Details

analyze605.0ms (5.2%)

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%	74.9%	25.1%	5
0%	74.9%	25.1%	6
0%	74.9%	25.1%	7
6.2%	56.2%	37.6%	8
7.8%	53%	39.2%	9
10.9%	45.6%	43.4%	10
18.3%	31.4%	50.3%	11
19.1%	29.5%	51.3%	12
21.4%	24.8%	53.8%	13
25.8%	16.7%	57.5%	14

Compiler

Compiled 25 to 21 computations (16% saved)

sample35.0ms (0.3%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
3.0ms	35×	body	128	invalid
2.0ms	28×	body	128	nan

Compiler

Compiled 49 to 44 computations (10.2% saved)

simplify577.0ms (5%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (383.0ms)

Iter	Nodes	Cost
0	5077	36

prune3.0ms (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: 5.4b

Counts

2 → 1

Compiler

Compiled 48 to 40 computations (16.7% saved)

localize18.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.1b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.2b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite66.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_13377` `add-sqr-sqrt_binary64_13399`
22×	`add-cube-cbrt_binary64_13412`
18×	`log-prod_binary64_13463`
12×	`associate--l+_binary64_13314`
11×	`add-log-exp_binary64_13416`
10×	`associate-+l+_binary64_13310`
9×	`distribute-rgt-in_binary64_13327` `times-frac_binary64_13383` `distribute-lft-in_binary64_13326`
8×	`add-exp-log_binary64_13415` `add-cbrt-cube_binary64_13413`
7×	`pow1_binary64_13438`
6×	`cancel-sign-sub-inv_binary64_13343`
5×	`associate-l_binary64_13318`
4×	`associate-r_binary64_13317`
3×	`associate-/r_binary64_13321` `associate-/l_binary64_13322`
2×	`diff-log_binary64_13469` `associate-/l/_binary64_13324` `sum-log_binary64_13468` `associate-*l/_binary64_13320` `flip3--_binary64_13381` `flip--_binary64_13352` `flip-+_binary64_13351` `sub-neg_binary64_13370` `flip3-+_binary64_13380`
1×	`prod-exp_binary64_13426` `+-commutative_binary64_13307` `associate-+l-_binary64_13312` `div-inv_binary64_13374` `clear-num_binary64_13376` `distribute-lft-out--_binary64_13329` `cbrt-unprod_binary64_13410` `unswap-sqr_binary64_13345` `difference-of-squares_binary64_13346` `pow-prod-down_binary64_13448` `*-commutative_binary64_13308` `distribute-lft-out_binary64_13328` `div-exp_binary64_13428` `log-pow_binary64_13466` `cbrt-undiv_binary64_13411` `frac-2neg_binary64_13388`

Counts

4 → 102

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
13.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
9.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
9.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

series1.2s (10.8%)

Counts

4 → 12

Calls

4 calls:

469.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
351.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
234.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
192.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify74.0ms (0.6%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4940	2164
1	4940	2164

prune269.0ms (2.3%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	102	12	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	103	12	115

Merged error: 3.5b

Counts

115 → 12

Compiler

Compiled 3993 to 2724 computations (31.8% saved)

localize45.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.3b	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite64.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`log-prod_binary64_13463`
30×	`distribute-rgt-in_binary64_13327` `distribute-lft-in_binary64_13326`
26×	`add-cube-cbrt_binary64_13412` `*-un-lft-identity_binary64_13377` `add-sqr-sqrt_binary64_13399`
24×	`cbrt-prod_binary64_13408` `associate-+l+_binary64_13310`
12×	`associate-+r+_binary64_13309`
9×	`times-frac_binary64_13383`
8×	`associate-*l/_binary64_13320`
6×	`add-log-exp_binary64_13416` `add-exp-log_binary64_13415` `add-cbrt-cube_binary64_13413`
4×	`pow1_binary64_13438` `flip3--_binary64_13381` `flip--_binary64_13352` `frac-add_binary64_13385`
3×	`associate-/r_binary64_13321` `associate-/l_binary64_13322`
2×	`associate-/l/_binary64_13324` `pow1/3_binary64_13459` `flip-+_binary64_13351` `flip3-+_binary64_13380`
1×	`+-commutative_binary64_13307` `div-inv_binary64_13374` `clear-num_binary64_13376` `sum-log_binary64_13468` `distribute-lft-out_binary64_13328` `div-exp_binary64_13428` `cbrt-undiv_binary64_13411` `frac-2neg_binary64_13388`

Counts

4 → 103

Calls

4 calls:

30.0ms	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
1.0ms	(cbrt.f64 x)
1.0ms	(cbrt.f64 x)

series1.5s (12.8%)

Counts

4 → 12

Calls

4 calls:

955.0ms	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
189.0ms	(cbrt.f64 x)
180.0ms	(cbrt.f64 x)
163.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify119.0ms (1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (77.0ms)

Iter	Nodes	Cost
0	4885	2171
1	4885	2171

prune331.0ms (2.9%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	115	12	127

Merged error: 3.5b

Counts

127 → 12

Compiler

Compiled 5043 to 3294 computations (34.7% saved)

localize46.0ms (0.4%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)
0.2b	(+.f64 2069265617858471/2251799813685248 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x))
0.3b	(+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (+.f64 2069265617858471/2251799813685248 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)))
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite93.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_13377`
24×	`add-cube-cbrt_binary64_13412` `log-prod_binary64_13463` `associate--l+_binary64_13314` `add-sqr-sqrt_binary64_13399`
20×	`add-log-exp_binary64_13416`
17×	`associate-+r+_binary64_13309`
16×	`distribute-rgt-in_binary64_13327` `distribute-lft-in_binary64_13326`
12×	`sqrt-prod_binary64_13393` `cancel-sign-sub-inv_binary64_13343`
9×	`times-frac_binary64_13383`
8×	`associate-+l+_binary64_13310`
7×	`sum-log_binary64_13468`
6×	`add-exp-log_binary64_13415` `add-cbrt-cube_binary64_13413`
5×	`flip-+_binary64_13351` `flip3-+_binary64_13380`
4×	`pow1_binary64_13438` `frac-add_binary64_13385` `associate-*r/_binary64_13319` `sub-neg_binary64_13370`
3×	`diff-log_binary64_13469` `associate-+r-_binary64_13311` `associate-/r_binary64_13321` `flip3--_binary64_13381` `flip--_binary64_13352` `associate-/l_binary64_13322`
2×	`+-commutative_binary64_13307` `associate-/l/_binary64_13324`
1×	`div-inv_binary64_13374` `clear-num_binary64_13376` `distribute-lft-out_binary64_13328` `div-exp_binary64_13428` `cbrt-undiv_binary64_13411` `frac-2neg_binary64_13388`

Counts

4 → 112

Calls

4 calls:

31.0ms	(+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (+.f64 2069265617858471/2251799813685248 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)))
21.0ms	(+.f64 2069265617858471/2251799813685248 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x))
14.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
10.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)

series515.0ms (4.4%)

Counts

4 → 12

Calls

4 calls:

205.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
118.0ms	(+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (+.f64 2069265617858471/2251799813685248 (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)))
100.0ms	(+.f64 2069265617858471/2251799813685248 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x))
92.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)

simplify111.0ms (1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (55.0ms)

Iter	Nodes	Cost
0	4978	3561
1	4978	3561

prune354.0ms (3.1%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	10	10
Picked	0	1	1
Done	0	1	1
Total	124	12	136

Merged error: 3.5b

Counts

136 → 12

Compiler

Compiled 5766 to 3597 computations (37.6% saved)

localize21.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
0.2b	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.3b	(/.f64 1 (/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936)))
5.0b	(/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936))

rewrite113.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

90×	`times-frac_binary64_13383`
64×	`*-un-lft-identity_binary64_13377`
62×	`add-cube-cbrt_binary64_13412` `add-sqr-sqrt_binary64_13399`
18×	`associate-/r*_binary64_13321`
17×	`add-exp-log_binary64_13415`
12×	`log-prod_binary64_13463` `associate--l+_binary64_13314`
11×	`add-log-exp_binary64_13416` `associate-/r/_binary64_13323` `add-cbrt-cube_binary64_13413`
10×	`associate-+l+_binary64_13310`
8×	`div-exp_binary64_13428`
6×	`distribute-rgt-in_binary64_13327` `div-inv_binary64_13374` `distribute-lft-in_binary64_13326` `flip-+_binary64_13351` `associate-/l*_binary64_13322` `flip3-+_binary64_13380` `cancel-sign-sub-inv_binary64_13343`
5×	`pow1_binary64_13438`
4×	`cbrt-undiv_binary64_13411`
2×	`diff-log_binary64_13469` `clear-num_binary64_13376` `sum-log_binary64_13468` `rec-exp_binary64_13427` `1-exp_binary64_13421` `frac-2neg_binary64_13388` `sub-neg_binary64_13370`
1×	`+-commutative_binary64_13307` `associate-+l-_binary64_13312` `pow-flip_binary64_13451` `inv-pow_binary64_13462` `distribute-lft-out_binary64_13328` `flip3--_binary64_13381` `flip--_binary64_13352`

Counts

4 → 157

Calls

4 calls:

32.0ms	(/.f64 1 (/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936)))
26.0ms	(/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936))
21.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
9.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)

series1.3s (10.9%)

Counts

4 → 12

Calls

4 calls:

373.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
370.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
310.0ms	(/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936))
208.0ms	(/.f64 1 (/.f64 x (+.f64 (.f64 z (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976)) 6004799503160637/72057594037927936)))

simplify161.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

169 → 169

Iterations

Useful iterations: 0 (85.0ms)

Iter	Nodes	Cost
0	4957	4912
1	4957	4912

prune429.0ms (3.7%)

Pruning

12 alts after pruning (10 fresh and 2 done)

	Pruned	Kept	Total
New	166	3	169
Fresh	2	7	9
Picked	1	0	1
Done	0	2	2
Total	169	12	181

Merged error: 2.4b

Counts

181 → 12

Compiler

Compiled 6247 to 4328 computations (30.7% saved)

regimes1.0s (8.7%)

Compiler: Compiled 10285 to 8095 computations (21.3% saved)

bsearch3.0ms (0%)

Compiler: Compiled 9 to 9 computations (0% saved)

simplify5.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	119	96
1	119	96

end0.0ms (0%)

sample2.5s (21.7%)

Algorithm

1×

intervals

Results

732.0ms	8000×	body	128	valid
121.0ms	1253×	body	128	invalid
60.0ms	739×	body	128	nan

Compiler

Compiled 1374 to 1082 computations (21.3% saved)

Details

analyze605.0ms (5.2%)

sample35.0ms (0.3%)

simplify577.0ms (5%)

prune3.0ms (0%)

localize18.0ms (0.2%)

rewrite66.0ms (0.6%)

series1.2s (10.8%)

simplify74.0ms (0.6%)

prune269.0ms (2.3%)

localize45.0ms (0.4%)

rewrite64.0ms (0.6%)

series1.5s (12.8%)

simplify119.0ms (1%)

prune331.0ms (2.9%)

localize46.0ms (0.4%)

rewrite93.0ms (0.8%)

series515.0ms (4.4%)

simplify111.0ms (1%)

prune354.0ms (3.1%)

localize21.0ms (0.2%)

rewrite113.0ms (1%)

series1.3s (10.9%)

simplify161.0ms (1.4%)

prune429.0ms (3.7%)

regimes1.0s (8.7%)

bsearch3.0ms (0%)

simplify5.0ms (0%)

end0.0ms (0%)

sample2.5s (21.7%)

Profiling