Details

analyze591.0ms (7.1%)

Algorithm

1×	search
2×	egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	4975	144
1	4975	144
0	3	3
1	3	3

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)

sample32.0ms (0.4%)

Algorithm

1×

intervals

Results

17.0ms	256×	body	128	valid
2.0ms	32×	body	128	invalid
1.0ms	24×	body	128	nan

Compiler

Compiled 49 to 44 computations (10.2% saved)

simplify111.0ms (1.3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (105.0ms)

Iter	Nodes	Cost
0	4823	36
1	4823	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

Error

5.5b

Counts

2 → 1

Compiler

Compiled 48 to 40 computations (16.7% saved)

localize16.0ms (0.2%)

Local error

Found 4 expressions with local error:

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

rewrite52.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

26×	`*-un-lft-identity_binary64_12354` `add-sqr-sqrt_binary64_12376`
22×	`add-cube-cbrt_binary64_12389`
18×	`log-prod_binary64_12440`
12×	`associate--l+_binary64_12291`
11×	`add-log-exp_binary64_12393`
10×	`associate-+l+_binary64_12287`
9×	`distribute-lft-in_binary64_12303` `distribute-rgt-in_binary64_12304` `times-frac_binary64_12360`
8×	`add-cbrt-cube_binary64_12390` `add-exp-log_binary64_12392`
7×	`pow1_binary64_12415`
6×	`cancel-sign-sub-inv_binary64_12320`
5×	`associate-l_binary64_12295`
4×	`associate-r_binary64_12294`
3×	`associate-/r_binary64_12298` `associate-/l_binary64_12299`
2×	`flip--_binary64_12329` `diff-log_binary64_12446` `associate-/l/_binary64_12301` `associate-*l/_binary64_12297` `sum-log_binary64_12445` `flip3--_binary64_12358` `flip-+_binary64_12328` `sub-neg_binary64_12347` `flip3-+_binary64_12357`
1×	`pow-prod-down_binary64_12425` `clear-num_binary64_12353` `cbrt-unprod_binary64_12387` `distribute-lft-out_binary64_12305` `div-inv_binary64_12351` `frac-2neg_binary64_12365` `cbrt-undiv_binary64_12388` `log-pow_binary64_12443` `distribute-lft-out--_binary64_12306` `difference-of-squares_binary64_12323` `prod-exp_binary64_12403` `associate-+l-_binary64_12289` `unswap-sqr_binary64_12322` `div-exp_binary64_12405` `+-commutative_binary64_12284` `*-commutative_binary64_12285`

Counts

4 → 102

Calls

4 calls:

14.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
12.0ms	(/.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)

series495.0ms (5.9%)

Counts

4 → 12

Calls

4 calls:

164.0ms	(-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x)
163.0ms	(+.f64 (-.f64 (*.f64 (-.f64 x 1/2) (log.f64 x)) x) 2069265617858471/2251799813685248)
97.0ms	(*.f64 (-.f64 x 1/2) (log.f64 x))
71.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify74.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

114 → 114

Iterations

Useful iterations: 0 (47.0ms)

Iter	Nodes	Cost
0	4964	2164
1	4964	2164

prune213.0ms (2.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	101	13	114
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	102	13	115

Error

3.3b

Counts

115 → 13

Compiler

Compiled 4001 to 2735 computations (31.6% saved)

localize21.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(+.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)

rewrite47.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

36×	`log-prod_binary64_12440`
30×	`distribute-lft-in_binary64_12303` `distribute-rgt-in_binary64_12304`
26×	`*-un-lft-identity_binary64_12354` `add-sqr-sqrt_binary64_12376` `add-cube-cbrt_binary64_12389`
24×	`cbrt-prod_binary64_12385` `associate-+l+_binary64_12287`
12×	`associate-+r+_binary64_12286`
9×	`times-frac_binary64_12360`
8×	`associate-*l/_binary64_12297`
6×	`add-log-exp_binary64_12393` `add-cbrt-cube_binary64_12390` `add-exp-log_binary64_12392`
4×	`flip--_binary64_12329` `pow1_binary64_12415` `flip3--_binary64_12358` `frac-add_binary64_12362`
3×	`associate-/r_binary64_12298` `associate-/l_binary64_12299`
2×	`pow1/3_binary64_12436` `associate-/l/_binary64_12301` `flip-+_binary64_12328` `flip3-+_binary64_12357`
1×	`clear-num_binary64_12353` `distribute-lft-out_binary64_12305` `div-inv_binary64_12351` `frac-2neg_binary64_12365` `cbrt-undiv_binary64_12388` `sum-log_binary64_12445` `div-exp_binary64_12405` `+-commutative_binary64_12284`

Counts

4 → 103

Calls

4 calls:

15.0ms	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
12.0ms	(/.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)

series672.0ms (8%)

Counts

4 → 12

Calls

4 calls:

433.0ms	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (cbrt.f64 x))))
85.0ms	(cbrt.f64 x)
77.0ms	(cbrt.f64 x)
77.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify88.0ms (1.1%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (62.0ms)

Iter	Nodes	Cost
0	4878	2160
1	4878	2160

prune221.0ms (2.6%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	2	10	12
Picked	1	0	1
Done	0	0	0
Total	116	12	128

Error

3.3b

Counts

128 → 12

Compiler

Compiled 5040 to 3299 computations (34.5% saved)

localize25.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.2b	(+.f64 (-.f64 (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 -1))) (+.f64 (*.f64 x 3) -3/2)) x) 2069265617858471/2251799813685248)
0.4b	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 -1))) (+.f64 (*.f64 x 3) -3/2))
0.6b	(cbrt.f64 (neg.f64 x))
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

20×	`*-un-lft-identity_binary64_12354` `add-sqr-sqrt_binary64_12376`
18×	`add-cube-cbrt_binary64_12389`
10×	`cbrt-prod_binary64_12385`
9×	`add-log-exp_binary64_12393` `pow1_binary64_12415` `times-frac_binary64_12360`
8×	`add-cbrt-cube_binary64_12390` `add-exp-log_binary64_12392`
6×	`associate-l_binary64_12295` `associate-+l+_binary64_12287`
3×	`pow-prod-down_binary64_12425` `associate-/r_binary64_12298` `associate-/l_binary64_12299` `pow1/3_binary64_12436` `log-pow_binary64_12443` `distribute-rgt-neg-in_binary64_12312` `associate-r_binary64_12294` `distribute-lft-neg-in_binary64_12311` `cancel-sign-sub-inv_binary64_12320` `flip-+_binary64_12328` `flip3-+_binary64_12357`
2×	`associate-/l/_binary64_12301` `distribute-lft-in_binary64_12303` `sum-log_binary64_12445` `associate-*r/_binary64_12296` `distribute-rgt-in_binary64_12304` `associate--l+_binary64_12291`
1×	`clear-num_binary64_12353` `cbrt-unprod_binary64_12387` `neg-mul-1_binary64_12350` `distribute-lft-out_binary64_12305` `diff-log_binary64_12446` `div-inv_binary64_12351` `frac-2neg_binary64_12365` `cbrt-undiv_binary64_12388` `prod-exp_binary64_12403` `associate-+l-_binary64_12289` `unswap-sqr_binary64_12322` `div-exp_binary64_12405` `sub-neg_binary64_12347` `+-commutative_binary64_12284` `*-commutative_binary64_12285`

Counts

4 → 92

Calls

4 calls:

13.0ms	(+.f64 (-.f64 (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 -1))) (+.f64 (*.f64 x 3) -3/2)) x) 2069265617858471/2251799813685248)
12.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 -1))) (+.f64 (*.f64 x 3) -3/2))
12.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
2.0ms	(cbrt.f64 (neg.f64 x))

series1.1s (13.1%)

Counts

4 → 12

Calls

4 calls:

597.0ms	(+.f64 (-.f64 (.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 -1))) (+.f64 (*.f64 x 3) -3/2)) x) 2069265617858471/2251799813685248)
325.0ms	(.f64 (log.f64 (.f64 (cbrt.f64 (neg.f64 x)) (cbrt.f64 -1))) (+.f64 (*.f64 x 3) -3/2))
93.0ms	(cbrt.f64 (neg.f64 x))
83.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify57.0ms (0.7%)

Algorithm

1×	egg-herbie

Counts

104 → 104

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	6002	2379

prune222.0ms (2.7%)

Pruning

12 alts after pruning (12 fresh and 0 done)

	Pruned	Kept	Total
New	103	1	104
Fresh	0	11	11
Picked	1	0	1
Done	0	0	0
Total	104	12	116

Error

3.3b

Counts

116 → 12

Compiler

Compiled 4372 to 3185 computations (27.2% saved)

localize26.0ms (0.3%)

Local error

Found 4 expressions with local error:

0.4b	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (pow.f64 x 1/3))))
0.6b	(cbrt.f64 x)
4.9b	(pow.f64 x 1/3)
5.0b	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

rewrite50.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

38×	`log-prod_binary64_12440`
31×	`distribute-lft-in_binary64_12303` `distribute-rgt-in_binary64_12304`
27×	`*-un-lft-identity_binary64_12354` `add-sqr-sqrt_binary64_12376` `add-cube-cbrt_binary64_12389`
24×	`associate-+l+_binary64_12287`
15×	`cbrt-prod_binary64_12385`
14×	`associate-+r+_binary64_12286`
9×	`unpow-prod-down_binary64_12433` `times-frac_binary64_12360`
8×	`associate-*l/_binary64_12297`
7×	`add-exp-log_binary64_12392`
6×	`add-log-exp_binary64_12393` `add-cbrt-cube_binary64_12390`
5×	`pow1_binary64_12415`
4×	`flip--_binary64_12329` `flip3--_binary64_12358` `frac-add_binary64_12362`
3×	`pow-unpow_binary64_12431` `associate-/r_binary64_12298` `associate-/l_binary64_12299` `sqr-pow_binary64_12326`
2×	`associate-/l/_binary64_12301` `flip-+_binary64_12328` `flip3-+_binary64_12357`
1×	`clear-num_binary64_12353` `distribute-lft-out_binary64_12305` `div-inv_binary64_12351` `frac-2neg_binary64_12365` `pow1/3_binary64_12436` `cbrt-undiv_binary64_12388` `pow-exp_binary64_12422` `pow-pow_binary64_12426` `sum-log_binary64_12445` `unpow1/3_binary64_12421` `div-exp_binary64_12405` `+-commutative_binary64_12284` `pow-to-exp_binary64_12423`

Counts

4 → 112

Calls

4 calls:

16.0ms	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (pow.f64 x 1/3))))
12.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)
2.0ms	(pow.f64 x 1/3)
1.0ms	(cbrt.f64 x)

series834.0ms (10%)

Counts

4 → 12

Calls

4 calls:

594.0ms	(+.f64 (.f64 (-.f64 x 1/2) (.f64 2 (log.f64 (cbrt.f64 x)))) (*.f64 (-.f64 x 1/2) (log.f64 (pow.f64 x 1/3))))
89.0ms	(cbrt.f64 x)
76.0ms	(pow.f64 x 1/3)
74.0ms	(/.f64 (+.f64 (.f64 (-.f64 (.f64 (+.f64 y 7320129949063637/9223372036854775808) z) 3202559735019045/1152921504606846976) z) 6004799503160637/72057594037927936) x)

simplify121.0ms (1.4%)

Algorithm

1×	egg-herbie

Counts

124 → 124

Iterations

Useful iterations: 0 (92.0ms)

Iter	Nodes	Cost
0	4873	2197
1	4873	2197

prune454.0ms (5.4%)

Pruning

12 alts after pruning (11 fresh and 1 done)

	Pruned	Kept	Total
New	124	0	124
Fresh	0	11	11
Picked	0	1	1
Done	0	0	0
Total	124	12	136

Error

3.3b

Counts

136 → 12

Compiler

Compiled 5058 to 3425 computations (32.3% saved)

regimes800.0ms (9.6%)

Accuracy

Total 0.3b remaining (7.6%)

Threshold costs 0.3b (7.6%)

Compiler

Compiled 10636 to 8558 computations (19.5% saved)

bsearch24.0ms (0.3%)

Steps

Iters	Range		Point
5	1.3404273195981578e+47	3.404963865561505e+47	1.5197935419204964e+47

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	109	99
1	109	99

end0.0ms (0%)

sample2.0s (23.6%)

Algorithm

1×

intervals

Results

560.0ms	8000×	body	128	valid
80.0ms	1154×	body	128	invalid
43.0ms	720×	body	128	nan

Compiler

Compiled 1400 to 1120 computations (20% saved)

Details

analyze591.0ms (7.1%)

sample32.0ms (0.4%)

simplify111.0ms (1.3%)

prune3.0ms (0%)

localize16.0ms (0.2%)

rewrite52.0ms (0.6%)

series495.0ms (5.9%)

simplify74.0ms (0.9%)

prune213.0ms (2.5%)

localize21.0ms (0.3%)

rewrite47.0ms (0.6%)

series672.0ms (8%)

simplify88.0ms (1.1%)

prune221.0ms (2.6%)

localize25.0ms (0.3%)

rewrite50.0ms (0.6%)

series1.1s (13.1%)

simplify57.0ms (0.7%)

prune222.0ms (2.7%)

localize26.0ms (0.3%)

rewrite50.0ms (0.6%)

series834.0ms (10%)

simplify121.0ms (1.4%)

prune454.0ms (5.4%)

regimes800.0ms (9.6%)

bsearch24.0ms (0.3%)

simplify4.0ms (0%)

end0.0ms (0%)

sample2.0s (23.6%)

Profiling