Details

analyze1.6s (8.4%)

Algorithm

1×

Search

True	Other	False	Iter
0%	49.9%	50.1%	0
0%	49.9%	50.1%	1
0%	49.9%	50.1%	2
0%	49.9%	50.1%	3
0%	49.9%	50.1%	4
0%	49.9%	50.1%	5
0%	49.9%	50.1%	6
0%	49.9%	50.1%	7
0%	49.9%	50.1%	8
0.4%	49.5%	50.1%	9
0.4%	49.3%	50.3%	10
0.6%	48.9%	50.5%	11
1.1%	48.1%	50.9%	12
1.5%	47.3%	51.2%	13
1.7%	46.9%	51.5%	14

Compiler

Compiled 31 to 24 computations (22.6% saved)

sample179.0ms (0.9%)

Algorithm

1×

intervals

Results

91.0ms	118×	body	2048	valid
34.0ms	84×	body	1024	valid
11.0ms	22×	body	512	valid
7.0ms	13×	body	2048	overflowed
7.0ms	314×	pre	128	true
5.0ms	15×	body	1024	overflowed
3.0ms	14×	body	512	overflowed
2.0ms	2×	body	4096	valid
2.0ms	24×	body	128	valid
1.0ms	6×	body	256	valid
1.0ms	6×	body	256	overflowed
1.0ms	10×	body	128	overflowed

Compiler

Compiled 55 to 46 computations (16.4% saved)

simplify175.0ms (0.9%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (17.0ms)

Iter	Nodes	Cost
0	5217	37

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: 58.3b

Counts

2 → 1

Compiler

Compiled 48 to 38 computations (20.8% saved)

localize17.0ms (0.1%)

Local error

Found 4 expressions with local error:

0.5b	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
2.2b	(-.f64 (exp.f64 (*.f64 a eps)) 1)
4.3b	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.8b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

rewrite40.0ms (0.2%)

Algorithm

1×	rewrite-expression-head

Rules

33×	`add-sqr-sqrt_binary64_1464`
26×	`*-un-lft-identity_binary64_1442`
15×	`cancel-sign-sub-inv_binary64_1408`
11×	`add-cube-cbrt_binary64_1477`
10×	`add-log-exp_binary64_1481` `difference-of-squares_binary64_1411`
9×	`flip3--_binary64_1446` `flip--_binary64_1417`
7×	`associate-r_binary64_1382` `associate-l_binary64_1383`
6×	`add-cbrt-cube_binary64_1478` `add-exp-log_binary64_1480` `pow1_binary64_1503`
5×	`sub-neg_binary64_1435` `difference-of-sqr-1_binary64_1412` `distribute-lft-out--_binary64_1394`
4×	`distribute-lft-in_binary64_1391` `frac-times_binary64_1452` `distribute-rgt-in_binary64_1392`
3×	`diff-log_binary64_1534`
2×	`associate-r/_binary64_1384` `associate-l/_binary64_1385`
1×	`cbrt-unprod_binary64_1475` `pow-prod-down_binary64_1513` `*-commutative_binary64_1373` `prod-exp_binary64_1491` `unswap-sqr_binary64_1410`

Counts

4 → 96

Calls

4 calls:

13.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
5.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

series268.0ms (1.4%)

Counts

4 → 12

Calls

4 calls:

99.0ms	(.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (-.f64 (exp.f64 (*.f64 b eps)) 1))
84.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
43.0ms	(-.f64 (exp.f64 (*.f64 b eps)) 1)
42.0ms	(-.f64 (exp.f64 (*.f64 a eps)) 1)

simplify75.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

108 → 108

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4986	2058
1	4986	2058

prune141.0ms (0.7%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	105	3	108
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	106	3	109

Merged error: 48.5b

Counts

109 → 3

Compiler

Compiled 3416 to 1406 computations (58.8% saved)

localize27.0ms (0.1%)

Local error

Found 4 expressions with local error:

4.0b	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
4.6b	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
5.8b	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)
12.1b	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))

rewrite62.0ms (0.3%)

Algorithm

1×	rewrite-expression-head

Rules

31×	`add-exp-log_binary64_1480`
26×	`add-cbrt-cube_binary64_1478`
14×	`prod-exp_binary64_1491`
12×	`add-sqr-sqrt_binary64_1464`
11×	`pow1_binary64_1503`
10×	`cbrt-unprod_binary64_1475` `*-un-lft-identity_binary64_1442`
8×	`associate-/r/_binary64_1388`
7×	`add-cube-cbrt_binary64_1477`
6×	`associate-*r/_binary64_1384` `add-log-exp_binary64_1481`
5×	`flip3--_binary64_1446` `flip--_binary64_1417`
4×	`associate-r_binary64_1382` `cbrt-undiv_binary64_1476` `associate-l_binary64_1383` `pow-prod-down_binary64_1513` `frac-times_binary64_1452` `flip3-+_binary64_1445` `flip-+_binary64_1416` `div-exp_binary64_1493`
3×	`cancel-sign-sub-inv_binary64_1408`
2×	`associate-/l/_binary64_1389` `-commutative_binary64_1373` `difference-of-squares_binary64_1411` `associate-l/_binary64_1385`
1×	`associate-/r_binary64_1386` `pow-exp_binary64_1510` `times-frac_binary64_1448` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `associate-/l_binary64_1387` `difference-of-sqr-1_binary64_1412` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `distribute-lft-in_binary64_1391` `distribute-rgt-in_binary64_1392` `distribute-lft-out--_binary64_1394` `pow-to-exp_binary64_1511` `unswap-sqr_binary64_1410`

Counts

4 → 91

Calls

4 calls:

18.0ms	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
14.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
7.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
5.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

series8.5s (43.2%)

Counts

4 → 12

Calls

4 calls:

8.1s	(/.f64 (.f64 eps (-.f64 (exp.f64 (.f64 (+.f64 a b) eps)) 1)) (.f64 (-.f64 (exp.f64 (.f64 a eps)) 1) (+.f64 (.f64 b eps) (.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (*.f64 eps eps)))))))
188.0ms	(.f64 (.f64 b b) (+.f64 (.f64 b (.f64 1/6 (pow.f64 eps 3))) (.f64 1/2 (.f64 eps eps))))
89.0ms	(.f64 b (.f64 1/6 (pow.f64 eps 3)))
78.0ms	(-.f64 (exp.f64 (*.f64 (+.f64 a b) eps)) 1)

simplify74.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 0 (37.0ms)

Iter	Nodes	Cost
0	5159	3682

prune230.0ms (1.2%)

Pruning

3 alts after pruning (3 fresh and 0 done)

	Pruned	Kept	Total
New	102	1	103
Fresh	0	2	2
Picked	1	0	1
Done	0	0	0
Total	103	3	106

Merged error: 0.0b

Counts

106 → 3

Compiler

Compiled 5242 to 2565 computations (51.1% saved)

localize5.0ms (0%)

Local error

Found 1 expressions with local error:

0.0b	(+.f64 (/.f64 1 b) (/.f64 1 a))

rewrite17.0ms (0.1%)

Algorithm

1×	rewrite-expression-head

Rules

13×	`*-un-lft-identity_binary64_1442`
7×	`distribute-lft-out_binary64_1393`
6×	`times-frac_binary64_1448`
4×	`div-inv_binary64_1439`
3×	`add-log-exp_binary64_1481` `add-sqr-sqrt_binary64_1464` `add-cube-cbrt_binary64_1477`
1×	`add-cbrt-cube_binary64_1478` `sum-log_binary64_1533` `+-commutative_binary64_1372` `add-exp-log_binary64_1480` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1_binary64_1503` `frac-add_binary64_1450`

Counts

1 → 19

Calls

1 calls:

15.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

series22.0ms (0.1%)

Counts

1 → 3

Calls

1 calls:

22.0ms

(+.f64 (/.f64 1 b) (/.f64 1 a))

simplify60.0ms (0.3%)

Algorithm

1×	egg-herbie

Counts

22 → 22

Iterations

Useful iterations: 0 (51.0ms)

Iter	Nodes	Cost
0	4970	287
1	4970	287

prune24.0ms (0.1%)

Pruning

5 alts after pruning (4 fresh and 1 done)

	Pruned	Kept	Total
New	20	2	22
Fresh	0	2	2
Picked	0	1	1
Done	0	0	0
Total	20	5	25

Merged error: 0.0b

Counts

25 → 5

Compiler

Compiled 366 to 286 computations (21.9% saved)

localize9.0ms (0%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
0.5b	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))

rewrite117.0ms (0.6%)

Algorithm

1×	rewrite-expression-head

Rules

139×	`*-un-lft-identity_binary64_1442`
114×	`cbrt-prod_binary64_1473`
81×	`distribute-lft-out_binary64_1393`
60×	`div-inv_binary64_1439`
42×	`times-frac_binary64_1448`
37×	`add-sqr-sqrt_binary64_1464`
33×	`cbrt-div_binary64_1474` `swap-sqr_binary64_1409`
29×	`add-cube-cbrt_binary64_1477`
13×	`associate-r_binary64_1382` `associate-l_binary64_1383`
11×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1_binary64_1503` `frac-add_binary64_1450`
9×	`frac-times_binary64_1452` `pow1/3_binary64_1524`
6×	`add-exp-log_binary64_1480`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `unswap-sqr_binary64_1410`
3×	`associate-r/_binary64_1384` `associate-l/_binary64_1385`
2×	`pow-prod-down_binary64_1513` `pow-sqr_binary64_1415` `pow-prod-up_binary64_1512`
1×	`pow2_binary64_1523` `cbrt-unprod_binary64_1475` `pow-plus_binary64_1505` `*-commutative_binary64_1373` `prod-exp_binary64_1491`

Counts

4 → 159

Calls

4 calls:

43.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
15.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
14.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

series615.0ms (3.1%)

Counts

4 → 12

Calls

4 calls:

178.0ms	(*.f64 (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))) (cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a))))
149.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
148.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))
141.0ms	(cbrt.f64 (+.f64 (/.f64 1 b) (/.f64 1 a)))

simplify79.0ms (0.4%)

Algorithm

1×	egg-herbie

Counts

171 → 171

Iterations

Useful iterations: 0 (35.0ms)

Iter	Nodes	Cost
0	4918	4109
1	4918	4109

prune345.0ms (1.8%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	170	1	171
Fresh	0	3	3
Picked	0	1	1
Done	0	1	1
Total	170	6	176

Merged error: 0.0b

Counts

176 → 6

Compiler

Compiled 5451 to 4249 computations (22.1% saved)

regimes338.0ms (1.7%)

Compiler: Compiled 4706 to 3308 computations (29.7% saved)

bsearch4.0ms (0%)

Compiler: Compiled 24 to 19 computations (20.8% saved)

simplify4.0ms (0%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	52	138
1	52	138

end0.0ms (0%)

sample6.6s (33.5%)

Algorithm

1×

intervals

Results

3.4s	4127×	body	2048	valid
950.0ms	2354×	body	1024	valid
220.0ms	9753×	pre	128	true
212.0ms	424×	body	2048	overflowed
186.0ms	593×	body	1024	overflowed
170.0ms	708×	body	512	valid
66.0ms	317×	body	512	overflowed
38.0ms	551×	body	128	valid
36.0ms	241×	body	256	valid
28.0ms	19×	body	4096	valid
20.0ms	141×	body	256	overflowed
19.0ms	273×	body	128	overflowed
4.0ms	5×	body	2048	invalid

Compiler

Compiled 1290 to 898 computations (30.4% saved)

Details

analyze1.6s (8.4%)

sample179.0ms (0.9%)

simplify175.0ms (0.9%)

prune3.0ms (0%)

localize17.0ms (0.1%)

rewrite40.0ms (0.2%)

series268.0ms (1.4%)

simplify75.0ms (0.4%)

prune141.0ms (0.7%)

localize27.0ms (0.1%)

rewrite62.0ms (0.3%)

series8.5s (43.2%)

simplify74.0ms (0.4%)

prune230.0ms (1.2%)

localize5.0ms (0%)

rewrite17.0ms (0.1%)

series22.0ms (0.1%)

simplify60.0ms (0.3%)

prune24.0ms (0.1%)

localize9.0ms (0%)

rewrite117.0ms (0.6%)

series615.0ms (3.1%)

simplify79.0ms (0.4%)

prune345.0ms (1.8%)

regimes338.0ms (1.7%)

bsearch4.0ms (0%)

simplify4.0ms (0%)

end0.0ms (0%)

sample6.6s (33.5%)

Profiling