Details

sample44.0ms

Algorithm

intervals

Results

11.0ms	198×	body	80	valid
7.0ms	21×	body	2560	valid
5.0ms	256×	pre	80	true
5.0ms	19×	body	1280	valid
2.0ms	12×	body	640	valid
0.0ms	3×	body	320	valid
0.0ms	3×	body	160	valid

simplify13.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (2.0ms)

Iter	Nodes	Cost
0	28	9
1	40	9
2	48	9
3	50	9
4	52	9
5	53	9
6	53	9

prune3.0ms

Filtered

1 candidates to 0 candidates (0.0%)

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: 11.6b

Counts

2 → 1

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(+ (* (* 4.0 p) p) (* x x))
0.0b	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite38.0ms

Algorithm

rewrite-expression-head

Rules

23×	`*-un-lft-identity`
22×	`add-sqr-sqrt`
21×	`add-cube-cbrt`
18×	`times-frac`
15×	`sqrt-prod`
8×	`add-log-exp`
6×	`add-exp-log` `associate-/r*` `add-cbrt-cube`
5×	`pow1`
4×	`expm1-log1p-u` `fma-def` `flip3-+` `sqrt-div` `flip-+` `log1p-expm1-u`
3×	`associate-/l*`
2×	`+-commutative` `sum-log` `associate-/r/`
1×	`cbrt-undiv` `rem-sqrt-square` `frac-2neg` `sqrt-pow1` `pow1/2` `div-exp` `clear-num` `div-inv` `distribute-lft-out`

Counts

4 → 91

Calls

4 calls:

6.0ms	(+ (* (* 4.0 p) p) (* x x))
12.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series229.0ms

Counts

4 → 12

Calls

4 calls:

33.0ms	(+ (* (* 4.0 p) p) (* x x))
59.0ms	(/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))
81.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
55.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify161.0ms

Algorithm

egg-herbie

Counts

103 → 103

Iterations

Useful iterations: 3 (151.0ms)

Iter	Nodes	Cost
0	296	867
1	1081	815
2	4584	798
3	5001	795

prune293.0ms

Filtered

103 candidates to 79 candidates (76.7%)

Pruning

11 alts after pruning (11 fresh and 0 done)

	Pruned	Kept	Total
New	92	11	103
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	93	11	104

Merged error: 11.3b

Counts

104 → 11

localize14.0ms

Local error

Found 4 expressions with local error:

0.0b	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.3b	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite49.0ms

Algorithm

rewrite-expression-head

Rules

15×	`*-un-lft-identity`
10×	`add-sqr-sqrt`
9×	`add-cube-cbrt`
8×	`log-prod`
7×	`pow1`
6×	`add-log-exp`
5×	`add-exp-log`
4×	`expm1-log1p-u` `log-div` `exp-prod` `flip3-+` `exp-sum` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`fma-def` `sqrt-prod` `distribute-lft-out`
2×	`exp-diff` `sqrt-div` `log-pow`
1×	`+-commutative` `rem-sqrt-square` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `rem-exp-log`

Counts

4 → 71

Calls

4 calls:

13.0ms	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
16.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series400.0ms

Counts

4 → 12

Calls

4 calls:

79.0ms	(exp (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
76.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
191.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify118.0ms

Algorithm

egg-herbie

Counts

83 → 83

Iterations

Useful iterations: 4 (110.0ms)

Iter	Nodes	Cost
0	247	768
1	653	703
2	1660	682
3	4373	674
4	5001	658

prune260.0ms

Filtered

83 candidates to 68 candidates (81.9%)

Pruning

9 alts after pruning (9 fresh and 0 done)

	Pruned	Kept	Total
New	78	5	83
Fresh	6	4	10
Picked	1	0	1
Done	0	0	0
Total	85	9	94

Merged error: 8.1b

Counts

94 → 9

localize21.0ms

Local error

Found 4 expressions with local error:

0.3b	(pow E (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
0.8b	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.3b	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite45.0ms

Algorithm

rewrite-expression-head

Rules

16×	`*-un-lft-identity`
11×	`add-sqr-sqrt`
10×	`add-cube-cbrt`
8×	`pow1` `log-prod`
6×	`add-exp-log` `add-log-exp`
4×	`unpow-prod-up` `expm1-log1p-u` `log-div` `pow-unpow` `flip3-+` `add-cbrt-cube` `flip-+` `log1p-expm1-u`
3×	`unpow-prod-down` `fma-def` `sqrt-prod` `distribute-lft-out`
2×	`sqrt-div` `pow-exp` `log-pow` `pow-sub`
1×	`+-commutative` `pow-to-exp` `rem-sqrt-square` `e-exp-1` `pow-pow` `sqrt-pow1` `pow1/2` `rem-log-exp` `sum-log` `sqr-pow`

Counts

4 → 78

Calls

4 calls:

14.0ms	(pow E (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
12.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
12.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series640.0ms

Counts

4 → 12

Calls

4 calls:

319.0ms	(pow E (log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))))
79.0ms	(+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x)))))
182.0ms	(log (+ 1.0 (/ x (sqrt (+ (* (* 4.0 p) p) (* x x))))))
59.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify85.0ms

Algorithm

egg-herbie

Counts

90 → 90

Iterations

Useful iterations: 3 (75.0ms)

Iter	Nodes	Cost
0	309	925
1	912	841
2	2950	825
3	5002	812

prune251.0ms

Filtered

90 candidates to 68 candidates (75.6%)

Pruning

6 alts after pruning (5 fresh and 1 done)

	Pruned	Kept	Total
New	88	2	90
Fresh	5	3	8
Picked	0	1	1
Done	0	0	0
Total	93	6	99

Merged error: 5.1b

Counts

99 → 6

localize12.0ms

Local error

Found 4 expressions with local error:

0.0b	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
0.2b	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.2b	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
14.4b	(sqrt (+ (* (* 4.0 p) p) (* x x)))

rewrite34.0ms

Algorithm

rewrite-expression-head

Rules

33×	`add-sqr-sqrt`
24×	`associate-r`
22×	`*-un-lft-identity` `times-frac`
20×	`add-cube-cbrt`
15×	`sqrt-prod`
13×	`add-exp-log`
10×	`pow1`
9×	`add-cbrt-cube`
6×	`sqrt-div` `add-log-exp`
5×	`unswap-sqr`
4×	`expm1-log1p-u` `flip3-+` `prod-exp` `flip-+` `log1p-expm1-u`
3×	`fma-def` `sqrt-pow1` `associate-r/` `associate-l*`
2×	`pow1/2` `div-exp` `pow-prod-down` `associate-/r/` `cbrt-unprod`
1×	`cbrt-undiv` `+-commutative` `rem-sqrt-square` `rec-exp` `1-exp` `sum-log` `un-div-inv` `*-commutative` `div-inv`

Counts

4 → 99

Calls

4 calls:

4.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
19.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
3.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
5.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

series478.0ms

Counts

4 → 12

Calls

4 calls:

287.0ms	(sqrt (* 0.5 (+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))))
58.0ms	(* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x)))))
78.0ms	(+ 1.0 (* x (/ 1 (sqrt (+ (* (* 4.0 p) p) (* x x))))))
54.0ms	(sqrt (+ (* (* 4.0 p) p) (* x x)))

simplify52.0ms

Algorithm

egg-herbie

Counts

111 → 111

Iterations

Useful iterations: 2 (41.0ms)

Iter	Nodes	Cost
0	407	966
1	1757	881
2	5001	845

prune241.0ms

Filtered

111 candidates to 84 candidates (75.7%)

Pruning

6 alts after pruning (4 fresh and 2 done)

	Pruned	Kept	Total
New	110	1	111
Fresh	1	3	4
Picked	0	1	1
Done	0	1	1
Total	111	6	117

Merged error: 5.1b

Counts

117 → 6

regimes176.0ms

Accuracy

85.3% (1.0b remaining)

Error of 7.8b against oracle of 6.8b and baseline of 13.5b

bsearch1.0ms

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	40	24
1	40	24

end0.0ms

sample1.1s

Algorithm

intervals

Results

301.0ms	6024×	body	80	valid
252.0ms	819×	body	2560	valid
156.0ms	609×	body	1280	valid
142.0ms	8000×	pre	80	true
60.0ms	311×	body	640	valid
24.0ms	152×	body	320	valid
8.0ms	85×	body	160	valid