Details

analyze306.0ms (9.5%)

Algorithm

1×

Search

True	Other	False	Iter
0%	100%	0%	0
0%	100%	0%	1
0%	100%	0%	2
25%	75%	0%	3
25%	62.5%	12.5%	4
25%	56.2%	18.8%	5
28.1%	50%	21.9%	6
29.7%	46.9%	23.5%	7
30.5%	45.3%	24.3%	8
30.8%	44.9%	24.3%	9
31.2%	44.5%	24.3%	10
31.3%	44.4%	24.3%	11
31.4%	44.3%	24.3%	12
31.4%	44.2%	24.3%	13
31.5%	44.2%	24.3%	14

Compiler

Compiled 8 to 6 computations (25% saved)

sample26.0ms (0.8%)

Algorithm

1×

intervals

Results

12.0ms	83×	body	1024	valid
3.0ms	41×	body	512	valid
3.0ms	103×	body	128	valid
2.0ms	10×	body	2048	valid
1.0ms	19×	body	256	valid

Compiler

Compiled 15 to 12 computations (20% saved)

simplify98.0ms (3%)

Algorithm

1×	egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	10	11
1	10	11

prune2.0ms (0.1%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Kept	Total
New	1	1
Fresh	1	1
Picked	0	0
Done	0	0
Total	2	2

Error

42.0b

Counts

2 → 1

Compiler

Compiled 14 to 10 computations (28.6% saved)

localize4.0ms (0.1%)

Local error

Found 2 expressions with local error:

1.2b	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
3.2b	(-.f64 (exp.f64 x) 1)

rewrite17.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

35×	`add-sqr-sqrt_binary64_1464`
30×	`*-un-lft-identity_binary64_1442`
21×	`times-frac_binary64_1448`
15×	`add-cube-cbrt_binary64_1477`
10×	`difference-of-squares_binary64_1411`
7×	`associate-/r*_binary64_1386`
5×	`difference-of-sqr-1_binary64_1412` `distribute-lft-out--_binary64_1394`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481`
3×	`cancel-sign-sub-inv_binary64_1408` `associate-/l*_binary64_1387` `add-exp-log_binary64_1480`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `pow1_binary64_1503`
1×	`cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `frac-2neg_binary64_1453` `diff-log_binary64_1534` `div-exp_binary64_1493`

Counts

2 → 63

Calls

2 calls:

8.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
5.0ms	(-.f64 (exp.f64 x) 1)

series64.0ms (2%)

Counts

2 → 12

Calls

2 calls:

47.0ms	(/.f64 (exp.f64 x) (-.f64 (exp.f64 x) 1))
17.0ms	(-.f64 (exp.f64 x) 1)

Compiler

Compiled 140 to 111 computations (20.7% saved)

simplify65.0ms (2%)

Algorithm

1×	egg-herbie

Counts

75 → 75

Iterations

Useful iterations: 0 (49.0ms)

Iter	Nodes	Cost
0	5105	1195

prune78.0ms (2.4%)

Pruning

2 alts after pruning (2 fresh and 0 done)

	Pruned	Kept	Total
New	73	2	75
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	74	2	76

Error

0.0b

Counts

76 → 2

Compiler

Compiled 1004 to 503 computations (49.9% saved)

localize12.0ms (0.4%)

Local error

Found 3 expressions with local error:

0.0b	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
0.1b	(*.f64 (pow.f64 x 3) 1/720)
0.4b	(*.f64 x 1/12)

rewrite24.0ms (0.7%)

Algorithm

1×	rewrite-expression-head

Rules

18×	`add-sqr-sqrt_binary64_1464`
15×	`associate-l_binary64_1383`
10×	`add-exp-log_binary64_1480`
9×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
8×	`add-log-exp_binary64_1481`
7×	`add-cbrt-cube_binary64_1478`
6×	`associate-r_binary64_1382`
5×	`pow1_binary64_1503` `unswap-sqr_binary64_1410`
4×	`cube-prod_binary64_1470` `prod-exp_binary64_1491` `unpow-prod-down_binary64_1521`
3×	`sum-log_binary64_1533`
2×	`cbrt-unprod_binary64_1475` `*-commutative_binary64_1373` `sqr-pow_binary64_1414`
1×	`cube-mult_binary64_1472` `pow-exp_binary64_1510` `associate-+l+_binary64_1375` `+-commutative_binary64_1372` `pow-prod-down_binary64_1513` `unpow3_binary64_1508` `flip3-+_binary64_1445` `flip-+_binary64_1416` `pow-to-exp_binary64_1511`

Counts

3 → 62

Calls

3 calls:

10.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
6.0ms	(*.f64 (pow.f64 x 3) 1/720)
4.0ms	(*.f64 x 1/12)

series96.0ms (3%)

Counts

3 → 15

Calls

3 calls:

45.0ms	(+.f64 (+.f64 1/2 (/.f64 1 x)) (*.f64 x 1/12))
32.0ms	(*.f64 (pow.f64 x 3) 1/720)
18.0ms	(*.f64 x 1/12)

Compiler

Compiled 330 to 288 computations (12.7% saved)

simplify63.0ms (2%)

Algorithm

1×	egg-herbie

Counts

77 → 77

Iterations

Useful iterations: 0 (50.0ms)

Iter	Nodes	Cost
0	4992	769
1	4992	769

prune85.0ms (2.6%)

Pruning

3 alts after pruning (2 fresh and 1 done)

	Pruned	Kept	Total
New	76	1	77
Fresh	0	1	1
Picked	0	1	1
Done	0	0	0
Total	76	3	79

Error

Counts

79 → 3

Compiler

Compiled 1477 to 1176 computations (20.4% saved)

localize15.0ms (0.5%)

Local error

Found 4 expressions with local error:

0.5b	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
0.5b	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
0.5b	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
0.5b	(.f64 (cbrt.f64 (+.f64 (.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))

rewrite62.0ms (1.9%)

Algorithm

1×	rewrite-expression-head

Rules

25×	`cbrt-prod_binary64_1473`
23×	`add-sqr-sqrt_binary64_1464`
18×	`cbrt-div_binary64_1474`
15×	`add-cube-cbrt_binary64_1477` `*-un-lft-identity_binary64_1442`
11×	`pow1_binary64_1503`
9×	`flip3-+_binary64_1445` `flip-+_binary64_1416` `pow1/3_binary64_1524`
6×	`associate-r_binary64_1382` `swap-sqr_binary64_1409` `associate-l_binary64_1383` `add-exp-log_binary64_1480`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481` `frac-times_binary64_1452` `unswap-sqr_binary64_1410`
2×	`associate-r/_binary64_1384` `pow-prod-down_binary64_1513` `pow-sqr_binary64_1415` `pow-prod-up_binary64_1512` `associate-l/_binary64_1385`
1×	`pow2_binary64_1523` `cbrt-unprod_binary64_1475` `pow-plus_binary64_1505` `*-commutative_binary64_1373` `prod-exp_binary64_1491`

Counts

4 → 87

Calls

4 calls:

25.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))
9.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
8.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
8.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))

series264.0ms (8.2%)

Counts

4 → 28

Calls

4 calls:

71.0ms	(.f64 (cbrt.f64 (+.f64 (.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))) (cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x)))))
69.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
64.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))
60.0ms	(cbrt.f64 (+.f64 (*.f64 x 1/12) (+.f64 1/2 (/.f64 1 x))))

Compiler

Compiled 1649 to 1431 computations (13.2% saved)

simplify120.0ms (3.7%)

Algorithm

1×	egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 0 (88.0ms)

Iter	Nodes	Cost
0	4887	2866
1	4887	2866

prune301.0ms (9.3%)

Pruning

3 alts after pruning (1 fresh and 2 done)

	Pruned	Kept	Total
New	115	0	115
Fresh	0	1	1
Picked	0	1	1
Done	0	1	1
Total	115	3	118

Error

Counts

118 → 3

Compiler

Compiled 5023 to 4122 computations (17.9% saved)

localize5.0ms (0.2%)

Local error

Found 2 expressions with local error:

0.0b	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
3.2b	(-.f64 1 (exp.f64 (neg.f64 x)))

rewrite15.0ms (0.5%)

Algorithm

1×	rewrite-expression-head

Rules

29×	`add-sqr-sqrt_binary64_1464` `*-un-lft-identity_binary64_1442`
18×	`times-frac_binary64_1448`
14×	`add-cube-cbrt_binary64_1477`
10×	`difference-of-squares_binary64_1411`
6×	`associate-/r*_binary64_1386` `add-exp-log_binary64_1480`
5×	`distribute-lft-out--_binary64_1394`
4×	`add-cbrt-cube_binary64_1478` `add-log-exp_binary64_1481`
3×	`cancel-sign-sub-inv_binary64_1408` `associate-/l*_binary64_1387` `pow1_binary64_1503`
2×	`associate-/r/_binary64_1388` `flip3--_binary64_1446` `flip--_binary64_1417` `div-exp_binary64_1493`
1×	`inv-pow_binary64_1527` `cbrt-undiv_binary64_1476` `div-inv_binary64_1439` `sub-neg_binary64_1435` `clear-num_binary64_1441` `1-exp_binary64_1486` `rec-exp_binary64_1492` `pow-flip_binary64_1516` `frac-2neg_binary64_1453` `diff-log_binary64_1534`

Counts

2 → 62

Calls

2 calls:

6.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
5.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

series59.0ms (1.8%)

Counts

2 → 12

Calls

2 calls:

42.0ms	(/.f64 1 (-.f64 1 (exp.f64 (neg.f64 x))))
17.0ms	(-.f64 1 (exp.f64 (neg.f64 x)))

Compiler

Compiled 140 to 131 computations (6.4% saved)

simplify79.0ms (2.4%)

Algorithm

1×	egg-herbie

Counts

74 → 74

Iterations

Useful iterations: 0 (64.0ms)

Iter	Nodes	Cost
0	4951	1118
1	4951	1118

prune53.0ms (1.6%)

Pruning

3 alts after pruning (0 fresh and 3 done)

	Pruned	Kept	Total
New	74	0	74
Fresh	0	0	0
Picked	0	1	1
Done	0	2	2
Total	74	3	77

Error

Counts

77 → 3

Compiler

Compiled 917 to 587 computations (36% saved)

regimes133.0ms (4.1%)

Accuracy

Total 0.2b remaining (98.3%)

Threshold costs 0.2b (98.3%)

Compiler

Compiled 1183 to 905 computations (23.5% saved)

bsearch1.0ms (0%)

Compiler: Compiled 2 to 2 computations (0% saved)

simplify3.0ms (0.1%)

Algorithm

1×	egg-herbie

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	44	46
1	44	46

end0.0ms (0%)

sample1.2s (36.7%)

Algorithm

1×

intervals

Results

367.0ms	2624×	body	1024	valid
101.0ms	1339×	body	512	valid
75.0ms	3145×	body	128	valid
42.0ms	262×	body	2048	valid
32.0ms	630×	body	256	valid
0.0ms	1×	body	128	overflowed

Compiler

Compiled 378 to 293 computations (22.5% saved)

Details

analyze306.0ms (9.5%)

sample26.0ms (0.8%)

simplify98.0ms (3%)

prune2.0ms (0.1%)

localize4.0ms (0.1%)

rewrite17.0ms (0.5%)

series64.0ms (2%)

simplify65.0ms (2%)

prune78.0ms (2.4%)

localize12.0ms (0.4%)

rewrite24.0ms (0.7%)

series96.0ms (3%)

simplify63.0ms (2%)

prune85.0ms (2.6%)

localize15.0ms (0.5%)

rewrite62.0ms (1.9%)

series264.0ms (8.2%)

simplify120.0ms (3.7%)

prune301.0ms (9.3%)

localize5.0ms (0.2%)

rewrite15.0ms (0.5%)

series59.0ms (1.8%)

simplify79.0ms (2.4%)

prune53.0ms (1.6%)

regimes133.0ms (4.1%)

bsearch1.0ms (0%)

simplify3.0ms (0.1%)

end0.0ms (0%)

sample1.2s (36.7%)

Profiling