Details

analyze463.0ms (21.7%)

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
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)

sample31.0ms (1.4%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	80	valid
3.0ms	38×	body	80	invalid
1.0ms	18×	body	80	nan

Compiler

Compiled 49 to 44 computations (10.2% saved)

simplify128.0ms (6%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (118.0ms)

Iter	Nodes	Cost
0	4928	36
1	4928	36

prune5.0ms (0.2%)

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: 6.5b

Counts

2 → 1

Compiler

Compiled 48 to 40 computations (16.7% saved)

localize16.0ms (0.7%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.2b	(-.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)
6.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite46.0ms (2.1%)

Algorithm

1×	rewrite-expression-head

Rules

24×	`*-un-lft-identity_binary64` `add-sqr-sqrt_binary64`
20×	`add-cube-cbrt_binary64`
18×	`log-prod_binary64`
12×	`associate--l+_binary64`
11×	`add-log-exp_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` `associate-+l+_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 → 96

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)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
8.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)

series90.0ms (4.2%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
25.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
24.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
15.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

simplify78.0ms (3.6%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4893	2145
1	4893	2145

prune180.0ms (8.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	97	11	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	11	109

Merged error: 4.3b

Counts

109 → 11

Compiler

Compiled 3833 to 2615 computations (31.8% saved)

localize24.0ms (1.1%)

Local error

Found 4 expressions with local error:

0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
0.6b	(cbrt.f64 x)
6.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite21.0ms (1%)

Algorithm

1×	rewrite-expression-head

Rules

15×	`*-un-lft-identity_binary64` `add-cube-cbrt_binary64` `add-sqr-sqrt_binary64`
9×	`times-frac_binary64` `cbrt-prod_binary64`
6×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
4×	`add-log-exp_binary64` `pow1_binary64`
3×	`associate-/r_binary64` `pow1/3_binary64` `associate-/l_binary64`
2×	`associate-/l/_binary64`
1×	`flip3-+_binary64` `cbrt-undiv_binary64` `clear-num_binary64` `frac-2neg_binary64` `div-inv_binary64` `div-exp_binary64` `flip-+_binary64`

Counts

4 → 62

Calls

4 calls:

15.0ms	(/.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)
1.0ms	(cbrt.f64 x)

series71.0ms (3.3%)

Counts

4 → 12

Calls

4 calls:

26.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
15.0ms	(cbrt.f64 x)
15.0ms	(cbrt.f64 x)
15.0ms	(cbrt.f64 x)

simplify101.0ms (4.7%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (78.0ms)

Iter	Nodes	Cost
0	4923	1155
1	4923	1155

prune115.0ms (5.4%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	73	1	74
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	74	11	85

Merged error: 4.3b

Counts

85 → 11

Compiler

Compiled 3533 to 2174 computations (38.5% saved)

localize21.0ms (1%)

Local error

Found 4 expressions with local error:

0.1b	(*.f64 (-.f64 x 1/2) (log.f64 x))
0.2b	(-.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)
6.1b	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))

rewrite49.0ms (2.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-sqr-sqrt_binary64`
25×	`*-un-lft-identity_binary64`
20×	`add-cube-cbrt_binary64`
18×	`log-prod_binary64`
17×	`associate-r_binary64`
15×	`add-exp-log_binary64`
12×	`associate--l+_binary64`
11×	`add-log-exp_binary64` `add-cbrt-cube_binary64` `times-frac_binary64`
9×	`pow1_binary64` `distribute-lft-in_binary64` `distribute-rgt-in_binary64`
8×	`associate-l_binary64`
7×	`associate-+l+_binary64`
5×	`prod-exp_binary64`
4×	`unswap-sqr_binary64` `associate-*l/_binary64`
3×	`flip3-+_binary64` `cbrt-unprod_binary64` `flip-+_binary64`
2×	`pow-prod-down_binary64` `sub-neg_binary64` `flip3--_binary64` `diff-log_binary64` `div-exp_binary64` `flip--_binary64` `frac-times_binary64` `sum-log_binary64` `*-commutative_binary64`
1×	`distribute-lft-out_binary64` `1-exp_binary64` `cbrt-undiv_binary64` `associate-*r/_binary64` `log-pow_binary64` `associate-+l-_binary64` `difference-of-squares_binary64` `rec-exp_binary64` `un-div-inv_binary64` `distribute-lft-out--_binary64` `div-inv_binary64` `+-commutative_binary64`

Counts

4 → 107

Calls

4 calls:

17.0ms	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))
12.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
8.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
8.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

series92.0ms (4.3%)

Counts

4 → 12

Calls

4 calls:

28.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
25.0ms	(.f64 (+.f64 (.f64 (-.f64 (*.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) (/.f64 1 x))
24.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
15.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))

simplify87.0ms (4.1%)

Algorithm

1×	egg-herbie

Counts

119 → 119

Iterations

Useful iterations: 0 (56.0ms)

Iter	Nodes	Cost
0	5173	2306

prune163.0ms (7.6%)

Pruning

10 alts after pruning (10 fresh and 0 done)

	Pruned	Kept	Total
New	117	2	119
Fresh	2	8	10
Picked	1	0	1
Done	0	0	0
Total	120	10	130

Merged error: 4.3b

Counts

130 → 10

Compiler

Compiled 4279 to 2981 computations (30.3% saved)

localize18.0ms (0.9%)

Local error

Found 4 expressions with local error:

0.2b	(-.f64 (.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)))) x)
0.2b	(+.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)))) x) 2069265617858471/2251799813685248)
0.5b	(.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2))))
6.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite71.0ms (3.3%)

Algorithm

1×	rewrite-expression-head

Rules

53×	`pow1_binary64`
28×	`sqrt-pow1_binary64`
20×	`pow-prod-down_binary64`
19×	`add-sqr-sqrt_binary64`
18×	`*-un-lft-identity_binary64`
16×	`add-cube-cbrt_binary64`
14×	`associate-*r/_binary64`
12×	`sqrt-div_binary64`
11×	`add-log-exp_binary64`
10×	`pow1/2_binary64` `pow-prod-up_binary64`
9×	`times-frac_binary64`
8×	`add-exp-log_binary64` `add-cbrt-cube_binary64`
7×	`flip3--_binary64` `flip--_binary64`
6×	`pow-sqr_binary64`
4×	`swap-sqr_binary64` `associate-r_binary64` `associate-l_binary64` `sqrt-prod_binary64` `frac-times_binary64`
3×	`associate-/r_binary64` `associate-/l_binary64`
2×	`flip3-+_binary64` `associate-/l/_binary64` `sub-neg_binary64` `diff-log_binary64` `flip-+_binary64` `associate-*l/_binary64` `sum-log_binary64`
1×	`cbrt-unprod_binary64` `distribute-lft-out_binary64` `cbrt-undiv_binary64` `rem-square-sqrt_binary64` `associate-+l+_binary64` `associate-+l-_binary64` `pow-plus_binary64` `sqrt-unprod_binary64` `unswap-sqr_binary64` `clear-num_binary64` `prod-exp_binary64` `frac-2neg_binary64` `difference-of-squares_binary64` `div-inv_binary64` `div-exp_binary64` `+-commutative_binary64` `pow2_binary64` `*-commutative_binary64`

Counts

4 → 113

Calls

4 calls:

19.0ms	(+.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)))) x) 2069265617858471/2251799813685248)
17.0ms	(-.f64 (.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)))) x)
16.0ms	(.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2))))
15.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

series130.0ms (6.1%)

Counts

4 → 12

Calls

4 calls:

43.0ms	(.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2))))
31.0ms	(+.f64 (-.f64 (.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)))) x) 2069265617858471/2251799813685248)
30.0ms	(-.f64 (.f64 (sqrt.f64 (.f64 (log.f64 x) (-.f64 x 1/2))) (sqrt.f64 (*.f64 (log.f64 x) (-.f64 x 1/2)))) x)
26.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify95.0ms (4.5%)

Algorithm

1×	egg-herbie

Counts

125 → 125

Iterations

Useful iterations: 0 (58.0ms)

Iter	Nodes	Cost
0	4977	3268
1	4977	3268

Details

analyze463.0ms (21.7%)

sample31.0ms (1.4%)

simplify128.0ms (6%)

prune5.0ms (0.2%)

localize16.0ms (0.7%)

rewrite46.0ms (2.1%)

series90.0ms (4.2%)

simplify78.0ms (3.6%)

prune180.0ms (8.4%)

localize24.0ms (1.1%)

rewrite21.0ms (1%)

series71.0ms (3.3%)

simplify101.0ms (4.7%)

prune115.0ms (5.4%)

localize21.0ms (1%)

rewrite49.0ms (2.3%)

series92.0ms (4.3%)

simplify87.0ms (4.1%)

prune163.0ms (7.6%)

localize18.0ms (0.9%)

rewrite71.0ms (3.3%)

series130.0ms (6.1%)

simplify95.0ms (4.5%)

prune46.0ms (2.1%)

Profiling