Details

analyze4.0ms (0.1%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
0%	100%	0%	3
75%	25%	0%	4
87.5%	12.5%	0%	5
93.7%	6.2%	0%	6
96.8%	3.1%	0%	7
98.4%	1.6%	0%	8
99.2%	0.8%	0%	9
99.6%	0.4%	0%	10
99.8%	0.2%	0%	11
99.9%	0.1%	0%	12
99.9%	0%	0%	13
99.9%	0%	0%	14

Compiler

Compiled 14 to 11 computations (21.4% saved)

sample23.0ms (0.5%)

Algorithm

1×

intervals

Results

9.0ms	72×	body	1024	valid
4.0ms	131×	body	128	valid
3.0ms	32×	body	512	valid
1.0ms	16×	body	256	valid
1.0ms	5×	body	2048	valid

Compiler

Compiled 27 to 22 computations (18.5% saved)

simplify73.0ms (1.5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (67.0ms)

Iter	Nodes	Cost
0	668	19
1	668	19

prune2.0ms (0%)

Pruning

2 alts after pruning (2 fresh and 0 done)

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

Merged error: 30.3b

Counts

2 → 1

Compiler

Compiled 26 to 20 computations (23.1% saved)

localize10.0ms (0.2%)

Local error

Found 3 expressions with local error:

0.0b	(/.f64 x (+.f64 x 1))
0.0b	(/.f64 (+.f64 x 1) (-.f64 x 1))
2.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite66.0ms (1.4%)

Algorithm

1×	rewrite-expression-head

Rules

110×	`*-un-lft-identity_binary64`
60×	`times-frac_binary64`
57×	`add-sqr-sqrt_binary64`
25×	`add-cube-cbrt_binary64`
20×	`distribute-lft-out_binary64`
18×	`distribute-lft-out--_binary64`
14×	`difference-of-squares_binary64`
11×	`associate-/r*_binary64`
7×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `associate-/l*_binary64`
5×	`add-log-exp_binary64` `difference-of-sqr-1_binary64`
4×	`associate-/r/_binary64`
3×	`pow1_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `flip3--_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip--_binary64` `flip-+_binary64`
1×	`sub-neg_binary64` `diff-log_binary64` `frac-sub_binary64`

Counts

3 → 113

Calls

3 calls:

40.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
9.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
6.0ms	(/.f64 x (+.f64 x 1))

series130.0ms (2.7%)

Counts

3 → 9

Calls

3 calls:

78.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
27.0ms	(/.f64 (+.f64 x 1) (-.f64 x 1))
25.0ms	(/.f64 x (+.f64 x 1))

simplify83.0ms (1.7%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (60.0ms)

Iter	Nodes	Cost
0	5943	2299

prune166.0ms (3.5%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	119	3	122
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	120	3	123

Merged error: 0.0b

Counts

123 → 3

Compiler

Compiled 2544 to 1816 computations (28.6% saved)

localize13.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
2.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite189.0ms (3.9%)

Algorithm

1×	rewrite-expression-head

Rules

189×	`*-un-lft-identity_binary64`
80×	`times-frac_binary64`
53×	`add-sqr-sqrt_binary64`
52×	`distribute-lft-out--_binary64`
32×	`distribute-lft-out_binary64`
16×	`difference-of-squares_binary64` `cbrt-prod_binary64`
10×	`add-log-exp_binary64`
5×	`add-cube-cbrt_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `frac-sub_binary64`
3×	`cbrt-div_binary64` `sub-neg_binary64` `diff-log_binary64`
1×	`pow1/3_binary64`

Counts

4 → 102

Calls

4 calls:

44.0ms	(cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
44.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
41.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
40.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series340.0ms (7.1%)

Counts

4 → 12

Calls

4 calls:

115.0ms	(cbrt.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))))
77.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
74.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
72.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify104.0ms (2.2%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (73.0ms)

Iter	Nodes	Cost
0	4837	3315
1	4837	3315

prune328.0ms (6.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	113	1	114
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	114	3	117

Merged error: 0.0b

Counts

117 → 3

Compiler

Compiled 6097 to 4501 computations (26.2% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(cbrt.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) 3)))
2.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite203.0ms (4.2%)

Algorithm

1×	rewrite-expression-head

Rules

238×	`*-un-lft-identity_binary64`
100×	`times-frac_binary64`
79×	`cbrt-prod_binary64`
68×	`add-sqr-sqrt_binary64`
65×	`distribute-lft-out--_binary64`
40×	`distribute-lft-out_binary64`
20×	`difference-of-squares_binary64`
16×	`unpow-prod-down_binary64` `cube-prod_binary64`
10×	`add-log-exp_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `frac-sub_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `cube-div_binary64`
1×	`pow1/3_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 127

Calls

4 calls:

50.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) 3)))
46.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
40.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
40.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series344.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

119.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) 3)))
77.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
76.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
72.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify94.0ms (2%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (57.0ms)

Iter	Nodes	Cost
0	4944	4288
1	4944	4288

prune470.0ms (9.8%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	138	1	139
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	139	3	142

Merged error: 0b

Counts

142 → 3

Compiler

Compiled 7758 to 5818 computations (25% saved)

localize17.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(cbrt.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) 3)))
2.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
2.5b	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

rewrite204.0ms (4.3%)

Algorithm

1×	rewrite-expression-head

Rules

238×	`*-un-lft-identity_binary64`
100×	`times-frac_binary64`
79×	`cbrt-prod_binary64`
68×	`add-sqr-sqrt_binary64`
65×	`distribute-lft-out--_binary64`
40×	`distribute-lft-out_binary64`
20×	`difference-of-squares_binary64`
16×	`unpow-prod-down_binary64` `cube-prod_binary64`
10×	`add-log-exp_binary64`
8×	`add-cube-cbrt_binary64`
6×	`cbrt-div_binary64`
4×	`pow1_binary64` `flip3--_binary64` `add-exp-log_binary64` `add-cbrt-cube_binary64` `flip--_binary64` `frac-sub_binary64`
3×	`sub-neg_binary64` `diff-log_binary64` `cube-div_binary64`
1×	`pow1/3_binary64` `sqr-pow_binary64` `unpow3_binary64` `cube-mult_binary64`

Counts

4 → 127

Calls

4 calls:

50.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) 3)))
44.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
41.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
40.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

series343.0ms (7.2%)

Counts

4 → 12

Calls

4 calls:

125.0ms	(cbrt.f64 (cbrt.f64 (pow.f64 (-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1))) 3)))
78.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
71.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))
69.0ms	(-.f64 (/.f64 x (+.f64 x 1)) (/.f64 (+.f64 x 1) (-.f64 x 1)))

simplify94.0ms (2%)

Algorithm

1×	egg-herbie

Counts

139 → 139

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4944	4288
1	4944	4288

prune530.0ms (11.1%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	139	0	139
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	139	3	142

Merged error: 0b

Counts

142 → 3

Compiler

Compiled 8103 to 6178 computations (23.8% saved)

regimes36.0ms (0.7%)

Compiler: Compiled 172 to 136 computations (20.9% saved)

bsearch55.0ms (1.2%)

Steps

Iters	Range		Point
9	125.32574934483407	83589579.36537166	10387.839376272022
11	-1.0362073982929842e+37	-6.2036275457540695	-13373.10811093312

Compiler

Compiled 1 to 1 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	93	133
1	93	133

end0.0ms (0%)

sample849.0ms (17.7%)

Algorithm

1×

intervals

Results

246.0ms	1986×	body	1024	valid
152.0ms	4292×	body	128	valid
94.0ms	1004×	body	512	valid
36.0ms	230×	body	2048	valid
31.0ms	488×	body	256	valid

Compiler

Compiled 174 to 135 computations (22.4% saved)

Details

analyze4.0ms (0.1%)

sample23.0ms (0.5%)

simplify73.0ms (1.5%)

prune2.0ms (0%)

localize10.0ms (0.2%)

rewrite66.0ms (1.4%)

series130.0ms (2.7%)

simplify83.0ms (1.7%)

prune166.0ms (3.5%)

localize13.0ms (0.3%)

rewrite189.0ms (3.9%)

series340.0ms (7.1%)

simplify104.0ms (2.2%)

prune328.0ms (6.8%)

localize17.0ms (0.4%)

rewrite203.0ms (4.2%)

series344.0ms (7.2%)

simplify94.0ms (2%)

prune470.0ms (9.8%)

localize17.0ms (0.4%)

rewrite204.0ms (4.3%)

series343.0ms (7.2%)

simplify94.0ms (2%)

prune530.0ms (11.1%)

regimes36.0ms (0.7%)

bsearch55.0ms (1.2%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample849.0ms (17.7%)

Profiling