Details

analyze1.0s

Algorithm

sampling

Space saved by range analysis: 0.146413%

Space saved by search: 59.586845%

Guaranteed chance to sample good point: 68.194842%

sample31.0ms

Algorithm

intervals

Results

17.0ms	256×	body	80	valid
2.0ms	29×	body	80	nan
1.0ms	18×	body	80	invalid

simplify52.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	37	12
1	84	12
2	245	12
3	581	12
4	1280	12
5	2462	12
6	5001	12

prune4.0ms

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

Merged error: 6.5b

Counts

2 → 1

localize20.0ms

Local error

Found 4 expressions with local error:

0.1b	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
0.1b	(* (- x 0.5) (log x))
0.2b	(- (* (- x 0.5) (log x)) x)
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

24×	`add-sqr-sqrt` `*-un-lft-identity`
20×	`add-cube-cbrt`
18×	`log-prod`
12×	`associate--l+`
11×	`add-log-exp`
9×	`distribute-rgt-in` `distribute-lft-in` `times-frac`
8×	`add-exp-log` `associate-+l+` `add-cbrt-cube`
7×	`pow1`
5×	`associate-l`
4×	`associate-r`
3×	`associate-/r` `associate-/l`
2×	`sub-neg` `flip3--` `flip3-+` `diff-log` `associate-*l/` `sum-log` `flip--` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `associate-+l-` `frac-2neg` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `log-pow` `*-commutative` `cbrt-unprod` `div-inv` `distribute-lft-out` `distribute-lft-out--` `difference-of-squares` `unswap-sqr`

Counts

4 → 98

Calls

4 calls:

10.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
7.0ms	(* (- x 0.5) (log x))
7.0ms	(- (* (- x 0.5) (log x)) x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series119.0ms

Counts

4 → 12

Calls

4 calls:

36.0ms	(+ (- (* (- x 0.5) (log x)) x) 0.91893853320467)
22.0ms	(* (- x 0.5) (log x))
38.0ms	(- (* (- x 0.5) (log x)) x)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify52.0ms

Algorithm

egg-herbie

Counts

110 → 110

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	543	875
1	1816	820
2	5001	763

prune233.0ms

Filtered

83 candidates to 110 candidates (-32.5%)

Pruning

13 alts after pruning (13 fresh and 0 done)

	Pruned	Kept	Total
New	97	13	110
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	98	13	111

Merged error: 4.7b

Counts

111 → 13

localize25.0ms

Local error

Found 4 expressions with local error:

0.3b	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
0.6b	(cbrt x)
0.6b	(cbrt x)
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite32.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
26×	`add-sqr-sqrt` `add-cube-cbrt` `*-un-lft-identity`
24×	`cbrt-prod` `associate-+l+`
12×	`associate-+r+`
9×	`times-frac`
8×	`associate-*l/`
6×	`add-exp-log` `add-cbrt-cube` `add-log-exp`
4×	`pow1` `flip3--` `frac-add` `flip--`
3×	`associate-/r` `associate-/l`
2×	`flip3-+` `pow1/3` `flip-+` `associate-/l/`
1×	`cbrt-undiv` `+-commutative` `frac-2neg` `div-exp` `clear-num` `sum-log` `div-inv` `distribute-lft-out`

Counts

4 → 103

Calls

4 calls:

14.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
1.0ms	(cbrt x)
1.0ms	(cbrt x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series177.0ms

Counts

4 → 12

Calls

4 calls:

108.0ms	(+ (* (- x 0.5) (* 2 (log (cbrt x)))) (* (- x 0.5) (log (cbrt x))))
22.0ms	(cbrt x)
25.0ms	(cbrt x)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify72.0ms

Algorithm

egg-herbie

Counts

115 → 115

Iterations

Useful iterations: 2 (58.0ms)

Iter	Nodes	Cost
0	652	1117
1	2321	989
2	5001	952

prune259.0ms

Filtered

101 candidates to 115 candidates (-13.9%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	113	2	115
Fresh	3	9	12
Picked	1	0	1
Done	0	0	0
Total	117	11	128

Merged error: 4.7b

Counts

128 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (- x 0.5) (* 3 (log (cbrt x)))) x)
0.3b	(* 3 (log (cbrt x)))
0.6b	(cbrt x)
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

36×	`log-prod`
30×	`distribute-rgt-in` `distribute-lft-in`
29×	`add-sqr-sqrt`
27×	`add-cube-cbrt` `*-un-lft-identity`
24×	`associate--l+`
21×	`cbrt-prod`
9×	`times-frac`
8×	`add-exp-log` `add-cbrt-cube`
7×	`pow1`
6×	`add-log-exp`
5×	`associate-r`
3×	`associate-l` `associate-/r` `associate-/l`
2×	`pow1/3` `log-pow` `associate-/l/`
1×	`cbrt-undiv` `sub-neg` `flip3--` `frac-2neg` `flip3-+` `diff-log` `div-exp` `pow-prod-down` `prod-exp` `clear-num` `*-commutative` `flip--` `cbrt-unprod` `flip-+` `div-inv` `unswap-sqr`

Counts

4 → 108

Calls

4 calls:

12.0ms	(- (* (- x 0.5) (* 3 (log (cbrt x)))) x)
5.0ms	(* 3 (log (cbrt x)))
1.0ms	(cbrt x)
11.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series195.0ms

Counts

4 → 12

Calls

4 calls:

109.0ms	(- (* (- x 0.5) (* 3 (log (cbrt x)))) x)
41.0ms	(* 3 (log (cbrt x)))
22.0ms	(cbrt x)
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify65.0ms

Algorithm

egg-herbie

Counts

120 → 120

Iterations

Useful iterations: 2 (53.0ms)

Iter	Nodes	Cost
0	504	928
1	1795	861
2	5001	840

prune229.0ms

Filtered

94 candidates to 120 candidates (-27.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	119	1	120
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	120	11	131

Merged error: 4.7b

Counts

131 → 11

localize20.0ms

Local error

Found 4 expressions with local error:

0.2b	(- (* (- x 0.5) (log x)) x)
0.2b	(- (* (- x 0.5) (log x)) x)
0.4b	(* (sqrt (- (* (- x 0.5) (log x)) x)) (sqrt (- (* (- x 0.5) (log x)) x)))
6.0b	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

36×	`add-sqr-sqrt`
24×	`add-cube-cbrt` `*-un-lft-identity`
19×	`pow1`
18×	`sqrt-prod`
12×	`log-prod` `sqrt-div` `associate--l+`
9×	`times-frac`
8×	`add-exp-log` `flip3--` `sqrt-pow1` `pow1/2` `swap-sqr` `add-cbrt-cube` `flip--` `add-log-exp`
6×	`distribute-rgt-in` `distribute-lft-in` `associate-r` `associate-l`
5×	`pow-prod-up`
4×	`frac-times` `unswap-sqr`
3×	`pow-prod-down` `associate-/r` `pow-sqr` `associate-/l`
2×	`sub-neg` `diff-log` `associate-r/` `associate-l/` `associate-/l/`
1×	`cbrt-undiv` `pow2` `frac-2neg` `flip3-+` `pow-plus` `sqrt-unprod` `div-exp` `prod-exp` `clear-num` `rem-square-sqrt` `*-commutative` `cbrt-unprod` `flip-+` `div-inv`

Counts

4 → 122

Calls

4 calls:

7.0ms	(- (* (- x 0.5) (log x)) x)
7.0ms	(- (* (- x 0.5) (log x)) x)
18.0ms	(* (sqrt (- (* (- x 0.5) (log x)) x)) (sqrt (- (* (- x 0.5) (log x)) x)))
13.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

series132.0ms

Counts

4 → 12

Calls

4 calls:

35.0ms	(- (* (- x 0.5) (log x)) x)
35.0ms	(- (* (- x 0.5) (log x)) x)
38.0ms	(* (sqrt (- (* (- x 0.5) (log x)) x)) (sqrt (- (* (- x 0.5) (log x)) x)))
22.0ms	(/ (+ (* (- (* (+ y 0.0007936500793651) z) 0.0027777777777778) z) 0.083333333333333) x)

simplify58.0ms

Algorithm

egg-herbie

Counts

134 → 134

Iterations

Useful iterations: 2 (42.0ms)

Iter	Nodes	Cost
0	424	1230
1	1531	1125
2	5001	1050

prune220.0ms

Filtered

87 candidates to 134 candidates (-54.0%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	133	1	134
Fresh	0	10	10
Picked	1	0	1
Done	0	0	0
Total	134	11	145

Merged error: 4.7b

Counts

145 → 11

Details

analyze1.0s

sample31.0ms

simplify52.0ms

prune4.0ms

localize20.0ms

rewrite38.0ms

series119.0ms

simplify52.0ms

prune233.0ms

localize25.0ms

rewrite32.0ms

series177.0ms

simplify72.0ms

prune259.0ms

localize20.0ms

rewrite34.0ms

series195.0ms

simplify65.0ms

prune229.0ms

localize20.0ms

rewrite49.0ms

series132.0ms

simplify58.0ms

prune220.0ms

regimes478.0ms

bsearch1.0ms

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