Details

sample46.0ms

Algorithm

intervals

Results

16.0ms	288×	body	80	valid
9.0ms	111×	body	80	nan

simplify55.0ms

Algorithm

egg-herbie

Counts

1 → 1

Iterations

Useful iterations: 0 (1.0ms)

Iter	Nodes	Cost
0	36	9
1	81	9
2	182	9
3	456	9
4	1557	9
5	5001	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: 14.1b

Counts

2 → 1

localize13.0ms

Local error

Found 4 expressions with local error:

2.6b	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
3.9b	(/ (* M D) (* 2.0 d))
4.2b	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
10.9b	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

rewrite332.0ms

Algorithm

rewrite-expression-head

Rules

453×	`add-sqr-sqrt`
342×	`times-frac`
307×	`associate-l`
186×	`associate-r`
178×	`unpow-prod-down` `*-un-lft-identity`
169×	`add-cube-cbrt`
118×	`unswap-sqr`
67×	`add-exp-log`
52×	`*-commutative`
41×	`sqrt-prod`
30×	`difference-of-squares`
27×	`prod-exp`
23×	`add-cbrt-cube`
19×	`div-exp`
16×	`associate-/l*`
15×	`associate-/r*`
11×	`associate-*r/`
10×	`pow-exp`
9×	`pow1`
7×	`cbrt-unprod` `sqr-pow`
5×	`cbrt-undiv`
4×	`expm1-log1p-u` `sqrt-div` `log1p-expm1-u` `distribute-lft-out--` `add-log-exp`
3×	`clear-num` `div-inv`
2×	`pow-to-exp` `flip3--` `frac-2neg` `pow-prod-down` `un-div-inv` `flip--`
1×	`rem-sqrt-square` `sqrt-pow1` `pow1/2`

Counts

4 → 482

Calls

4 calls:

96.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
13.0ms	(/ (* M D) (* 2.0 d))
125.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
62.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

series1.5s

Counts

4 → 12

Calls

4 calls:

417.0ms	(* w0 (sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l)))))
28.0ms	(/ (* M D) (* 2.0 d))
371.0ms	(sqrt (- 1.0 (* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))))
697.0ms	(* (pow (/ (* M D) (* 2.0 d)) 2.0) (/ h l))

simplify85.0ms

Algorithm

egg-herbie

Counts

494 → 494

Iterations

Useful iterations: 1 (40.0ms)

Iter	Nodes	Cost
0	2155	4067
1	5002	4010

prune1.5s

Filtered

494 candidates to 375 candidates (75.9%)

Pruning

6 alts after pruning (6 fresh and 0 done)

	Pruned	Kept	Total
New	488	6	494
Fresh	0	0	0
Picked	1	0	1
Done	0	0	0
Total	489	6	495

Merged error: 7.3b

Counts

495 → 6

localize14.0ms

Local error

Found 4 expressions with local error:

3.8b	(* h (pow (/ (* M D) (* 2.0 d)) 2.0))
3.9b	(/ (* M D) (* 2.0 d))
4.2b	(sqrt (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 l))))
4.8b	(* (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 l))

rewrite375.0ms

Algorithm

rewrite-expression-head

Rules

656×	`add-sqr-sqrt`
539×	`associate-r`
505×	`times-frac`
398×	`associate-l`
336×	`unpow-prod-down`
266×	`*-un-lft-identity`
243×	`add-cube-cbrt`
210×	`unswap-sqr`
165×	`add-exp-log`
91×	`prod-exp`
77×	`*-commutative`
40×	`div-exp`
31×	`sqrt-prod`
30×	`add-cbrt-cube`
25×	`pow-exp` `difference-of-squares`
16×	`associate-/l*`
15×	`associate-/r*`
12×	`pow1`
11×	`cbrt-unprod`
10×	`sqr-pow`
9×	`associate-*r/`
8×	`rec-exp` `1-exp`
6×	`cbrt-undiv`
5×	`pow-to-exp`
4×	`expm1-log1p-u` `pow-prod-down` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`clear-num` `un-div-inv` `distribute-lft-out--`
2×	`frac-2neg` `sqrt-div`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 678

Calls

4 calls:

52.0ms	(* h (pow (/ (* M D) (* 2.0 d)) 2.0))
13.0ms	(/ (* M D) (* 2.0 d))
165.0ms	(sqrt (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 l))))
95.0ms	(* (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 l))

series1.6s

Counts

4 → 12

Calls

4 calls:

714.0ms	(* h (pow (/ (* M D) (* 2.0 d)) 2.0))
28.0ms	(/ (* M D) (* 2.0 d))
254.0ms	(sqrt (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 l))))
566.0ms	(* (* h (pow (/ (* M D) (* 2.0 d)) 2.0)) (/ 1 l))

simplify127.0ms

Algorithm

egg-herbie

Counts

690 → 690

Iterations

Useful iterations: 1 (54.0ms)

Iter	Nodes	Cost
0	3067	5774
1	5001	5663

prune1.8s

Filtered

690 candidates to 487 candidates (70.6%)

Pruning

5 alts after pruning (5 fresh and 0 done)

	Pruned	Kept	Total
New	686	4	690
Fresh	4	1	5
Picked	1	0	1
Done	0	0	0
Total	691	5	696

Merged error: 7.0b

Counts

696 → 5

localize21.0ms

Local error

Found 4 expressions with local error:

3.9b	(/ (* M D) (* 2.0 d))
4.2b	(sqrt (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l)))))
5.9b	(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
7.4b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))

rewrite856.0ms

Algorithm

rewrite-expression-head

Rules

1711×	`add-sqr-sqrt`
800×	`unswap-sqr`
767×	`times-frac`
546×	`unpow-prod-down`
387×	`associate-r`
380×	`associate-l`
311×	`*-un-lft-identity`
241×	`add-cube-cbrt`
183×	`sqrt-prod`
177×	`difference-of-squares`
128×	`add-exp-log`
76×	`*-commutative`
59×	`prod-exp`
52×	`sqr-pow`
38×	`div-exp`
25×	`pow-exp`
23×	`add-cbrt-cube`
16×	`associate-/l*`
15×	`associate-/r*`
9×	`pow1` `associate-*r/`
7×	`rec-exp` `1-exp` `cbrt-unprod`
5×	`cbrt-undiv` `pow-to-exp`
4×	`expm1-log1p-u` `log1p-expm1-u` `div-inv` `add-log-exp`
3×	`clear-num` `un-div-inv` `distribute-lft-out--`
2×	`frac-2neg` `sqrt-div` `pow-prod-down`
1×	`rem-sqrt-square` `flip3--` `sqrt-pow1` `pow1/2` `flip--`

Counts

4 → 805

Calls

4 calls:

13.0ms	(/ (* M D) (* 2.0 d))
641.0ms	(sqrt (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l)))))
51.0ms	(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
65.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))

series1.6s

Counts

4 → 12

Calls

4 calls:

33.0ms	(/ (* M D) (* 2.0 d))
263.0ms	(sqrt (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l)))))
719.0ms	(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
630.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))

simplify211.0ms

Algorithm

egg-herbie

Counts

817 → 817

Iterations

Useful iterations: 0 (24.0ms)

Iter	Nodes	Cost
0	4840	13509
1	5001	13509

prune3.4s

Filtered

817 candidates to 639 candidates (78.2%)

Pruning

4 alts after pruning (3 fresh and 1 done)

	Pruned	Kept	Total
New	816	1	817
Fresh	2	2	4
Picked	0	1	1
Done	0	0	0
Total	818	4	822

Merged error: 7.0b

Counts

822 → 4

localize20.0ms

Local error

Found 4 expressions with local error:

5.9b	(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
6.4b	(cbrt (* (sqrt (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))))) (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))))))
7.4b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))
7.4b	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))

rewrite1.8s

Algorithm

rewrite-expression-head

Rules

3019×	`add-sqr-sqrt`
1515×	`unswap-sqr`
1098×	`times-frac`
939×	`unpow-prod-down`
715×	`associate-l`
577×	`associate-r`
389×	`*-un-lft-identity`
376×	`cbrt-prod`
354×	`difference-of-squares`
249×	`add-cube-cbrt`
207×	`add-exp-log`
184×	`sqrt-prod`
102×	`sqr-pow`
99×	`prod-exp`
76×	`*-commutative`
64×	`div-exp`
45×	`pow-exp`
20×	`associate-*r/`
16×	`add-cbrt-cube`
14×	`rec-exp` `1-exp`
10×	`pow1`
9×	`pow-to-exp`
8×	`cbrt-div` `associate-/l*`
6×	`flip3--` `sqrt-div` `associate-/r*` `un-div-inv` `flip--` `distribute-lft-out--`
5×	`cbrt-unprod` `div-inv`
4×	`expm1-log1p-u` `frac-times` `clear-num` `log1p-expm1-u` `add-log-exp`
3×	`pow-prod-down`
2×	`cbrt-undiv` `frac-2neg` `associate-*l/`
1×	`cube-unmult` `pow1/3` `rem-cbrt-cube`

Counts

4 → 1054

Calls

4 calls:

56.0ms	(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
1.5s	(cbrt (* (sqrt (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))))) (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))))))
65.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))
66.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))

series2.2s

Counts

4 → 12

Calls

4 calls:

730.0ms	(* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)))
267.0ms	(cbrt (* (sqrt (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))))) (- 1.0 (* (* h (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2))) (* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))))))
620.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))
628.0ms	(* (pow (/ (* M D) (* 2.0 d)) (/ 2.0 2)) (/ 1 l))

simplify311.0ms

Algorithm

egg-herbie

Counts

1066 → 1066

Iterations

Useful iterations: 0 (30.0ms)

Iter	Nodes	Cost
0	5001	30539

prune6.2s

Filtered

1066 candidates to 881 candidates (82.6%)

Pruning

4 alts after pruning (2 fresh and 2 done)

	Pruned	Kept	Total
New	1066	0	1066
Fresh	0	2	2
Picked	0	1	1
Done	0	1	1
Total	1066	4	1070

Merged error: 7.0b

Counts

1070 → 4

regimes292.0ms

Accuracy

-96.7% (2.3b remaining)

Error of 9.6b against oracle of 7.3b and baseline of 8.5b

bsearch134.0ms

Steps

Iters	Range		Point
7	-6.1351541412578234e-208	-1.1993792672908946e-209	-1.2126969796915484e-209
10	-9.10620483866524e+270	-3.856494509717509e+257	-8.922655310600056e+270

simplify1.0ms

Algorithm

egg-herbie

Iterations

Useful iterations: 0 (0.0ms)

Iter	Nodes	Cost
0	37	20
1	37	20

end0.0ms

sample1.2s

Algorithm

intervals

Results

571.0ms	9412×	body	80	valid
189.0ms	3138×	body	80	nan