0ms (0.1%)

localize10.0ms (0.2%)

rewrite36.0ms (0.7%)

series506.0ms (9.8%)

simplify70.0ms (1.4%)

prune130.0ms (2.5%)

localize10.0ms (0.2%)

rewrite42.0ms (0.8%)

series524.0ms (10.2%)

simplify55.0ms (1.1%)

prune106.0ms (2%)

localize13.0ms (0.3%)

rewrite35.0ms (0.7%)

series475.0ms (9.2%)

simplify69.0ms (1.3%)

prune109.0ms (2.1%)

localize16.0ms (0.3%)

rewrite21.0ms (0.4%)

series568.0ms (11%)

simplify83.0ms (1.6%)

prune87.0ms (1.7%)

regimes150.0ms (2.9%)

bsearch39.0ms (0.7%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.4s (27.9%)

Profiling