Details

analyze474.0ms (6.2%)

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)

sample33.0ms (0.4%)

Algorithm

1×

intervals

Results

19.0ms	256×	body	128	valid
2.0ms	31×	body	128	invalid
1.0ms	19×	body	128	nan

Compiler

Compiled 49 to 44 computations (10.2% saved)

simplify288.0ms (3.8%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (279.0ms)

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: 5.7b

Counts

2 → 1

Compiler

Compiled 48 to 40 computations (16.7% saved)

localize17.0ms (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 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
0.2b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
5.2b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite55.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
22×	`add-cube-cbrt_binary64`
18×	`log-prod_binary64`
12×	`associate--l+_binary64`
11×	`add-log-exp_binary64`
10×	`associate-+l+_binary64`
9×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `times-frac_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`pow1_binary64`
6×	`cancel-sign-sub-inv_binary64`
5×	`associate-l_binary64`
4×	`associate-r_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `flip--_binary64` `flip-+_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`pow-prod-down_binary64` `cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `log-pow_binary64` `associate-+l-_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `*-commutative_binary64`

Counts

4 → 102

Calls

4 calls:

14.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
9.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

series922.0ms (12.1%)

Counts

4 → 12

Calls

4 calls:

310.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
300.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
163.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
148.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify74.0ms (1%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4953	2164
1	4953	2164

prune857.0ms (11.2%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	103	11	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	104	11	115

Merged error: 3.3b

Counts

115 → 11

Compiler

Compiled 13505 to 10213 computations (24.4% saved)

localize17.0ms (0.2%)

Local error

Found 4 expressions with local error:

0.1b	(.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z)
0.1b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.3b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 x 2069265617858471/2251799813685248))
5.2b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite56.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

30×	`add-sqr-sqrt_binary64`
26×	`*-un-lft-identity_binary64`
22×	`add-cube-cbrt_binary64`
12×	`log-prod_binary64`
10×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
9×	`add-log-exp_binary64` `pow1_binary64` `times-frac_binary64`
8×	`associate-l_binary64` `cancel-sign-sub-inv_binary64` `associate-*l/_binary64`
7×	`flip3--_binary64` `associate-r_binary64` `flip--_binary64`
6×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate--l+_binary64`
4×	`associate--r+_binary64` `frac-sub_binary64`
3×	`associate-/r_binary64` `diff-log_binary64` `associate-/l_binary64`
2×	`pow-prod-down_binary64` `associate-/l/_binary64` `sub-neg_binary64` `cbrt-unprod_binary64` `unswap-sqr_binary64` `prod-exp_binary64` `difference-of-squares_binary64` `distribute-lft-out--_binary64` `*-commutative_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `associate--r-_binary64` `log-pow_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 110

Calls

4 calls:

13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
12.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 x 2069265617858471/2251799813685248))
10.0ms	(.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

series680.0ms (8.9%)

Counts

4 → 12

Calls

4 calls:

309.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) (-.f64 x 2069265617858471/2251799813685248))
165.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
149.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
57.0ms	(.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z)

simplify76.0ms (1%)

Algorithm

1×	egg-herbie

Counts

122 → 122

Iterations

Useful iterations: 0 (45.0ms)

Iter	Nodes	Cost
0	4995	2470
1	4995	2470

prune345.0ms (4.5%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	120	2	122
Fresh	0	10	10
Picked	0	1	1
Done	0	0	0
Total	120	13	133

Merged error: 3.3b

Counts

133 → 13

Compiler

Compiled 7204 to 5239 computations (27.3% saved)

localize20.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.1b	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)) 2069265617858471/2251799813685248)
0.1b	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)
0.2b	(+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x))
5.2b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite81.0ms (1.1%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64`
24×	`log-prod_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64` `associate--l+_binary64`
20×	`add-log-exp_binary64`
16×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64` `associate-+r+_binary64`
12×	`cancel-sign-sub-inv_binary64` `sqrt-prod_binary64`
9×	`associate-+l+_binary64` `times-frac_binary64`
7×	`sum-log_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
5×	`flip3--_binary64` `flip--_binary64`
4×	`sub-neg_binary64` `pow1_binary64` `associate-*r/_binary64` `frac-add_binary64`
3×	`flip3-+_binary64` `associate-/r_binary64` `diff-log_binary64` `associate-/l_binary64` `flip-+_binary64`
2×	`associate-/l/_binary64` `associate-+r-_binary64` `+-commutative_binary64`
1×	`distribute-lft-out_binary64` `cbrt-undiv_binary64` `associate-+l-_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64`

Counts

4 → 112

Calls

4 calls:

20.0ms	(+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x))
19.0ms	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)) 2069265617858471/2251799813685248)
16.0ms	(/.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)

series379.0ms (5%)

Counts

4 → 12

Calls

4 calls:

150.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
84.0ms	(+.f64 (+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)) 2069265617858471/2251799813685248)
74.0ms	(+.f64 (.f64 (log.f64 (sqrt.f64 x)) (-.f64 x 1/2)) (-.f64 (.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x))
71.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 (sqrt.f64 x))) x)

simplify82.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4910	3346
1	4910	3346

prune356.0ms (4.7%)

Pruning

13 alts after pruning (12 fresh and 1 done)

	Pruned	Kept	Total
New	122	2	124
Fresh	1	10	11
Picked	1	0	1
Done	0	1	1
Total	124	13	137

Merged error: 3.3b

Counts

137 → 13

Compiler

Compiled 7710 to 5170 computations (32.9% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (.f64 (-.f64 x 1/2) (+.f64 (log.f64 (sqrt.f64 x)) (.f64 2 (log.f64 (cbrt.f64 (sqrt.f64 x)))))) (-.f64 (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) (-.f64 x 1/2)) x))
0.6b	(cbrt.f64 (sqrt.f64 x))
0.6b	(cbrt.f64 (sqrt.f64 x))
5.2b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite57.0ms (0.8%)

Algorithm

1×	rewrite-expression-head

Rules

19×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
16×	`frac-add_binary64`
14×	`flip3--_binary64` `flip--_binary64`
12×	`associate-+r+_binary64` `cbrt-prod_binary64`
9×	`add-log-exp_binary64` `cancel-sign-sub-inv_binary64` `times-frac_binary64`
8×	`flip3-+_binary64` `flip-+_binary64` `frac-times_binary64` `associate--l+_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64` `sqrt-prod_binary64`
5×	`distribute-lft-in_binary64` `distribute-rgt-in_binary64`
4×	`pow1_binary64` `associate-r/_binary64` `associate-l/_binary64`
3×	`associate-/r_binary64` `sub-neg_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64` `pow1/3_binary64` `associate-+l+_binary64` `sum-log_binary64`
1×	`associate-+r-_binary64` `diff-log_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64`

Counts

4 → 100

Calls

4 calls:

21.0ms	(+.f64 (.f64 (-.f64 x 1/2) (+.f64 (log.f64 (sqrt.f64 x)) (.f64 2 (log.f64 (cbrt.f64 (sqrt.f64 x)))))) (-.f64 (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) (-.f64 x 1/2)) x))
13.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
2.0ms	(cbrt.f64 (sqrt.f64 x))
2.0ms	(cbrt.f64 (sqrt.f64 x))

series511.0ms (6.7%)

Counts

4 → 12

Calls

4 calls:

163.0ms	(+.f64 (.f64 (-.f64 x 1/2) (+.f64 (log.f64 (sqrt.f64 x)) (.f64 2 (log.f64 (cbrt.f64 (sqrt.f64 x)))))) (-.f64 (*.f64 (log.f64 (cbrt.f64 (sqrt.f64 x))) (-.f64 x 1/2)) x))
138.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
118.0ms	(cbrt.f64 (sqrt.f64 x))
92.0ms	(cbrt.f64 (sqrt.f64 x))

simplify87.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

112 → 112

Iterations

Useful iterations: 0 (41.0ms)

Iter	Nodes	Cost
0	4993	5686
1	4993	5686

prune328.0ms (4.3%)

Pruning

14 alts after pruning (12 fresh and 2 done)

	Pruned	Kept	Total
New	111	1	112
Fresh	0	11	11
Picked	0	1	1
Done	0	1	1
Total	111	14	125

Merged error: 3.3b

Counts

125 → 14

Compiler

Compiled 7421 to 4204 computations (43.3% saved)

regimes307.0ms (4%)

Compiler: Compiled 3752 to 2938 computations (21.7% saved)

bsearch15.0ms (0.2%)

Steps

Iters	Range		Point
3	3.03190198401938e+72	4.168272658326166e+72	3.492635277100554e+72

Compiler

Compiled 1 to 3 computations (-200% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	120	81
1	120	81

end0.0ms (0%)

sample1.5s (19.3%)

Algorithm

1×

intervals

Results

609.0ms	8000×	body	128	valid
94.0ms	1237×	body	128	invalid
47.0ms	711×	body	128	nan

Compiler

Compiled 642 to 500 computations (22.1% saved)

Details

analyze474.0ms (6.2%)

sample33.0ms (0.4%)

simplify288.0ms (3.8%)

prune3.0ms (0%)

localize17.0ms (0.2%)

rewrite55.0ms (0.7%)

series922.0ms (12.1%)

simplify74.0ms (1%)

prune857.0ms (11.2%)

localize17.0ms (0.2%)

rewrite56.0ms (0.7%)

series680.0ms (8.9%)

simplify76.0ms (1%)

prune345.0ms (4.5%)

localize20.0ms (0.3%)

rewrite81.0ms (1.1%)

series379.0ms (5%)

simplify82.0ms (1.1%)

prune356.0ms (4.7%)

localize26.0ms (0.3%)

rewrite57.0ms (0.8%)

series511.0ms (6.7%)

simplify87.0ms (1.1%)

prune328.0ms (4.3%)

regimes307.0ms (4%)

bsearch15.0ms (0.2%)

simplify4.0ms (0%)

end0.0ms (0%)

sample1.5s (19.3%)

Profiling